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Java Modelling Tools users manual

1. Class parameters Name Class Type Closed v Priority 0 gt Population closed classes 1 Distribution open classes Exponential Y Figure 3 63 The Class parameters modification window e Name The default name for each newly created class of customers is Class followed by a progressive integer starting from 1 indicating how many classes you have created so far It can be set to any alphanumerical string which automatically will be followed by the same numbering scheme e Type The default class type is Closed If open classes are used more often you may want to change to Open as default so as to minimize the type changes in the class definition section e Priority The default class priority is 0 Higher numbers correspond to higher priority e Population This parameter applies only to closed classes the default value is 1 i e all closed classes are created with 1 customer each Change the value if you want larger populations by default in each closed class e Distribution This parameter applies only to open classes the default value is Exponential since it is the most popular distribution that characterizes customer interarrival times at a system Change it to any of the distributions available if most of your customer interarrival times follow a non exponential pattern 60 CHAPTER 3 JSIMGRAPH Station Parameters These settings are general parameters
2. Figure 6 53 Apache log file format definition 150 CHAPTER 6 JWAT WORKLOAD ANALYZER TOOL Appendix A Basic Definitions Arrival Rate A Rate at which customers of a given open class arrive in the system Batch workload Closed workload class composed of customers that do not require interaction with delay stations during their execution i e the users think time is zero Bottleneck Station s The station s with the highest utilization in the system Class of customers A group of customers with service demands on the different stations statistically equal Open classes are specified by an arrival rate job s closed classes are composed by a fixed number of jobs specified as a population job Closed Class Workload class in which customers that have completed service leave the system and are in stantaneously replaced by a new customer A closed model has thus a fixed population of requests Customer or Job or Transaction or Request It is the element that will require service from network stations For example it can be an http request a database query a ftp download command or an I O request Delay station Customers at a delay station are each logically allocated their own server so there is no competition for service no queue The time spent by a customer at a delay station is exactly its service demand In delay stations for consistency with Little s law the utilization is computed as the average nu
3. 3 123 Export to JMVA A simulation model created with JSIMgraph can be exported to the analytic solver component of the JMT suite namely JMVA In the Action menu click Export to MVA If there are errors or conditions not allowed in models to be solved by analytical techniques a dialog window with information about such errors appears If you want to continue with the analytical solution you must correct the errors Refer to JMVA user s guide for specific help on JMVA functionalities 3 13 Examples Two simple examples of performance evaluation studies executed using JSIMgraph are shown We believe that readers could benefit from their analysis by concentrating on the abstraction process and on the model design rather than on the actual quantitative results presented in the projects The first example is a single simulation run whereas the second one is a What If Analysis 3 13 EXAMPLES 67 TJ Kea U 0 006 0 038 0 030 16 101 60 40 1 Table 3 1 The parameters for the single class model of Example 1 3 13 1 Example 1 A model with single closed class For teaching purposes we are considering here the same Example 1 presented in the JMVA user manual We will see that the results obtained with JSIMgraph include in their confidence intervals the correct values obtained with the exact solver JMVA The model The digital infrastructure of a company consists of a computing server and a storage server equipped wit
4. Routing Options Destination Probability 60 0 40 0 Figure 3 75 Setting the probabilities or the visits in output of CPU station System Response Time System Throughput Customers number sec job sec jobs 20 510 0 134 2 952 0 149 3 047 Table 3 3 The results of the simulation at the system level both the classes According to some enterprise objectives we need to study the behavior of this system when the Service Times for all classes of WebServer1 increase from current values to 150 Particularly we want to forecast the System Response Time for both Class0 and Classi customers at Confidence Interval 0 99 and Maximum Rel ative Error 0 05 We want also to know the global throughput of WebServer1 at Confidence Interval 0 90 and Maximum Relative Error 0 10 Thus the control parameter that should be selected in the What If Analysis is the Service Times for all classes Defining the model Insert Source Fork Join Routing Queueing Stations and Sink as required in the problem considered Then connect them according to the specifications Double click on the added resource rename each of them as given in the problem Hold Ctrl key on the keyboard and select Load Balancer Web Server 1and Web Server 2 Then click on the Wl icon It will create a new Finite Capacity Region consisting of those three elements Double click on the finite capacity region rename it as Apache uncheck the infin
5. Shortcut on Toolbar i gt Accelerator Key CTRL 0O Save Use this command in order to save the active document with its current name in the selected directory When you save a document for the first time JMVA displays the Save As dialog box so you can rename your document If you save a model after its resolution results are stored with model definition data Shortcut on Toolbar Accelerator Key CTRL S Exit Use this command in order to end a JMVA session You can also use the Close command on the application Control menu If current model was modified since its creation or last save action a popup window will be shown for confirmation Accelerator Key CTRL Q 2 3 2 Action Solve Use this command when model description is terminated and you want to start the solution of the model At the end of the process the window in Figure 2 15 will popup Shortcut on Toolbar Accelerator Key CTRL L In previous versions of the JMT suite JMODEL was the name of the JSIMgraph application Thus jmodel files are files saved in previous versions of the tool 2 4 EXAMPLES 15 Randomize Use this command in order to insert random values into Service Demands or Service Times table Generated values are automatically adjusted to avoid saturation of resources Shortcut on Toolbar gt gt Accelerator Key CTRL R Import in JSIM This command will import current model into JSIM to solve it using simulator A simpl
6. Aha Traffic Analysis Characterization of the arrival traffic of requests analyzing the timestamp in a log file and deriving the parameters that refer to the burstiness of requests Workload Analysis Characterization of the workload of a system through the analysis of the log files applying a clustering algorithm k Means or Fuzzy k Means and other statistical techniques The input data can be loaded directly from standard log files e g Apache log files IIS or from files with any format described by the users Several graphical representations of the results are also provided for their statistical comparison histograms pie charts dispersion matrix QQ Plot QQ Plot matrix scatter plots E Path Analysis The navigation paths followed by the users of a web site allow the identification of the access paths that should be considered as representatives of the workload analyzed 125 126 CHAPTER 6 JWAT WORKLOAD ANALYZER TOOL ea JWaT Java Workload Analysis Tool Workload 5 a A Type gt see New OOo Analysis war Analysis gt Figure 6 1 Main window of JWAT Workload Analyzer Tool 6 1 Workload analysis To perform a workload analysis press the button of the JWAT window and the window of Figure 6 2 will be opened This application help the user to perform in the proper sequence the various steps of the workload characterization from the data loading to the statistical analysis to the results visu
7. As can be seen in Figure 2 5 a class type can be selected in a combo box The input boxes No of Customers N referring to closed classes accept only positive integer numbers the input boxes of the Arrival Rate A referring to open classes accept positive real numbers Figure 2 6 Mo of Customers Arrival Rate 4 100 3 140000 Figure 2 6 Workload definition of the number of customers of a closed class N 100 and the arrival rate of an open class A 3 14 2 2 3 Stations Tab The number of stations of the model can be specified in the corresponding input area Figure 2 7 and can be modified using the keyboard or the spin controls Using the delete button X associated to a specific station a station can be removed provided that there will be at least one station after the deletion Similar result may be obtained using spin controls decreasing stations number in this case last inserted station will be removed Default station names are Station1 Station2 StationN In order to personalize your model you can change and give names other than default ones In Figure 2 8 there is only one station with default name Station4 and there are three stations with cus tomized names CPU Disk1 and Disk2 A station type can be Load Independent Load Dependent or Delay You can insert in your model a Load Depend center only if there is a unique closed class in all other cases the combo box will be disabled lMulticlass
8. DDS E A O E E ZO Oman Lab a Box oh gsc Ae See ee Se Ge Aa BR ee oe a Be eS ZA Expression Pye liaror ma oe bd eyed a a Sed bate ee ewe we Oe BS 22 8 Model Solution 4 4 2 444 866 lt 4 9 Re tow ete eee bbe A ERS we Es 2 29 Model Solution Wihiaten analysis ui ee rayunane Mek A WA te e a 2210 Modification OF ac model a mue IE ue eR Re Se Boe oh me BH Be Be Ds MCTOM e 2G o oe eek oa ee AA ee ee Oe oo Aa Dios UTC he te se ch he nt A A tt ah Sek see eG ne ne he ee ee ee Ge ee ae OD INCOME oo oe exh a a Ee Sa Sx ses eh ee a see eS A Ee ds eee Doyo WACO Mgt e BA E ey ot Ee esi PEE e ee E EA Das ABU See ae e cs oe ee eee e Modes EE a ne ee E ae at ae ae ee Be eee ES 2 4 1 Example 1 A model with a single closed class 0 2 0000 2 2 4 2 Example 2 A model with two open classes o 2 4 3 Example 3 A model with a load dependent station a 2 4 4 Example 4 A model with one open and one closed class 004 2 45 Example 5 Find optimal Population Mix values 4 JSIMgraph DE ONCE beaet A a ea AE AE E SAS a A a a A 232 Ene nome window is ii g edad Pte choke eee Ohh SO Od e a wee e 3 3 Working with the graphical interface dano Deine Mew Model eto da Bas mem Re ee ena om e e id AR ee 3 3 2 Defining the classes of customers oaoa a 2A Dist baois 23 ch a bcm ke ede Gok eae Boe hh tee Gh Gon ae db eee eR ee we ee Bae 9 0 Performance I
9. 2 2 MODEL DEFINITION La JMVA PFON exact solver File Action Help Dee gt Res Classes Stations Service Demands Comment Service Demands ClosedClass Openclass Class3 Input service demands of each 6 000000 0 100000 4 000000 station for each class Diski 10 000000 0 300000 8 000000 If station type is set to Load Disk2 8 000000 0 200000 7 000000 Dependent you can set values of Stationg 2 500000 0 150000 6 000000 service demands for each number of customers by double clicking on any button in station s row If you whish to input service times and visits instead of service demands press Service Times and Visits button Service Times and visits Figure 2 9 The Service Demands Tab y ClosedClass Station LD Settings Figure 2 10 Defining a load dependent station service demand a Editing Service Demands for Station1 Enter the expression to be evaluated using r For the number of customers For syntax details and a list of supported Functions click on Figure 2 11 Load Dependent editing window Ls JMVA PFON exact solver File Action Help Doe gt Be Classes Stations Service Times isits Comment y Visits ClosedClass Average number of accesses of 1 000000 each class to the station Disk1 1 000000 Disk 1 000000 Station 1 000000 OpenClass 1 000000 1 000000 1 000000 110000000 Class3 1 0000010 1 000000 1 000000 1 000000 lt Back Mext g
10. A two class model Solve the two class model specified in Figure 5 18 A Disk gt y o i Kon Disk CPU X Disk O gt Disk 2 Figure 5 18 Example 1 network topology There are three stations named CPU Disk1 and Disk2 Service demands for each station are reported in Table 5 1 CPU Disk1 Disk2 FirstClass 2 60 7 02 4 81 SecondClass 7 02 4 51 5 70 Table 5 1 Example 1 service demand Step 1 Classes Tab e use New command to create a new JABA document e by default you have already two classes e if you like substitute default Class1 and Class2 name with a customized one FirstClass and SecondClass in our example At the end of this step the Classes Tab should look like Figure 5 19 5 4 EXAMPLES 119 Classes characteristics Humber customized name type of classes and number of Number Max 3 Be customers closed class or arrival rate open class Mew Class Clase ou can add classes one by one or define total number at once Name Type Closed A Mo oF Customers Arrival Rate Further VE FirstClass SecondClass Figure 5 19 Example 1 input data Classes Tab Step 2 Stations Tab e use Next gt command to switch to Stations Tab e digit number 3 into stations number textbox or select number 3 using spin controls or push New Station button twice Now your model has three stations with a default name e if you want you can change station names
11. Performance Evaluation Lab Dipartimento di Elettronica e Informazione Politecnico di Milano Italy JMT Java Modelling Tools users manual Version 0 5 il Copyright 2008 Performance Evaluation Lab Dipartimento di Elettronica e Informazione Politecnico di Milano All rights reserved Java Modelling Tools is free you can redistribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 2 of the License or at your option any later version Java Modelling Tools is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the GNU General Public License for more details You should have received a copy of the GNU General Public License along with Java Modelling Tools if not write to the Free Software Foundation Inc 675 Mass Ave Cambridge MA 02139 USA Contents Contents 1 Introduction 2 3 La Starting withthe JMT suite sas Seow ee oe a hae eee bee CHAS REE JMVA ZE OAO tars te a ty Ge eH es Bt ee Bhs eel DASS AS Glee a a 2 1 1 Starting the alphanumeric MVA solver e 2d Modelden On 222 dara a Ge BO eed ERR She Ae eS 221 DEAN a mer models gt par aaa AR eae a 2AM Classe 1a a rada AA da lA E ARAS A DOS A AAA 2 2 4 Service Demands Service Times and Visits Tabs
12. e Erlang e Exponential e Gamma e Hyperexponential e Normal e Pareto e Poisson e Replayer e StudentT e Uniform A load dependent service time indicates that the amount of time the server spends with each customer depends upon the current number of customers in the station A set of intervals for the number of jobs in the station is specified either by adding one range at a time via the button or by specifying the total number at once Each range must them be specified by its lower From and upper To extremes Each such range can be associated with different service times as for the distribution the mean and the coefficient of variation or a subset thereof To set the parameters of a Load Dependent service time click the button and then specify the parameters for each added range 94 CHAPTER 4 JSIMWIZ Hm Editing Class1 Load Dependent service strategy Edit Help Load Dependent Service Time Distribution Define the distribution and the values of service times for a range of number of jobs inside the station Mean value of the distribution can be specified with an arithmetic expression as a function of the current value of n Ta see Help for operators Ranges E For each customer number range you must specify the following parameters Distribution you can choose among Burst general Burst MMPP2 Pareto Erlang Exponential Hyper exponential Poisson Uniform Constant Gamma and
13. to mean All Classes e Conf In Max Rel Err This is the Confidence Interval and Maximum Relative Error of the computed index e Analyzed Samples This is the number of samples used to compute the performance index e Min This is the minimum value observed for the index e Max This is the maximum value observed for the index e Average Value This is the computed average value of the index usually the value of greater interest Click on the graph to magnify it Each graph plotted represents the values of the corresponding index blue line with the Confidence Interval red lines see Figure 3 69 Seles 9 18 27 36 45 54 63 72 81 Figure 3 69 Plots representing the value of a performance index and its Confidence Interval 66 CHAPTER 3 JSIMGRAPH 3 12 2 Result of What If Analysis simulation run At the end of a What If Analysis simulation run a panel showing the statistical values of the indices a plot of the indices behavior with respect to the control variable of the What If Analysis and a table are shown The panel shows a number of tabs corresponding to the number of indices inserted For each tab i e each performance index the results are grouped into three parts Y Simulation Results Queue Time Residence Time Utiization Throughput Queue Length Average number of customers for each chosen dass at each chosen station Description Station Neme CPU Class Nama Class0 S z068 Corf intiMax R
14. Change State Region of these Indices to CPU Disk1 Disk2 and Users e From the drop down menu at the right select Throughput Click on Add Selected Index for four times Change State Region of these Indices to CPU Disk1 Disk2 and Users e From the drop down menu at the right select Residence Time Click on Add Selected Index for four times Change State Region of these Indices to CPU Disk1 Disk2 and Users 3 13 EXAMPLES 69 JSIMgraph Advanced queuing network design tool lo i 23 Editing Users Properties Station Name EJ Station Name Users Editing Class0 distribution Users Parameters Definiton Selected Distribution Exponential Service Section Routing Sectio P L Number of Servers Exponential exp A f z Ae Service Time Distributions Class di 0 0625 Class0 mean 16 OK Cancel Done Figure 3 73 Setting the mean value of Users think time for the delay station e From the drop down menu at the right select Utilization Click on Add Selected Index for four times Change State Region of these Indices to CPU Disk1 Disk2 and Users The Define Performance Indices window should look like Figure 3 78 It should be noted that we can change the Confidence Interval and or Maximum Relative Error for any performance index from this window At the end click on Done Running
15. Convex Hull Graphic whith a filtered area e The station that are bottleneck e The switching point or the switching segment bound points This tab could be helpful in the Saturation Sector graphic of three classes of costumers subsection 5 2 6 5 2 9 Modification of a model To modify system parameters return to the main window and enter new data or moving a station in Convex Hull graphic tab see subsection 5 2 7 After the modifications if you use Solve command the new graphs will show You can save this new model with the previous name overwriting the previous one or save it with a different name or in a different directory 5 3 Menu entries 5 3 1 File New Use this command in order to create a new JABA model Shortcut on Toolbar Accelerator Key CTRL N Open Use this command to open an existing model You can only open one model at time to edit two or more models start more than one instance of JABA If current model was modified since its creation or last save action a popup window will be shown for confirmation It s possible to open not only models saved with JABA jaba but also with other programs of the suite for example JMVA jmva JSIM sim and JMODEL jmodel Whenever a foreign data file is opened a conversion is performed and error warnings occurred during conversion will be reported in a window Models are stored in XML format see JMT system manual for a detailed description Shortcut on Toolba
16. Customer Classes from the menu bar or click on the Bs icon e Click on Add Class Set Population as 3 and Reference Station as Users Note that that reference station is the station which initiates and completes the flow of customers in the network Setting the values of the parameters e Double click on Users delay station e Click on Edit 68 CHAPTER 3 JSIMGRAPH Disk1 Disk2 Figure 3 72 The system represented with JSIMgraph e The default Selected Distribution should be Exponential Set Mean value as 16 recall that the Customer think time is Z 16s Click OK Note that the value of A is automatically computed by the tool e Click Done on the window of Figure 3 74 e Double click on CPU Click on Service Section tab Click on Edit e The default Selected Distribution should be Exponential Set Mean value as 0 006 Click OK Note that the value of A is automatically computed by the tool e Click on the Routing Section tab Set Routing Strategies as Probabilities As there are 3 outgoing links from CPU we have to set a job s probability to choose each of these paths This is done by setting the probabilities of Disk1 Disk2 and Users as 60 40 and 1 respectively see Figure 3 75 Click on Done Note that the values of the Probabilities are automatically adjusted by the tool e Double click on Disk1 Click on Service Section tab Click on Edit e The default Selected Distribution should be Exponential Set Mean value as 0
17. When you add a new performance index the station for which it is defined must be specified otherwise the error message above appears Specify the missing station as described in subsection subsection 4 2 5 106 CHAPTER 4 JSIMWIZ 4 7 Simulation Results When a simulation terminates successfully performance indices are plotted on tabbed windows as illustrated below F Simulation Results Response Timo System Bespores Time Response Time Aaga response time for gach chosen class at each chosen gation Staton Meme Servet Ces Names Oe Conf intimas Beltre 04101 Ana samples 2560 wD Mn 0 31 Max O74 Average value 0 3360 IPA ASAS A COMPLE MATT EF A COMA DER EA rad bres 40d Ele repite midi palaba Sr hor Servet Class Herre cie Cond irtiday Beles 0 9 0 1 Analyzed samples 7 Pasi Ssiabor Cannot compute ds mhana a a paaks ver nicer haa Marea Servant Class Hara ls uiia Rel Er 09 01 frayzsd samples J x Min Hs Average value 2 5727 smubstor Hed bo compare as messure bh tht Speoried conhcence interval and masini relatives error a In each window results for all the stations for which the performance index is specified are listed Numerical values and graphs are given Successful results are indicated by a checkmark sign on a green bullet In case of errors or of early termination a cross on a red bullet indicates that the results obtained are not within the requested confidence interval I
18. click and drop Define Customer Classes and select the Reference Station for each class Set the parameters for each object Select the performance indices to be collected and evaluated If needed insert one or more Finite Capacity Regions FCR Choose or change the simulation parameters Enable What If Analysis and set its parameters if required Start the simulation If diagnostic errors are detected click on them and the related window that allows immediately to fix them will be shown OONDPAN Step 1 Create the new model To draw a new network select or choose New from File menu A white area in which the model should be drawn will be shown Utilize the pre defined objects like queueing station delay source sink logger connection routing station and fork join Step 2 Define customer classes In all the networks implemented one or more Customer Classes must be defined To describe them see subsection 4 2 1 Defining Customers Classes and parameterize the classes to use For each class of customers a Reference Station should be set This station is used to compute the system throughput for each class i e the number of customers of that class that flow through the system in a time unit It is a required parameter in order to compute correctly the simulation results If a simulation is started without its prior definition an error message will appear Step 3 Define station parameters
19. e you can input all Service Times in the table At this point the Service Times Tab should look like Figure 5 25 Saturation Sectors Text Classes Stations Service Times Visits Comment Saturation Sectors Graphics Convex Hull Graphics Service Times Class 4 l Class B Class C Input service times of each station 0 01 0 38 0 30 for each class Diski 0 02 0 62 0 80 If station type is set to Load Disk 0 09 0 42 0 50 Dependent vou can set values of service times for each number ot customers by double clicking on any button in stations row If you wWhish to input service demands instead of service times and visits press Service Demands button Service Demands Figure 5 25 Example 2 input data Service Times Tab e use Next gt command to switch to Visits Tab e input number of visits for each center in the table At the end of this step the Visits Tab looks like Figure 5 26 Visits Average number of accesses of each class to the station A O Diski 44 00 16 00 27 00 Disk2 63 010 1 00 Ao 00 Figure 5 26 Example 2 input data Visits Tab 5 4 EXAMPLES 123 Step 4 Saturation Sectors Graphics Use Solve command to start the solution of the input model In the Saturation Sector Graphic Tab will be displayed a graphic like the one of Figure 5 27 Class E el IE Diski E E Diski Disk CPU Disk Disk CPU Disk Disk CPU Dis
20. from the Define menu or by clicking the Define Simulation Parameters icon from the toolbar see Figure 3 30 The parameters required by the simulator are e Simulation Seed is the number used by the simulation engine to generate pseudo random numbers If you change the seed you will obtain a different sequence of pseudo random numbers If a simulation is repeated using the same seed the same sequence of pseudo random numbers will be generated thus leading to identical results The default value is random which indicates that the simulation engine will pick a seed of its choice in a pseudo random fashion each time it is started deselect random and insert a number if you want a custom simulation 3 6 SIMULATION PARAMETERS 43 p x lt _____________ gt PO e i 1 Al 4 xXx in valid YP gt A E PP AL dll I X p invalid Figure 3 29 Confidence intervals for the correct parameter value uy evaluated in 10 runs The coverage is 80 since two of them do not include the correct value Define Simulation Parameters 2 aia Simulation Parameters Simulation random seed 7 M randorr Define simulation parameters and initial state E Maximum duration sec 1 M infinite Maximum number of samples 500 000 _ no auto Animation update interval sec 2 Y animati CPU Users Disk1 Disk2 ClosedClass Ni 3 3 0 0 0 _ Class0
21. link from other stations for open class jobs to be able to leave the system Only the Source station does not have a backward link To see how to connect stations see subsection 4 2 3 ew Error Mo reference station defined For Class4 For each class you must define a Reference Station that is used to compute the performance indices for the class To see how to define a reference station see subsection 4 2 6 o J Error No performance indices defined This error occurs when you try to start the simulation but no performance index is defined Performance indices are defined through subsection 4 2 5 o Som Waning Fork found but no join Ju Error Join without Fork Fork and Join stations should be inserted together in the model If you have inserted only one of the two stations when the simulation is run JSIM will show a diagnostic message Having a Fork without a Join is possible although it may lead the system to saturate quickly hence the Warning message Having a Join without a Fork is a mistake hence the Error message The missing station must be added with the corresponding links see subsection subsection 4 2 2 and subsection subsection 4 2 3 respectively o Y Error No classes defined Customer classes are a mandatory parameter of a model If you forget to define any the simulator will raise an error Add classes as described in o Y Error 4 performance index is defined more than once In the definition of the model output
22. mint imax min Figure 6 33 Parameters of the clustering algorithm k Means 138 CHAPTER 6 JWAT WORKLOAD ANALYZER TOOL Fuzzy k Means algorithm The fuzzy k Means algorithm implemented in the tool requires the following parameters Figure 6 34 e the maximum number k of clusters that the algorithm has to produce The results for all the partitions from two to the selected maximum value will be provided The higher is this value the higher is the execution time of the algorithm e the maximum number of iterations to perform in order to find the optimal partition Four is a suggested value See the comments reported above for the K means algorithm e the fuzziness level to apply during the algorithm execution It is the value used by algorithm to determine the fuzziness degree of final solution It ranges from 2 to 100 e the transformation type to apply to selected variables if needed See the comments reported above for the K means algorithm Clustering options Fuzzy k Means Clustering Specify maximum number of clusters iterations and fuzziness Clusters Clustering iteration number oF clusters number of iterations Select maximum number of Select maximum number of Clusters that the algorithm has iterations that the algorithm has to produce to perform to find solutions Fuzzy options Fuzziness level Fuzziness Level Fuzziness level is
23. q2 4jobs q3 1jobs Shortest Response Time with this algorithm jobs are sent to the station where the average response time for the job s class is the smallest at the moment a job leaves the routing station The figure shows that at the time of routing the middle station has the smallest average response time R so the job will be sent to it Input job Pa R3 R1 3 sec R2 2 5 sec R3 2 9sec Least Utilization with this strategy the destination device is chosen as the one with the smallest average utilization at the time routing is performed In the example depicted in the picture the top station is the least utilized so it will receive the next job to leave the blue station 92 CHAPTER 4 JSIMWIZ U1 34 U2 44 U3 45 Fastest Service with this strategy a job is routed to the device with the smallest average service time S for the job s class In the figure the exiting job will be routed to the top station since it service time is the minimum among the three 91 0 34 s 2 0 69s 53 1 02s Service section How to Define the Service Strategy This section is present in server and delay stations This section allows the specification of the number of servers for server stations and the service time distribution for both server and delay stations Delay stations are infinite servers with identical service time therefore they only need the service time distribution The infinite number of s
24. see section 6 1 4 The basic idea is to partition the given set of observations into classes of components having homogeneous characteristics Among the various clustering algorithms the most commonly applied to workload characterization problems belong to the non hierarchical k means family The algorithm produces a number of classes ranging from 1 to k where k is a parameter that must be specified by the user The observations are assigned to a class so that the sum of the distances between all the elements and the centroid of the class is minimized A set of representative components will then be selected from the classes according to some extraction criteria usually the centroids of the clusters and used in the construction of the workload model 4 A panel is available for the visualization of the results of the clustering analysis Several graphics and tables are reported in order to describe the clusters composition and the goodness of a partition Scatter plots are available for all the variables considered see section 6 1 5 6 1 2 Input definition The panel for the description of the input data Figure 6 2 is a very important one since it allows the selection of the input file that contains the data to be analyzed and the description of their structure In such a way we may take into consideration the log files generated by different systems and tools The format definition structure of the input file is described in detail in S
25. 2 23 Example 1 input data Stations Tab Classes Stations Service Times visits Comment iy Service Times ClosedClass Input service times of each station 0 006000 for each class Diski 0 038000 If station type is set to Load Disk 0 030000 Dependent you can set values of Users 16 000000 service times for each number of customers by double clicking on any button in station s row If you whish to input service demands instead of service times and visits press Service Demands button Service Demands Figure 2 24 Example 1 input data Service Times Tab 18 CHAPTER 2 JMVA e use Next gt command to switch to Visits Tab e input numbers of visits for all centers in the table In this case the number of visits of the Users the infinite server station is equal to 1 since a customer at the end of an interaction with the system visits this station At the end of this step the Visits Tab looks like Figure 2 25 Classes i Stations i Service Times isits 1 Comment A Visits Average number of accesses of each class to the station Diski 60 000000 Disk 40 000000 Users 1 000000 Figure 2 25 Example 1 input data Visits Tab Step 4 Model Resolution Use Solve command to start the solution of the input model Model results will be displayed in a new window like the one of Figure 2 26 Throughput Y Queue length Y Residence Times 1 Utilization fi Synopsis i Throughput T
26. 27 Example 1 output data Synopsis Tab 2 4 2 Example 2 A model with two open classes Solve the multiclass open model specified in Figure 2 28 The model is characterized by two open classes A and Figure 2 28 Example 2 network topology B with arrival rate the workload intensity A respectively of Aa 0 15 job s and Ag 0 32 job s There are three stations of load independent type identified with names CPU Disk1 and Disk2 Service times and visits for stations are shown in Table 2 5 and Table 2 6 CPU Disk1 Disk2 Class A s 0 006 0 038 0 030 Class B s 0 014 0 062 0 080 Table 2 5 Example 2 service times Since this model is similar to the network of Figure 2 21 solved in subsection 2 4 1 we will show how to easily create it from a saved copy of Example 1 1 Open the saved instance of Example 1 model 2 Go to Classes Tab change ClosedClass name to A change its type to Open and set its arrival rate to AA 0 15 job s 3 Click on New Class button sets name of new class to B change its type to Open and set its arrival rate to Ag 0 32 job s 4 Go to Stations Tab and remove Users delay center 5 Go to Service Times Tab and sets service times for Class B according to Table 2 5 6 Go to Visits Tab and sets visits for Class B according to Table 2 6 20 CHAPTER 2 JMVA CPU Disk1 Disk2 Class A 101 0 60 0 40 0 Class B 44 0 16 0 27 0 Table 2 6 Example 2 number of visits
27. 34 Selection of the final value of service time in a What If Analysis of the service time of class Classi at station Server The service time distribution will not change Only its average will be modified to span the range defined by the initial value specified in the Station Parameters tab and the final value specified here in the To field If the Change service time of all classes option is selected the range of service time to explore is expressed in percentage starting from the initial value specified at model definition which is considered as 100 The station whose service time should be modified must be specified e Seed for all types of classes Unlike the previous cases where the analysis is performed for a range of values of one of the model parameters in order to investigate the system behavior under a variety of conditions a What If Analysis on the seed aims at evaluating the sensitivity of the simulation engine to numerical conditions in particular to the numerical value used by the pseudo random number algorithm to generate the sequence of numbers i e the seed The simulation engine uses a pseudo random number generator to generate the sequence Steps n of exec 10 Figure 3 35 Selection of the number of repeated executions with different seeds in a What if analysis of values used in each execution By changing the seed a different sequence of values is produced thus leading
28. 433 346E 3 4 552 9326 3 2651 680E 3 66 4 162E 5 Fuzzy k Means We have visualized different statistics for each algorithm by varying the number of clusters in particular we show the scatter plots matrix for the partition with 5 clusters as can be seen from the OMSR values this partition has been evaluated as a good one 6 1 WORKLOAD ANALYSIS 145 Timestamp Clusterized Access request Bytes transferred Clusterized t Figure 6 49 K Means algorithm scatter plots matrix Timestamp Clusterized Access request Bytes transferred Clusterized Figure 6 50 Fuzzy k Means algorithm scatter plots matrix 146 CHAPTER 6 JWAT WORKLOAD ANALYZER TOOL 6 1 7 Menus description File New Use this command to start a new analysis selecting a new log file Shortcut on Toolbar E Accelerator Key CTRL N Exit Use this command to terminate the JWAT current session It is possible to utilize Exit button in the buttons bar of application If the session has been modified after its creation or after its last saving a popup window asks confirmation to save session Accelerator Key CTRL Q Action Solve Use this command when enabled to start the algorithm selected in the clustering panel It is possible to obtain the same result by using Solve button in the buttons bar of the application Shortcut on Toolbar gt Accelerator Key CTRL L Help J WAT Help Use this command to visualize t
29. If resource k is a delay center representing a client station it is a convention assign a unitary value to number of visits to this station Appendix B List of Symbols A Arrival rate of class i N Global population N Population of class 7 bi Population Mix p N gt gt Nk Qk queue length at station k V average number of visits at station k W residence time at station k Wk Rk Vk Rx response time at station k Uy utilization of station k D service demand at station k single class Dk i service demand at station k of class 2 R response time of the system R Wk X system throughput Xp throughput at station k 153 154 APPENDIX B LIST OF SYMBOLS Bibliography BBCT81 G Balbo S C Bruell L Cerchio D Chialberto and L Molinatti Mean value analysis of closed load dependent queueing networks Dipartimento di Informatica Universit di Torino Oct 1981 BCMP75 F Baskett K M Chandy R R Muntz and F G Palacios Open Closed and Mixed Networks of Queues with Different Classes of Customers J ACM April 1975 CS04 G Casale and G Serazzi Bottlenecks identification in multiclass queueing networks using convex polytopes In Proc of IEEE MASCOTS Symposium pages 223 230 IEEE Press 2004 CZS07 G Casale E Z Zhang and E Smirni Characterization of moments and autocorrelation in MAPs ACM Perf Eval Rev Special Issue on MAMA Workshop 35 1 27 29 2007 Lit61 John D C
30. Substitute CPU for default name Station1 substitute Disk for default name Station2 substitute Disk2 for default name Station3 At the end of this step the Stations Tab should look like Figure 5 20 Stations characteristics rz Humber customized name and type of stations Number 313 You can add stations one by one or define total number at ance Mew Station ae Natne o Oe 1 CPU x 2 Diski 3 Disk2 lt Figure 5 20 Example 1 input data Stations Tab Step 3 Service Demand Tabs e use Next gt command to switch to Service Demands Tab e you can input all Demands in the table e press Service Time and Visit button if you don t know the Service Demands of the three stations After button pressure the Service Demands Tab will be hidden and Service times Tab and Visit Tab will appear Now Service Times and number of Visits should be typed At this point the Service Demands Tab should look like Figure 5 21 Step 4 Saturation Sectors Graphics Use Solve command to start the solution of input model In the Saturation Sector Grlaphic Tab will be displayed a graphic like the one of Figure 5 22 This graphic show the range of mix population where two or more stations are both bottleneck In this example Disk1 and Disk2 are both bottleneck when FirstClass is among 0 545 0 689 and SecondClass is among 0 311 0 455 120 CHAPTER 5 JABA ASYMPTOTIC BOUND ANALYSIS Convex Hull Graphics Satura
31. Tab The instructions that are the same given in Step 1 of subsection 2 4 1 in this case N must be 8 Step 2 Stations Tab The instructions are given in Step 2 of subsection 2 4 1 in this case the model has two stations a Load Dependent station and a Delay Center Step 3 Service Demands Tab l Ze use Next gt command to switch to Service Demands Tab double click on cell with text LD Setting to open the editor of load dependent service demands in a separate window shown in Figure 2 31 it isnot mandatory to insert all values one by one You can click or drag to select cells enter the expression n 1 n into the textbox at the bottom of the window and click the Evaluate button at the end of this phase editor window looks like Figure 2 32 Now you may press OK button to confirm changes and return to JMVA main window el Editing Service Demands for Station 0 000000 0 000000 o 000000 0 000000 0 000000 0 000000 O 000000 Enter the expression to be evaluated using r For the number of customers For syntax details and a list of supported Functions click on Help Y ta Figure 2 31 Example 3 editor for the description of service demands for a load dependent station corresponding to the different number of customers before the parametrization Step 4 Model Resolution Use Solve command to resolve the model results are shown in Table 2 9 22 CHAPTER 2 JMVA 2 000000 3333333 4 25000
32. a single element in the input log file The considered log file contains several data e g IP client address that submits the request for a resource to a web server request timestamp etc that are called variables After the selection of the input file the format definition table is empty see Figure 6 2 since no information regarding current format has already been defined Two types of format definition are available e Manual that consists of the definition of the format of each single variable through relative table and relative commands e Automatic that load one of the predefined standard formats previously defined and loaded in files 7wat format Manual definition At the beginning the correct number of variables of each observation in the log file is to be set use the spinner Number By using the New var button a new variable is added to the format table The same result is obtained using the spinner Number at the right top of the table see Figure 6 8 To remove one or more variables by a format table we can utilize e the button at the end of each row of the table The result is the deletion of the concerning variable e turned arrow towards the bottom of the spinner The result is the deletion of the last variable of the table e the right button of the mouse on a single selected variable or on a set to delete them from the format table Figure 6 9 Comment Perl5 Reg Exp L De
33. be computed with the following formulas Q k ClosedClass N N Qr OpenGiass N A Dk OpenClass 1 Qk ClosedClass N 1 A Dp OpenOlass And the results will be equal to the ones shown in Figure 2 38 2 4 5 Example 5 Find optimal Population Mix values Perform a what if analysis to find the value of population mix that will maximize System Throughput and minimize System Response Time in the model shown in Figure 2 39 This model has two closed classes named Class1 and Class2 with a total population of N 20 and three load independent stations named Station Station2 and Station with the service demands shown in Table 2 11 2 4 EXAMPLES 25 Throughput Queue length Residence Times 4 Utilization i Synopsis QueueLength Average number of customers for each class at each station Aggregate 187 000000 130 000000 57 000000 Station 39 000000 20 000000 19 000000 Station 33 000000 80 000000 19 000000 Station3 49 000000 30 000000 19 000000 Figure 2 38 Example 4 queue lengths EOL Station 1 Station2 Station 3 Figure 2 39 Example 5 network topology Step 1 Classes Tab Follow the instructions of Step 1 in the previous examples as we will change population mix initial allocation of the N 20 jobs is irrelevant For example we can allocate Ni 10 jobs to Class1 and N 10 jobs to Class2 The Classes Tab is shown in Figure 2 40 Step 2 Stations Tab Follow the in
34. components one may select interactive commands database queries and updates web site requests web downloads programs scripts servlets applets traffic intensity source level instructions etc In the following we will refer to a workload basic component as an observation i e an item in the input file and to the parameters that describe each component as variables 1 The first step consists of the selection of the file containing the data that are to be considered as input of the variables to load and of their format see section 6 1 2 Let us remark that each observation may be described in the input file by n variables but that the number of variables that are considered in the actual statistical analysis may be less than n It is also possible to decrease the number of observations of the original input file decrease its size that will be loaded considered in the characterization study 6 1 WORKLOAD ANALYSIS 127 TWAT Workload Analysis Figure 6 2 Main window for the Workload analysis oa Figure 6 3 Men and application toolbar Figure 6 4 Tabs selector Figure 6 5 Navigation buttons 128 CHAPTER 6 JWAT WORKLOAD ANALYZER TOOL Several filtering criteria for the construction of a sample of data are available random selection of a given number of observations selection of the observations that belong to a given interval of their sequence number At the end of the data loading a panel describing
35. default Classes are created as Closed Priority can be changed as in the case of Open class the default value is 0 the minimum The population size also referred to as N is the parameter that characterizes a closed class For a closed class N is constant and does not change during the execution of the simulation Its default value is 1 and it may be changed by clicking on the corresponding area in the class properties matrix A Reference Station for the class must be selected from the Reference Station menu With a closed class all Reference Station F LoadSplitterO F LoadSplitterO ServerO A LoadSplitter1 Forko we Serverl Figure 3 9 Selection of a Reference Station for a closed class of customers the type of stations can be selected but neither a Source nor a Sink The Reference Station is used to compute the system throughput and response time for the class considered 3 4 Distributions Open class models are workloads where the number of requests in the system fluctuates over time and new requests arrive at the system as if generated by an infinite source The arrival pattern can be described by a probability distribution simple or very complex It is often used the distribution of the inter arrival times of consecutive requests or customers A probability distribution f x can be characterized by Mean if it exists CoO EA J x f x dx 00 Variance if it exists CoO Var X J x E X f x de E
36. during the loading operation Figure 6 18 The error messages that are contained in the log file are e Error in row xx Element y is wrong if you defined separators the element corresponding to the variable y for the row xx does not correspond to the defined regular expression e Error in row xx Line does not match format element y not found The element corresponding to the variable y is not present in the row observation xx of the input file e Error in row xx Too many fields the row xx contains elements in excess compared to the defined format This may indicate with high probability that the format definition described by the user is not correct for the considered observation 6 1 3 Data processing A tabs substructure Figure 6 19 shows the groups of the various statistics available Univariate descriptive statistics graphs and transformations Sample construction methods of sample construction and data filtering 132 CHAPTER 6 JWAT WORKLOAD ANALYZER TOOL Ll gt Loading Data observations read 72000 errors 3642 Figure 6 16 Window showing the loading progress Loading Complete x observations processed 153817 correct observations 97978 To see errors press Show Log Figure 6 17 Loading phase results 2 Error log Error in row 1 Line doesn t match format element 8 not Found Error in row 120 Line doesn t match Format element 8 not Found Error in row 122 Li
37. fatal or warning are shown The results of a simulation are described in section 3 12 Step 9 Fatal Errors and Warning Messages The detected errors and warning messages are shown in section 3 11 3 3 2 Defining the classes of customers The workload intensity is described by one of the following parameters A the arrival rate for open models N the population size for closed models In open models the workload intensity is specified by the parameter A i e the rate at which requests customers arrive at the system In these type of models there is an infinite stream of arriving customers and the customer population i e the number of customers in execution varies over time Customers that have completed their execution leave the system and reach a sink station The class of customers of an open model is also referred to as Open Class In closed models the workload intensity is specified by a parameter N indicating the average number of jobs customers in execution In these models the population is fixed i e N is kept constant Customers that have completed their service are considered as if they left the model and have been replaced immediately by a new customer The class of customers in execution in a closed model is also referred as Closed Class Multiple class models consist of N customer classes each of which has its own workload intensity and its own service demand at each center Within each class the customers are
38. indistinguishable i e statistically equal Models in which the customers belong to both of the two types of classes open and closed are referred to as Mixed models The parameters defining the two types of classes are given below e Open Classes parameters priority interarrival time distribution reference station service time dis tributions of the stations e Closed Classes parameters priority population value reference station service time distributions of the stations The classes of customers identify different customer behavior and characteristics such as the type closed or open the size of the customer population for closed classes or the interarrival time distribution for open classes the path among the resources the service time required They can be set from the Define menu by choosing Customer Classes The following panel will be shown __ AddClass Classes Characteristics Define type name and parameters for each customer class Classes 0 a Figure 3 2 Window for the definition of the classes of customers Classes must be explicitly added to the model either one at a time by clicking the Add Class button or by selecting directly the desired final number of classes from the Classes counter The newly added classes will be listed with default parameters 3 3 WORKING WITH THE GRAPHICAL INTERFACE 33 Double click on the default name i e Class0 Classl etc to change it Each new cla
39. it right click to save it In EPS or PHG format Performance index System Throughput ha ho al al ma ma Se ho System Throughput ha E 0 22 tmin oos max osf 041 0 2 03 04 05 06 07 08 03 min Ymax Population mix Bi for Class Figure 2 45 Example 5 System Throughput Chapter 3 JSIMgraph 3 1 Overview In the JMT suite a discrete event simulator for the analysis of queueing network models is provided It can be used through two interfaces alphanumerical JSIM wiz and graphical JSIMgraph JSIMgraph is the GUI front end to JMT simulation engine It helps the users to perform an evaluation study in two ways Firstly critical statistical decisions such as transient detection and removal variance estimation and simulation length control have been completely automated thus freeing the users from taking decisions about parameters s he may not be familiar with The simulation is automatically stopped when all performance indexes can be estimated with the required accuracy Secondly a user friendly graphical interface allows the user to describe both the network layout and the input parameters Furthermore the graphical interface also provides support for the use of advanced features several of them are for networks with very general characteristics usually referred to as non product form networks like fork and join of customers blocking mechanisms regions with capacity constraints on population state depende
40. it is requested that one class has at least one job and customer number must be integer the minimum value is 1 N and the maximum value is N 1 N Stationl Station2 Station3 Class1 s Class2 s Table 2 11 Example 5 service demands 26 CHAPTER 2 JMVA Classes Y Stations x Service Demands i what if Comment i Classes characteristics Number 212 Number customized name type of classes and number of customers closed class or arrival rate open class Add classes one by one or define total number at once New Class Mo of Customers Arrival Rate 4 Class1 Class2 Figure 2 40 Example 5 Class Tab Classes Stations Service Demands what if Comment i Stations characteristics umber Number customized name and type of stations Add stations one by one or define total number at once Mew Station Load Independent 2 i Load Independent De 3 Station3 Load Independent e Figure 2 41 Example 5 Stations Tab Classes Stations Service Demands Y Wwihat iF Comment A Service Demands Input service demands of each Station 1 000000 5 000000 station and class Station2 5 000000 1 000000 If the station is Load Dependent Stations 1 000000 5 ooo00d vou can set the service demands for each number of customers by double click on LD Settings button Press Service Times and visits button to enter service times and visits instead of service demands Servic
41. location real number it is the mean of the distribution and o scale real number it is the standard deviation of the distribution i e the square root of the variance The density is symmetrical around the mean and the variance The probability density function is 1 21 f x e302 z v2T0 The standard normal distribution is the normal distribution with y 0 mean equal 0 and o 1 variance and standard deviation equal 1 A family of normal density functions is shown in Figure 3 19 Pareto par a k distribution This distribution is usually utilized to describe the behavior of social and economical phenomena e g the distribution of wealth where a small portion of the people owns the larger part of the wealth It is characterized by the parameters k gt 0 location real and a gt 0 shape real The probability density function is f a aka et 3 4 DISTRIBUTIONS 39 206 006 OS 00o 0 00 ur20o 0 6 Figure 3 19 Family of normal density functions The standard normal density is the green colored If k and a are provided as input parameters the simulator compute the mean ka a 1 for k gt 1 and the variance a Q x 12 A family of Pareto density functions is shown in Figure 3 20 N bb GC 006 N OS 0 6 0 4 Figure 3 20 Family of Pareto density functions Poisson poisson A distribution The Poisson distribution describes the number of events occurring in a
42. must be estimate using only a small sample size It is the basis of the Student t s test that is used to evaluate the statistical significance of the difference between two sample means and for the difference between two population means 40 CHAPTER 3 JSIMGRAPH a co bb H0 e 5 0 0 o o i T 10 15 20 Figure 3 21 Family of Poisson probability mass functions It is a special case of the generalized hyperbolic distribution The mean is 0 for v gt 1 and the variance is vj v 2 for v gt 2 infinite otherwise The probability density function is f x where I t is the Eulero function A family of probability density functions for a set of y values is shown in Figure 3 22 4 2 0 2 4 Figure 3 22 Family of Student T density functions Uniform U min max distribution The Uniform distribution also referred to as Rectangular distribution due the shape of its density function describes a random variable that may assume all the values in the range min max with the constant probability 1 maxz min The probability is 0 outside the considered range The user can either provide the pair min max or the mean m max min 2 and variance c max min 12 Two uniform density functions are plotted in Figure 3 23 min max 3 min 2 max Figure 3 23 Uniform density functions with different range of values 3 5 PERFORMANCE INDICES Al 3 5 Per
43. number of customer N for closed classes and arrival rate A for open classes 2 Stations service centers 3 Service demands or Service Times and Visits 4 Optional short Comment The execution of JMVA provides for each class and each station the following performance indices e Throughput e Queue Length e Residence Time e Utilization The following aggregate indices are provided e System Throughput e System Response Time e Average number of customers in the system Input tabs As can be seen in Figure 2 1 the parameters that must be entered in order to define a new model are divided in four tabs Classes Stations Service Demands and Comment Tabs number can become five if you click Service Times and Visits button in Service Demands Tab As will be discussed in subsection 2 2 4 the Service Demands Tab will be hidden and it will appear Service Times Tab and Visit Tab You can navigate through tabs e using sequential wizard buttons if enabled at the bottom of the window Figure 2 2 e using sequential buttons located in menu e using the tab selector clicking on the corresponding tab Figure 2 3 Figure 2 2 Wizard buttons Classes Y Stations Service Demands Comment Figure 2 3 Tab selector 2 2 MODEL DEFINITION 5 2 2 2 Classes Tab An example screenshot of this tab can be seen in Figure 2 1 This tab allows to characterize customer classes of the model Your model will be a single class model if and o
44. open and mixed models with load dependent stations are not supported yet 6 CHAPTER 2 JMVA Mumber New Station Figure 2 7 Number of stations oad Independent Load Independent Load Independent Station Load Independent Delay Infinite Server Load Independent Load Dependent Figure 2 8 Defining the stations type It is important to define each station type because if a station is Load Dependent a set of service demand or a set of service times and the number of visit must be defined one service demand time for each possible value of queue length inside the station In subsection 2 2 4 we will explain this concept with more details 2 2 4 Service Demands Service Times and Visits Tabs Service Demands can be defined in two ways e directly by entering Service Demands Dke e indirectly by entering Service Times Ske and Visits Vic Service demand Dj is the total service requirement that is the average amount of time that a customer of class c spends in service at station k during one interaction with the system i e it completes execution Service time Sy is the average time spent by a customer of class c at station k for a single visit at that station while V is the average number of visits at that resource for each interaction with the system Remember that Dx Vke Ske so it is simple to compute service demands matrix starting from service times and visits matrixes Inverse calculation is perform
45. queue is the shortest 1 customer e Shortest Response time Customers are sent to the station where the average response time for the job s class is the smallest at the moment a customer leaves the routing station Figure 3 46 shows that at the time of routing the middle station has the smallest average response time R so the customer will be sent to it 50 CHAPTER 3 JSIMGRAPH q1 3 jobs q2 4jobs a3 1jobs Figure 3 45 Routing according to the Join the Shortest Queue algorithm ee Input job Cy O x R2 R3 R1 3 sec R2 2 5 sec R3 2 9sec Figure 3 46 Routing according to the Shortest Response Time algorithm e Least Utilization The destination station is chosen as the one with the smallest average utilization at the time routing is performed In the example shown in Figure 3 47 depicted in the picture the top station is the least utilized so it will receive the next customer to leave the blue station A 2 Input job U1 34 U2 44 UI 45 Figure 3 47 Routing according to the Least utilization algorithm e Fastest Service A customer is routed to the device with the smallest average service time S for the job s class In Figure 3 48 the exiting customer will be routed to the top station since its service time is the minimum among the three 3 9 2 Sink Station Open class customers leave the system once they have received all the services they need Sink stations are used to model customers leavi
46. tO VIVAS o ee E A AE SER BES ee ES e EEE 66 LO ELNE 2 85 Y IIA E das ls e RARA 66 3 13 1 Example 1 A model with single closed class 0 0 0 67 3 13 2 Example 2 What If Analysis of a system with multiclass customers 69 JSIMwiz 81 MN MOVOTO W 2 us on a fenk de cet Uh ot ence we he vr es Sere Beh os ee A He Ge ee ee a ee 81 4 1 1 Starting the discrete event simulator e 82 4 2 Defining a tew model s eos mura ER E ee in ae Se A ew AO E a 82 AoA Denne Classes s hs ve oe la is AA as de de a 83 AA Denne tA ONS Ys e st E a AD eee ee 85 423 Define Connections b b64444 6 6 here SS bd dA ho pa eS A AE G 94 AWA station aT aiMie Cbs apa oy Gee es de Es LANA at a ee ete 95 4 2 5 Define Performance Indices 1 a a a 95 4 26 Reference Stations wes hak 6s kde o wa BE ee eh eae Se ED 97 EZ Emite Capacity Recon r es da be A a tee a hae ee Oe ees 97 4 2 8 Define Simulation Parameters ys foe ee le Bod Ow ows Wee BS ee Ew 98 A29 Meine what Tamal y AD BU A A A A Be ye oe a 99 A TMPO nI AE 0d ar Ud add BL be A ARE Oo ee eS ee 101 AA ANlodibydetauilt parameters e ao ache we Bed ok ARAN eR a 101 AS Modity The Current Models ii AOS Ee ENE SS DA A ERM eA EERE EY 104 4 6 Error and warning messages 2 oG Me a we wh GO A Y AE OR 104 Ast Simulation Results rodas dass ada OSes be eee ee 106 ALS Tano IIA LION 4 E A e E A e A A 106 JABA Asymptotic Bound Analysis 109 AMES ao II 109
47. that Dre Vie Ske so it s simple to compute service demands matrix starting from service times and visits matrixes Inverse calculation is performed with the following algorithm Ve 1 if Dr gt 0 EF O if Dp 0 ME Dir if Dre gt 0 ke 0 if Dre 0 Service Demands Tab In this tab you can insert directly Service Demands Dz for each pair station k class c in the model Figure 5 7 shown a reference screenshot can be seen notice that a value for every D element of the D matrix has already been specified because the default value assigned to newly created stations is zero KES File Action Help DEA Saturation Sectors Text Classes Stations Service Demands Comment Saturation Sectors Graphics Convex Hull Graphics Service Demands Class1 Class Input service demands of each 8 00 station for each class i 13 18 If station type is set to Load 20 00 Dependent vou can set values of 14 62 service demands for each number of customers by double clicking on any button in stations row If you whish to input service times and visits instead of service demands press Service Times and Visits button Service Times and Visits E Back Solve Exit Help Figure 5 7 The Service Demands Tab In Figure 5 7 each job of Classi requires an average service demand time of 6 sec to CPU 16 53 sec to Disk1 8 sec to Disk2 and 9 75 sec to Station4 Service Times an
48. the Simulation To run the simulator press Alt s or select Simulate from the Solve menu or press from the toolbar Note that if you had run the simulation for the same program before JSIMgraph asks for a confirmation whether you want to replace the previous simulation results or not Choose yes to confirm In the drawing window of the Simulator Figure 3 79 the colored parts of a station represents the percentages of station busy time and of the queue length due to the customers of Class0 In the Simulation Results window Figure 3 80 opened automatically when simulation starts the progress of the average values of the selected performance indices and the extremes of the confidence intervals are shown Table 3 2 shows the average min and max values of the indexes at the station level at the end of the simulation Table 3 3 shows the average min and max values of Response Time Throughput and number of customers at the level of the global system Note that the results of different simulation runs may slightly vary due to the differences in the sequence of random numbers generated with different seeds 3 13 2 Example 2 What If Analysis of a system with multiclass customers The problem Consider an intranet consisting of a storage server and an Apache server The storage server consists of three disks used according to a RAIDO algorithm striping The web server consists of two independent systems that for performan
49. the need Sink stations are used to model customers leaving the system as they enter the sink station but do not ever leave it Sink stations have no parameters only incoming connections from one or more stations depending upon the model 8 Logger station A logging station i e Jogger reads information flowing through it and writes it to a file In the simplest way it is a tool to understand and debug the traffic flow moving through the interesting 88 CHAPTER 4 JSIMWIZ part s of the model Place the logger station into the model choose the parameters and trace the data as it passes through the model Set or change of the properties Double click on the Logger Station icon to open the Editing Logger Properties station s config uration dialog see Figure 4 2 There are two sections Logger Section and Routing Section Lala Comper opiti flee See Mairia Legan mpy i aramalara a Lo alki 1 A aie ee i Ligar pisa Ling ie Mhi imis Lo Line ee E Lege Pani Piri E ov a PiE sof Tdi ev Lira a bi TL apts Aphis T Che D Lees ME a r Tierra rs r bg Cabra Fle Crio io E e rol mod Figure 4 2 Window for the Logger Station configuration Logger Section The configuration properties of the Logger Section are e Logging Options The Logfile s name to use either individual or merged Logger0 csv or global csv respectively The information to log fields Logger Name Job Arrival Time simulatio
50. the same index has been added more than once for the same station and class Multiple occurrences must be removed see subsection subsection 4 2 5 o J Error Close class Class1 routed to station Serverd linked only to sink Customers of closed classes keep circulating in the system They may not visit a Sink station or a station that is connected on the outgoing link only to the Sink since this would cause them to leave the system The station connections must be changed see subsection 4 2 3 Round Robin routing strategy in Class0 for Source is not eo allowed This was considered as RandomRouting When exporting a JSIM model to JMVA a few constraints apply as for the admissible routing strategies Round Robin routing is not implemented in JMVA so it will be automatically transformed into Random if you click the Continue button Otherwise you can change it as described in subsetion subsection 4 2 4 o Warming Different service times inside FCFS station Serveri When exporting a JSIM model to JMVA a few constraints apply as for the admissible service time distributions A FCFS station must have exponentially distributed service time with the same mean for all the classes of customers that visit the station If you click the Continue button the station service time is reset to the default value the same for all classes Otherwise you can change it as described in subsection 4 2 4 o Error Undefined station in performance index
51. the window a riepilogative table is presented depending on selected control parameter that table is used to show the initial state of involved parameters Every class currently selected for what if analysis is Shown in red La JMVA PFON exact solver File Action Help bb gt RAGS Classes Stations Service Demands What if i Comment What if analysis Control Parameter Service Demands Solve models with increasing or decreasing service demand at station station selected station for selected class aereo lessee From 3 To fs Steps in of executions Classi Class Class3 Class4 0 0222 0 4241 0 3054 0 4296 Figure 2 14 What if Tab Service Demands A brief description of each field is now presented Station available only with Service Demands control parameter This combo box allows to select at which station service demand values will be modified Class allows to select for which class the selected parameter will be changed A special value namely A11 classes proportionally is used to modify the control parameter for each class keeping constant the proportion between different classes This special value is not available in Population Mix analysis as we are changing the proportion of jobs between two closed classes From the initial value of what if analysis It was chosen to leave this value fixed to the initial value specified by the user in the previous steps to avoid confusions s
52. time allow for distinct service demands De k FCFS Priority under this policy customers are ordered according to their arrival time but customers with higher priority jump ahead of customers with lower priority conventionally a small priority number low priority Customers with the same priority are served FCFS LCFS under the Last Come First Served queuing discipline an arriving job jumps ahead of the queue and will be served first unless other jobs arrive before the one currently in service finishes The LCFS discipline implemented in JSIM is not the preemptive resume type LCES Priority under this policy the next customer to be served is one with the highest priority conventionally a small priority number low priority so an arriving customer can only jump ahead of the queue of the other jobs with the equal or smaller priority Customers with the same priority are served LCFS e Drop Rule it is not active when infinite capacity is selected For each class you can select a rule to apply when a customer cannot enter a station since the max number of customers allowed is reached 3 9 5 Join Station Join stations are complementary to fork stations see Figure 3 54 In classical queueing network theory a task arrives at a join station from the corresponding Fork station In JSIM a Join station may have incoming links from stations other than the corresponding Fork one A Join station has no service time as it is
53. type of classes and number of customers closed Number Lali class or arrival rate topen class You can add classes one by one or define total number at once Mo of Customers Arrival Rate 5 Figure 2 1 Classes tab Menu it is organized into three groups of functions To use a menu click on the menu heading and choose the appropriate option For the description of menu entries see section 2 3 Toolbar contains some buttons to speed up access to JMVA functions e g New model Open Save See section 2 3 for details If you move the mouse pointer over a button a tooltip will be shown up 3 4 CHAPTER 2 JMVA Page Area this is the core of the window All MVA parameters are grouped in different tabs You can modify only a subset of them by selecting the right tab as will be shown later 2 2 Model definition Models with one or multiple customer classes provide estimates of performance measures For a brief description of basic terminology please refer to Appendix A In the case of single class models the workload is characterized by two inputs the set of service demands one for each resource and the workload intensity On the other hand in multiple class models a matrix of service demands is requested LZGS84 2 2 1 Defining a new model To define a new model select toolbar button LA or the New command from File menu The following parameters must be defined 1 Classes with their workload intensities
54. utilize as match element one of the values within square brackets a bcdje gt abe ace ade it indicates that there are zero or more instances of the preceding character ba gt b ba baa baaa it indicates that there are zero or one instance of the preceding character ba gt b ba it has two different meanings depending on the use The former permits to require that a pattern starts with a particular character abc abcdef abc fg If it is utilized within square brackets as first character it allows to match any character that doesn t belong to the defined group a bcd wedfer it defines a pattern that permits to use as match element the string that is contained between brackets ab gt ab abab ababab A list of Escape Sequences used to identify intervals of characters follows Ad it identifies whichever number 0 9 D it identifies whichever thing except a number 0 9 w it identifies whichever character or number 0 9a zA Z W it identifies whichever thing except a character or a number 0 9a zA Z As it identifies a white space character t n r f AS it identifies whichever thing except a white space character t n r f 148 CHAPTER 6 JWAT WORKLOAD ANALYZER TOOL it identifies whichever character except the new line character An Combining in an opportune way the characters the options and the Escape Sequences it is possible to d
55. within a given Confidence Interval and Max Relative Error both defined on the 0 1 range by performing the following steps 1 Select the index you want to add to the model from this menu Queue Length Queue Length Queue Time Residence Time Response Time System Throughput System Response Time 2 Click and the index will be added to the panel Next the index parameters must be set 3 Select from the Class menu a single class or All Classes for which the index must be computed All Classes Al 4 Select the Station for which the index must be computed from Station menu In case of system wide indices namely System Throughput and System Response Time this option is not available me Serverl la Server 4 2 DEFINING A NEW MODEL 97 5 Double click on the values to modify the default values for the Confidence Interval size of the solution and for the Max Relative Error of the greatest sample error if you want more less accurate results Confidence Interval Max Relative Error 6 Repeat these steps for all the indices you want to include in the model output NOTE erroneous parameter settings will be detected only when the simulation is started raising a warning or an error message 4 2 6 Reference Stations The Reference Stations tab allows you to specify the Reference Station for each customer class For each customer class a reference station must be specified in order t
56. 0 3 200000 6 166667 71142057 8 125000 Enter the expression to be evaluated using r For the number of customers For syntax details and a list of supported Functions click on Help pew OOO O Figure 2 32 Example 3 editor for the description of service demands for a load dependent station In this case an arithmetic function has been defined S n n 1 n Aggregate Station Users Throughput job s Queue Length job Residence Time s Utilization Table 2 9 Example 4 model outputs 2 4 4 Example 4 A model with one open and one closed class The mixed queueing network model is shown in Figure 2 33 Workload intensities the open class has an arrival Ss oro Station 1 Station2 Station 3 Figure 2 33 Example 4 network topology rate A 1 job s the closed class has a customers number N 57 Service demands are shown in Table 2 10 Step 1 Classes Tab Follow the instructions of Step 1 in the previous examples the Classes Tab is shown in Figure 2 34 Step 2 Stations Tab Follow the instructions of Step 2 in the previous examples in this case the model has three Load Independent stations see Figure 2 35 Step 3 Service Demands Tab Follow the instructions of Step 3 in the previous examples and define service demands for both classes as illustrated in Table 2 10 see Figure 2 36 Step 4 Model Solution Use Solve command Results can be verified by computing the equiv
57. 0 0 002882 Station4 3 146376 0 003494 3 140000 0 002882 Figure 2 15 Model Solution Throughput Tab Using the tab selector all the other computed performance indices can be seen Throughput Queue lengths Residence Times Utilizations and a synopsis panel with schematic report of input model Both results and synopsis tab data can be copied to clipboard with the standard CTRL C keyboard shortcut When open classes are used the resource saturation control is performed For multiple class models the following inequality must be satisfied max Y Ae Dre lt 1 C This inequality ensures that no service center is saturated as a result of the combined loads of all the classes Let us consider as example the model with the classes shown in Figure 2 5 with the D matrix shown in Figure 2 9 Since A 3 14 lt 3 33 1 0 3 1 Dmaz the model is not in saturation and the Solve command will be executed correctly In this example substituting DDisk1 OpenClass With values gt 1 3 14 0 318 will cause the saturation of resource Disk1 and the error message of Figure 2 16 will appear Input data error 63 One or more resources are in saturation Decrease arrival rates or service demands Figure 2 16 Input data error message 2 2 9 Model Solution What if analysis Use Solve command to solve the model During model solution a progress window see Figure 2 17 shows up It displays the cumulative number of models currently solved the
58. 038s Click OK The value A is automatically computed by the tool e Click on the Routing Section tab Choose Routing Strategies as Probabilities Since there is only one outgoing link which goes to the CPU from Disk1 so select the Probability of going to CPU under the Routing Options subsection as 1 see Figure 3 76 Click on Done e Double click on Disk2 Click on Service Section tab Click on Edit e The default Selected Distribution should be Exponential Set Mean value as 0 030 Click OK The value of A is automatically computed by the tool e Click on the Routing Section tab Choose Routing Strategies as Probabilities Since there is only one outgoing link which goes to CPU from Disk2 set the Probability of going to CPU in the Routing Options subsection to 1 Click on Done Defining the Performance Indices Before start the simulation we must select the performance indices to analyze In Example 1 we want to study the following indices Queue length jobs for CPU Disk1 Disk2 Users and the global System Throughput jobs sec for CPU Disk1 Disk2 Users and the System Residence time sec for CPU Disk1 Disk2 Users and the System Utilization for CPU Disk1 Disk2 and Users The following actions should be done e From menu bar select Define gt Performance Indices or select from the toolbar e From the drop down menu at the right select Queue Length Click on Add Selected Index for four times
59. 10 442926564433 mean 3 200000000003 c 1 192424001773 Figure 3 82 Definition of the hyperexponential distribution of Class0 customers 76 CHAPTER 3 JSIMGRAPH a Editing Requests Properties ai E x Station Name Station Name Requests Parameters Definiton Routing Section Routing Strategies foes Routing Strategy Eis possible to define the routing Probabilities probability for each connected station If the sum of the probabilities is different from 1 all the values will be scaled to sum 1 Pecan ea Tas oi FOB SOEs Routing Options Destination Probability RAIDO LoadBalancer m Poe Figure 3 83 Setting the Routing strategy probabilities in output of station Requests for Classl1 customers Editing RAIDO Properties Station Name Station Name A RAIDO Parameters Definiton f Fork Section Queue Section Fork degree Number of tasks to be generated on each output link for each input job 3H Fork join section capacity _ Enable Finite Capacity limit maximum number of jobs inside a fork join section Capacity max number of jobs NOT tasks Figure 3 84 Setting the RAIDO Fork station properties 3 13 EXAMPLES 7 Editing LoadBalancer Properties N Station Name Station Name LoadBalancer LoadBalancer Parameters Definiton Routing Section Routing Strategies Description Routing Strategy Jo
60. 16 CHAPTER 5 JABA ASYMPTOTIC BOUND ANALYSIS Disk2 Figure 5 14 Convex Hull Graphic while is dragging a point Identify a point s label in a crowded area It is possible that a area of the graph could be crowded of points whose names are difficult to read as showed in thefollowing graph Figure 5 15 Class Class2 Figure 5 15 Convex Hull Graphic whith a crowded area It is difficult to understand or simply read which of the dominated point the label belongs to at first we can try to change the zoom we can therefore zooming in by a double click on the mouse s left button or zooming out by a double click on the mouse s right button If the zooming is no enough we can try filtering the zone and freeing only some points In order to filter the area is enough to select it keeping the mouse s left button pressed The background of the selected area will become grey points will become dark grey and their labels will disappear Figure 5 16 Convex Hull Graphic whith a filtered area Now we try to reduce the filtered area adding some free area to do that we select the area that we wish to free keeping the mouse s right button pressed In the following example we have set the tallest point free Only the name of the station that is in the free area is showed 5 2 8 Saturation Sector Text It s a simple report about the saturation sector for each saturation sector you can find 5 3 MENU ENTRIES 117 Figure 5 17
61. 4 1 Overview Simulation can be applied when the characteristics of the network to be analyzed make analytical techniques no longer useful for its performance evaluation A simulator is a dynamic model able to follow the evolution in time of both the system complexity it represents and the pattern of arrival requests to be executed In the JMT suite a discrete event simulator JSIM for the analysis of queueing network models is provided It can be used through two interfaces alphanumerical JSIMwiz and graphical JSIMgraph The manual of JSIMgraph is more detailed than this one If some information are omitted or unclear in the present manual you may consult it An intuitive user interface allows even an unexperienced user to build with JSIMwiz system models with sophisticated characteristics It helps the users to perform an evaluation study in two ways Firstly critical statistical decisions such as transient detection and removal variance estimation and simulation length control have been completely automated thus freeing the users from taking decisions about parameters s he may not be familiar with The simulation is automatically stopped when all performance indexes can be estimated with the required accuracy Secondly a user friendly graphical interface allows the user to describe both the network layout and the input parameters Furthermore the graphical interface also provides support for the use of advanced features several of them are f
62. 5 1 1 Starting the alphanumeric JABA solver ee 2 109 a Model denmiom cimas ds cra da AA AE Se 110 521 Denia new mod l say as a A AA A A E eee 110 A AAA EE IA 111 23 OOS labo yaa dd bd ee eee a tr ee te EA 111 5 2 4 Service Demands Service Times and Visits Tabs aooaa a a a a a aa 111 2d Comment Lab te A A E Ea Ee ee ee O 112 52 0 Daturaction Sector Graphic s ssa 260 8 ba E e A A 112 dat COnN uls Gra pine T 2 548 a ie A AA wee A A 114 ZO Da tUratio Sector LEK 4 ak sarna adas AA 116 D29 Modinication Ola model uti ios ua e te da a gei e ee Oe ee ee eee 117 o A NR E RR 117 on EMS has ada A AA a ee eS 117 DOE A a aa a a r a O santo 118 a ACIDO a o aaae Meee Ges x Se Hh a eaan A ad ee ee eS 118 Oe wee A Ge are bs eS Oe See OR ae ee AOS eee oe E 118 5 4 1 Example 1 A two class model 0 0 118 5 4 2 Example 2 A three class model 121 CONTENTS 6 JWAT Workload Analyzer Tool Ol Workldad analysis g era a amp amp So come ed ae eB ae ee Sk Boe oe A oe 6 1 1 A workload characterization study a a O22 Input dano 4 6 ak a is Ss ere a eee de ta amp is eee Ok Data Process ds SSA De eS Se ates AA ee wee SS Gta Cisternas lc OAMI ee Sve ee EB a a DA E ee 6 1 5 The results of a clustering execution ee 6 1 6 An example of a web log analysis socios woe a a ee ee Sn EO hw Boe A we es Ole Men s descnipvion s 2222 oe EE A ADA 0 Eormiat denon y gs aot Shee ede e
63. 7 Select Solve action The Synopsis Tab with a schematic report of the model created is shown on Figure 2 29 while the computed performance indices of this model are shown in Table 2 7 Throughput Queue length Residence Times Utilization Synopsis i jJMVA Model Details Classes Type Population Arrival Rate open 0 15 open 0 32 Stations Name Type CPU Load Independent Disk1 Load Independent Disk Load Independent Service Demands Figure 2 29 Example 2 output data Synopsis Tab Class A Aggregate CPU Disk1 Disk2 Throughput job s Queue Length job Residence Time s Utilization Class B Aggregate CPU Diski Disk2 Throughput job s Queue Length job Residence Time s Utilization Table 2 7 Example 2 model outputs 2 4 3 Example 3 A model with a load dependent station The network is shown in Figure 2 30 It comprises only two stations one is of delay type named Users and the other is a load dependent station named Station This model has one closed class only with N 8 customers The user s think time is Z 21 s while the service demands for the load dependent Station shown in Table 2 8 are function of n number of customers in the station D n n 1 n 2 4 EXAMPLES 21 Users Z Station Figure 2 30 Example 3 network topology 1 2 3 4 5 6 T 8 Day E Table 2 8 Example 3 service demands for Station a load dependent service center Step 1 Classes
64. APTER 6 JWAT WORKLOAD ANALYZER TOOL Clustering Info Cluster Info y Dispersion Matrix Cluster Information This panel show s information of variables center and statistics within a single cluster Cluster 4 6 has 2928 observations 100 541 10 210 975E5 483 244E2 675 751E 3 Access request 121 370E2 240 936E1 115 122E 2 345 082E 3 Result status code 20 164E0 FOO 604E 1 245 405E 2 210 9 5E 2 Bytes transferred adz ra1El 150 041E1 300 1850E 3 903 244E 5 1168 0 1 009417274 12 14433 0 200 0 4200 0 1168 0 1 009417307 12 14489 0 200 0 8191 0 1169 0 1 008417235E12 14490 0 200 0 5224 0 1168 0 1 008417384E12 14493 0 200 0 4796 0 1187 0 1 009416999E12 9170 0 200 0 5326 0 1197 0 1 0084169E 12 14230 0 200 0 9937 0 1187 0 1 008417025E12 8173 0 200 0 8465 0 Figure 6 38 Descriptive statistics of the clusters obtained with the k means algorithm and their visual charac terization through the dispersion matrix Timestamp Access request Clusterized a E EA ees e E a A e a vie a Resul Status code 4 it ere t E a 4 orde oem Bytes transferred atlas A ted Clusterized Figure 6 39 K Means scatter plots matrix Each observation is represented with the color corresponding to the cluster it is assigned 6 1 WORKLOAD ANALYSIS 141 Fuzzy K Means algorithm results When the fuzzy k Means results are selected the panel is uploaded and in the table of Figure 6 35 a new table containing a row fo
65. All the stations have default parameters The proper parameters of the objects should be defined either the numeric values or the qualitative parameters such as routing strategy queueing policy maximum number of customers in a FCR region etc See section 3 9 Defining Network Topology for details Step 4 Define performance indices The performance indices that will be evaluated during the simulation should be selected Select the indices and set the class and the station which each index refers to See section 3 5 Performance Indices for details Step 5 Define a Finite Capacity Region 32 CHAPTER 3 JSIMGRAPH A Finite Capacity Region FCR is a section of the model that may consists of one or more stations in which the number of customers is limited Several FCRs can be defined in a network provided that they do not overlap See section 3 8 Finite Capacity Region FCR to learn how to set this type of region Step 6 Setting simulation parameters The parameters that control the simulation and the initial state of the network should be defined See section 3 10 Modification of the parameters for details Step 7 Enabling a What If Analysis If you decide to set up a What If Analysis read section 3 7 Step 8 Start the simulation Press or select Simulate from the Solve menu to start the simulation Before starting the simulation a check if the defined network is correct is performed and the errors detected
66. DUCTION techniques allow the identification of cluster of customers having similar characteristics The clusters centroids represent the mean values of the parameters of the classes e g CPU time n o of I Os n o of web pages pages accessed that can be used for the workload parameterization 1 1 Starting with the JMT suite Double click on the JMT icon on your program group or on the desktop or open the command prompt and type from the installation directory java jar JMT jar The window of Figure 1 1 will be shown Ord JMT Java Modelling Tools v 0 7 4 Textual Model JMT Java Modelling Tools v 0 7 4 lt Performance Evaluation Lab Simulation Graphical Dipartimento di Elettronica e Informazione 3 Politecnico di Milano Italy Model Definition Project Coordinator prof G Serazzi E Method e MVA Textual axacl y Introduction to IMT Estat Analytical Solution gt Online Documentation Chain o Asymptotic Markov Figure 1 1 The JMT suite Starting Screen This starting screen is used to select the application of the suite to be executed by clicking on the corre sponding button The flow chart should help the user to select the application that best fits its needs In the following chapters the tools will be examined in details and some examples are given This manual is intended for the general user that wants to learn how to interact with JMT Advanced users that wa
67. ED lt p Figure 3 11 Main structure of the Burst MMPP2 distribution Constant Const k distribution This distribution describes a constant deterministic flow of customers arriving exactly every k time units The probability density function is fo 1 TE 10 xk The only parameter that should be specified is the mean equal to k Figure 3 12 Constant distributions for two different mean values Erlang erl a r distribution The Erlang distribution is a continuous distribution with two parameters the shape r an integer value and the rate a a real value It is a special case of a Gamma distribution with integer shape parameter The probability density function is Q F 1 0 1 I r is called Eulero function and when r is a non null positive integer as in the case of the Erlang distribution the Eulero function reduces to T r r 1 A random variable with Erlang distribution of order r can be obtained as a sum of r exponentially distributed random variables with mean 1 ra see Figure 3 13 When the values of and r are changed the system Figure 3 13 Simulation of an Erlang distribution with a sequence of exponential stages will automatically recompute the mean r a and the variance Var r a A family of probability density functions that illustrate the impact of various a r pairs is shown in Figure 3 14 Exponential exp A distribution This is a continuous probability distribut
68. Figure 6 32 that report the progress state and allows to interrupt the execution is shown K Means algorithm The non hierarchical k Means algorithm implemented in the tool requires the specification of the following parameters Figure 6 33 e the maximum number k of clusters that the algorithm has to produce Note that the algorithm produces the results for all partitions from 1 to k clusters CHAPTER 6 JWAT WORKLOAD ANALYZER TOOL 136 Timestamp T di T lr A E E x o Bytes transferred Figure 6 29 QQ plot matrix for the comparison of the distributions of two variables Timestamp uh ha S ma ha jun Ww 5 Figure 6 30 Scatter matrix 6 1 WORKLOAD ANALYSIS 137 Clustering Variables Access request Result status code Figure 6 31 Clustering algorithm used and variables selected that will be considered in the analysis x i Processing Clustering 2 Iteration 4 Figure 6 32 Clustering progress panel e the maximum number of iterations to perform in order to find the optimal partition The initial subdivision into k clusters is iteratively improved by shifting based on the selected criterion in this case the Euclidean distance the elements of a cluster to another and computing after each assignment the new center of mass of the clusters The optimum configuration is obtained when points can no longer be reassigned The selected value is an upper limit
69. Little A Proof of the Queueing Formula L AW Operations Research 9 383 387 1961 LZGS84 E D Lazowska J Zahorjan G S Graham and K Sevcik Quantitative System Performance Prentice Hall 1984 RL80 M Reiser and S S Lavenberg Mean Value Analysis of Closed Multichain Queuing Networks J ACM Vol 27 No 2 pp 313 322 April 1980 155
70. MQICOS s ss s s oes Rhee A oe OEE AES ERY ERE ER ee ES ook Gonndence lmtervals x 4 2 lt io ce ere Ads ete A eR ii e ooo Max Relative Errore owe a See ee eS wu eR EA Be She ee BAe ek 3 6 Simulation Parameters 4 2 2 sans ob oe ead bee OME e eee ede bese eben dec Oot Wh t FAnalysis 3 2 ogoi i Feit ow ot eters Ob air eh ae eds Bo od EE I E a 30 Finite Capacity Region BOR dsp da Ae AR Hs A ee 3 9 Defining Network Topology x s s a amie aod OR a dl ee Se EAR A GS SJT DOUFCE Station se s d hehe 046 h HAE ADE RARH REDD AAA 2 DISTA LIO pd 4 3 6 katie ee OO eA ana bbe eee ae eee Ons CTA OU AOU o ec psp AE as I eB ies we as E 94 FOrk Stato e 44 4 rare bea SS Se OS Se ew Bee hed CERES ill ili CONTENTS Sd BOM SAMOA oe ee ee AS CE CRE Oe eS EE Se 54 290 ROHE SAU cae ee eo we GRADED ARA AA e a 55 PO QUEN Oa co cal Mika Mens amp ANN 56 Deco WOR CCGG AION oo a sepa ee ms Sch ia eee Be Gee Ge Ge EE ee a ee ee ee 97 3 10 Modiicati n of the Para meters lt c ace bib Sua amp amp amp e Do e o e e A A ee 58 3 10 1 Modifying Simulation Parameters escaso a a a AR A ee 58 3 10 2 Modifying station parameters 2 a e 59 3 10 3 Modifying the default values of parameters a a a a 59 3 11 Error and Warning Messages oaoa aa a A a A ca 62 Orbe Results ol Similar ly Bele ek ewe A RE Aa 64 3 12 1 Results from a single simulation run aoaaa aa 64 3 12 2 Result of What If Analysis simulation TU 66 312 3 EXPO
71. Ni 10 0 10 0 Done Figure 3 30 Window for the definition of the Simulation Parameters e Maximum duration sec It represents the maximum amount of time in seconds that the simulation will run If the simulation ends before the maximum duration the parameter is ignored and does not affect the results The default value is infinite deselect it and specify the preferred maximum time if you do not want the simulation to run for a possibly very long time In this case the simulation stops when the time limit is reached although a reliable solution may not be available yet e Maximum number of samples It is the greatest number of samples for each index that JSIMgraph collects before ending the simulation During a simulation measurements can be stopped in case of Success if the results have reached the required Confidence Interval and the Max Relative Error Failure if the simulation has analyzed the maximum number of samples but has not reached the required Confidence Interval or Max Relative Error Failure if timeout occurs before successfully calculating the final results The default value for the maximum number of samples is 500 000 you may increase it for a more accurate simulation or decrease it for a faster simulation e Representation Interval sec This is the granularity at which results are plotted on the screen i e the time interval before a new point is added to the graphs as the simulation procee
72. Normal distribution Mean the mean value of each distribution is specified in the Mean form by double clicking on it Insert a number or an arithmetic expression that will be evaluated with JFEP Java Fast Expression Parser For a complete list of the command supported by JFEP you can read the Help tab or see the JFEP web site at http jfep sourceforge net c The coefficient of variation of each distribution when C exist can be specified by double clicking on the c form For example in the previous picture two policies are defined From 1 to 4 jobs in the station the server will behave according to an Erlang distribution with mean 1 and c 0 5 For any number of jobs greater or equal to 5 in the station the system will behave according to an Exponential distribution with mean 1 If you want to delete a range click 4 2 3 Define Connections The Connections tab allows you to define how stations are connected with each other In order to create a connection from station 7 to a station j check the table entry i j in the connection matrix rows identify source stations columns identify destination stations Station Connections Click on table entry 1 3 to connect station i to station j Station Stations Station1 O O Station NOTE if there are open classes in the model the Source and Sink station automatically created by the system appear in the connection matrix A Source station may have only outgoing links a Si
73. Probabilities Join the Shortest Queue JSQ Shortest Response time Least Utilization Fastest Service To know details about these algorithms please refer to the subsection 3 9 1 Source Station 3 9 6 Routing Station A routing station is a dummy station with service time equal 0 which is used to create more sophisticated routing strategies by sending customers through one or more such stations For example if we want that two thirds of the incoming traffic at station Z to be randomly routed to either station A or B or the remaining third to go either to station C or D depending on the shortest queue at the two stations we could implement the following Add a routing station Y to the output of Z station and define random routing for the three stations connected in output namely A B Y Then connect Y to C and D and define shortest queue routing JSQ for C and D H RoutingStation0 Figure 3 58 The Routing Station 56 CHAPTER 3 JSIMGRAPH Set or change of properties With a double click on the routing station icon the Editing Routing Station Properties window is shown see Figure 3 57 It has only one tab Routing Section Routing Section In the routing section for each class you can decide how the completed jobs are routed to the other devices connected to the considered station For each class the user should select the algorithm applied to determine the path followed by the outgoing customers The following a
74. Ratio 216 70262 Ratio value 271 445E 2 Clusters details _ E E Cluster Mum observations Percentage Cluster 33 557 Yo 3 008 Access request 23 673 Result status code 12 612 oe Vo 22 UG Yo Figure 6 37 Characterization of the clusters e Clusters Info It shows statistics concerning the clusters Figure 6 38 Besides the classic descriptive univariate statistics the SC that indicates which variables have been used for the clustering and the center values that refer to the centroid coordinates of each cluster are reported The panel at the bottom shows a preview it can be magnified by a left double click of the mouse of the graph concerning the comparisons of the distributions of the variables used in each cluster It is also possible to visualize the list of observations that belong to a cluster through the Show Observations button attention this operation may requires several minutes e Dispersion Matrix this panel shows the matrix of all the possible variable vs variable scatter plots Figure 6 39 These graphs allows a visual interpretation of the compositions of the clusters since the observations are represented with the color corresponding to the cluster it is assigned With a left double click of the mouse on a preview the graph is magnified and several options can be selected with a right click on the graph 140 CH
75. Show Obser Save Info Figure 6 42 Descriptive statistics of the clusters obtained with the fuzzy k means algorithm and their visual characterization through the dispersion matrix Cae aaa dota r Ht EZ a oe d F 1 Timestamp Clusterized Access request Ti da Bytes transferred gt Clusterized Figure 6 43 Fuzzy k Means scatter plot matrix Each observation is represented with the color corresponding to the cluster it is assigned 6 1 WORKLOAD ANALYSIS 143 6 1 6 An example of a web log analysis In this section we will describe an example of application of the JWAT tool for a workload analysis The analyzed set of data consists of observations stored in the log file of a web server of a university site The input file Demo1Data jwat and its format DemolFormat jwatformat can be found in the subfolders Exam ples and jwatFormats respectively of the Java Modelling Tools folder installed with the JMT tools Step 1 Input panel 15 Dec 2001 i homepagehomepage php 3914 15 Dec 2001 homepage homepage php 7825 15 Dec 2001 lnagesz000 home ombrasmussolive gif 223 15 Dec 2001 E lmnagesz000 home ombralive gif 131 15 Dec 2001 E l inagesz000 home spacer gif 43 Comment PerlS Reg Exp IP Address d d d d x Timestamp Timestamp of the visit as 5 ydd wydd x Access request The request made E x Bytes transferred The number of bytes
76. X EX 00 Coefficient of variation c when mean and variance exist and mean is not 0 y variance mean C The following probability distributions are currently supported Burst General distribution The Burst General distribution is a complex distribution obtained combining two different distributions It allows the simulation of complex patterns of arrivals and may be suitable for simulating the load generated by web 2 0 applications A Burst General distribution consists of two different types of intervals A and B independent among each other For both the interval types the following parameters have to be specified 3 4 DISTRIBUTIONS 39 e the probability of occurrence of that type of interval in the generated stream e the length distribution for that type of intervals e the distribution of the values generated into each interval The Burst General distribution behaves as follows As soon as the simulation starts an interval is chosen based on the specified probability of occurrence If for example interval type A has probability of occurrence of 0 7 and interval B has 0 3 then an interval of type A is chosen with 70 probability In order to determine the duration of an interval an event from the interval length distribution is obtained The distribution of the events of an interval is then used to compute the arrival time of customers or the service time of a station depending on where the Burst Genera
77. _ANYCLASS Logger0 0 199 1 Class0 0 000 0 199 Logger0 0 559 2 Class0 0 341 0 341 Fork section How to define the Forking Behavior This section is characteristic only of fork stations It defines the parallelism degree of a job in terms of the number of tasks it is split into and how many jobs can be serviced concurrently 4 2 DEFINING A NEW MODEL 89 In this section you can define the station forking degree i e the number of tasks created for each job arriving at the fork station and its capacity i e the maximum number of of jobs that can be in a fork join section when a join is present Fork degree Number of tasks to be generated on each output link For each input job MS Fork join section capacity Enable Finite Capacity limit maximum number of jobs inside a fork join section Capacity max number of jobs WOT tasks Forking degree it is the number of tasks that are routed on each outgoing link of the fork station Therefore each job is split into forking degree number of outgoing links tasks By default the forking degree is 1 and it can be modified using this form Number of tasks to be generated on each output link For each input job 1 Capacity 1t is the maximum number of jobs that can be served by a fork join section simultaneously It makes sense only if there is a join station matching the fork one It can be finite in which case once the limit is reached jobs wait in the queue of the
78. a ee De ee ye eee RE SATA Eee Eo 6 2 1 Example of a format definition s a a a a 6 2 2 Example of the definition of the Apache log ee o A Basic Definitions B List of Symbols Bibliography 125 126 126 128 131 135 138 143 146 147 148 149 151 153 155 vi CONTENTS Chapter 1 Introduction The Java Modelling Tools JMT is a free open source suite consisting of siz tools for performance evaluation capacity planning workload characterization and modelling of computer and communication systems The suite implements several state of the art algorithms for the exact asymptotic and simulative analysis of queueing network models either with or without product form solution Models can be described either through wizard dialogs or with a graphical user friendly interface The workload analysis tool is based on clustering techniques The suite incorporates an XML data layer that enables full reusability of the computational engines The JMT suite is composed by the following tools JSIMwiz a wizard based interface for the discrete event simulator JSIM for the analysis of queueing network models A sequence of wizard windows helps in the definition of the network properties The JSIM simulation engine supports several probability distributions for characterizing service and inter arrival times Load dependent strategies using arbitrary functions of the current queue length can be s
79. alent model where the open class slows down the closed class by subtracting utilization to it 2 4 EXAMPLES 23 Stationl Station2 Station3 OpenClass s ClosedClass s Table 2 10 Example 4 service demands Classes Stations Service Demands Comment Classes characteristics Number customized name type of classes and number of customers closed Number a class or arrival rate open class You can add classes one by one or define total number at once Mo of Customers Arrival Rate 4 OpenClass ClosedClass Figure 2 34 Example 4 Class Tab Classes Stations Y Service Demands Comment Stations characteristics those E Number customized name and type of stations fou can add stations one by one or define total number at once Mew Station Load Independent E i Load Independent Xx 3 Stations Load Independent x Figure 2 35 Example 4 Stations Tab Classes Stations Service Demands Y Comment Service Demands Openclass ClasedClass Input service demands of each Station1 0 500000 10 000000 station for each class Station 0 800000 4 000000 If station type is set to Load Station3 0 600000 8 000000 Dependent you can set values of service demands for each number of customers by double clicking on any button in station s row If you whish to input service times and visits instead of service demands press Service Times and visits button S
80. alization and to their evaluation The main components of the workload analysis window are e Men three groups of functions are available File Action Help To utilize the menu select the desired option For the description of menu options see Section subsection 6 1 7 e Toolbar several buttons are available to facilitate and to speed up the access to the functions e g New input file Help see Section subsection 6 1 7 When the cursor is over a button tooltips appear e Tabbed pane It concerns the main functions of the application All the operations that can be performed on the input data are shown in four navigable tabs input statistics clustering clustering information Figure 6 4 e Navigation buttons used for navigate between panels The buttons are enabled and disabled automatically depending on the operations to be performed in the actual step Figure 6 5 In the following sections the utilization of the panels will be described in detail together with the available options 6 1 1 A workload characterization study In this section the main operations to be performed in a workload characterization study are described The definition of the workload basic components that is the identification of the smallest level of detail that is to be considered and of the set of variables to be used for their description is among the first operations to be performed Depending on the intended use of the study as workload basic
81. aller values will increase results accuracy while bigger values allow for larger errors in the samples This metric is intended as the maximum ratio between the half width of the confidence interval and the estimated mean 104 CHAPTER 4 JSIMWIZ Simulation Seed this parameter is used to initialize the pseudo random number generator it should be changed very cautiously since the statistical quality of the sequence of pseudo randomly generated numbers is affected by the seed choice Maximum Duration this parameter is set to infinite by default so that even lengthy simulations can com plete and satisfy even narrow confidence intervals finite values in seconds may force termination before the end of the simulation Maximum Number of Samples this parameter is set by default to 500 000 with a smaller number of samples it may not be possible to achieve the requested confidence interval a larger number may not necessarily increase the results accuracy and simply extend the simulation time Animation Update Interval this parameter indicates the time interval between consecutive graph updates on the screen the default value is 2 sec as it provides for a smooth progression of the graphs on the screen Larger values will make the evolution of the simulation appear jerky Number of classes in queue animation this parameter controls the number of classes for which graphs will be plotted for the selected performance indices by settin
82. and of the two customer classes For example a queue with service demands 10 sec for class 1 and 15 sec for class 2 is represented as a point with coordinates 10 15 Then JABA builds the convex hull of this set of points that is the smallest convex set containing all the points The distinction of queues among the different types of bottleneck and non bottleneck classes can be imme diately operated from the knowledge of the convex hull using the following rules e All potential bottlenecks lie on the boundary of the convex polytope e All dominated station are interior points P of the convex polytope such that there is at least one point Q whose co ordinates are all higher or equal in value than those of P e All non dominated stations in the interior of the convex polytope are masked off stations The application of these rules is described below in the case study From this plot Figure 5 11 we can see that Disk1 and Disk2 depicted in red lie on the boundary of the convex hull thus are potential bottlenecks CPU green is instead a dominated non bottleneck station since it is dominated by Sation4 and Disk1 Sation4 blue is also in the interior of the convex hull but it is a non bottleneck station as there is no other point with all coordinates greater than those of Sation4 so it is a masked off station Determining points coordinates In order to gain exact information about the coordinates of a point it is sufficient to cli
83. and specify whether you want to apply the variation to all classes or just to one class Number of Customers only for models with closed classes JSIM repeats the simulation changing the number of jobs in each run starting from the number inserted in the From N field to the value inserted in the To N field The simulation is repeated Steps n of exec number of times Type of population growth 8 Increase number of job of one closed class From M To N Steps n of exec Class Population mix Chiusa Mi 10 Gi 1 00 100 CHAPTER 4 JSIMWIZ In the figure above a what if analysis is planned on a single class model The initial value of the number of customers is not modifiable from this window as it is part of the Classes tab The final value is specified in the field To N In this case with a final value of 20 and 6 Steps simulations are run for 10 12 14 16 18 and 20 customers respectively Only the customer number in the class selected in the Class Chiusa in the picture will be changed The remaining classes will keep their initial number of customers The simulator makes sure that the sum of the percentages of customers in various classes add up to 1 as shown in the Population mix table on the bottom of the window If the all classes option is selected the overall population is increased while keeping the relative proportion of jobs in the various classes constant Because the number of customers in each class can
84. andom the number of observations to be loaded should be specified in the panel of Fig Figure 6 13 Workload sampling method Choose sampling method Random Sampling Loading size options Number of observations 12 500 For filtering on variable see next step Figure 6 13 Random method for the construction of a sample e Interval the panel of Figure 6 14 that requires to specify the interval of observations according to their id numbers to load will be shown Workload sampling method Choose sampling method By interval 4 Loading size options From observation To observation 10 000 For filtering on variable see next step Figure 6 14 Interval method options Loading of log file After the definition of the input file the loading of the selected observations will be started After pressing the LOAD button Figure 6 15 the loading window of Figure 6 16 will be opened The percentage of loading completion the number of processed observations and the number of observations discarded because not con sistent with the specified format are shown At the end of the load a window summarizing the total number Figure 6 15 Button for the loading of the input data of observations loaded and the total number of observations loaded correctly Figure 6 17 is shown It is possible to visualize the log file that contains the description of the errors found
85. arrival times Click on the Selected Distribution drop down menu to choose one of the following distributions Burst General Burst MMPP2 Constant Erlang Exponential Gamma Hyperexponential Normal Pareto Poisson Replayer StudentT Uniform For each distribution the correct values of the parameters should be described default values can eventually be used Parameters that are related each others are automatically updated when one of them is modified For example for an Erlang distribution when you set the a r pair the mean c pair is automatically set to the 34 CHAPTER 3 JSIMGRAPH correct values The Replayer distribution allows the user to use trace of data collected from real experiments Click OK to return to Class parameters definition The final step of a class definition is the identification of the Reference Station i e the station of the model used to compute the system throughput and response time of a class It can be selected from the Reference Station menu Figure 3 7 For Open Classes only one of the stations of Source type can be selected as Reference Station Reference Station Us Sourceo vw Figure 3 7 Selection of the Reference Station for an open class of customers Defining Closed Classes Coke Name Type PrortyiPopulstiori Arrival Time Distribution Reference Station MB Class C cosd o i Server0 v X Figure 3 8 Closed class definition parameters By
86. ate G0 plot Matrix Scatter plot Matrix i i Figure 6 19 Tabs structure for the processing of the data Statistics The univariate and bivariate panels show respectively several statistical indexes concerning each variable of the observations Figure 6 20 and the correlation coefficients of the variables Figure 6 21 Mean Variance Std Dev Coeff of war Minimum Maximum Range Median Kurtosis Skewness Mum Obs TP 330 431E0 boy s47E2 262 175E0 793 426E 3 000 000E0 908 000E0 908 000E0 164 000E0 680 929E 3 13 959E 3 358 300E imestamp 100 839E10 25 B05E12 150 2685 149 018E 100 837E10 100 841E10 417 500E5 100 839E10 166 636E 2 180 260E 4 358 380E2 Access request 335 612E1 185 306E5 430 471E1 129 034E 2 000 0000 142 380DE2 142 550E2 735 000E0 441 502E 4 116 237E 2 358 380E2 Result status 202 568E0 390 93580 197 72ZE 1 376 073E 4 100 000E 2 404 000E0 403 000E0 D0 O DED 46 764E 1 620 855 2 308 3G0E2 Bytes transfe 492 681E1 301 57 9E6 195 340E2 396 4356 2 000 000E0 103 972E4 103 972E4 356 000E0 646 421E0 00 340E 1 358 360E2 Referrer URL 1 195 323E 6 416 5246 6 204 579E 4 104 736ED 000 000E0 300 000E 2 300 0006 2 000 000E0 157 631E2 120 562E0 358 360E2 Figure 6 20 Descriptive statistics of the variables Timestamp Access request Result status code Bytes transferred 402 161E 135 193 8535E 9 124 G85E 7 191 049E 10 Timestamp 402 161E 13 717 968E 14 457 6476 12 fea 4556 15 A
87. ay not start and errors must be corrected In case of warnings you can still start the simulation but the results may not be consistent If another simulation was executed before the current one JSIM will warn you that previous simulation results will be overwritten if you continue Click Yes if you do not care about previous results click No if you wish to save previous results first and then restart the simulation 4 8 START SIMULATION 107 JMT Warning A This operation will overwrite old simulation results Continue anyway After the simulation has started the results window appears with partial values In particular for each performance index and for each station the index has been selected the current number of analyzed samples the current average value and the graph of the latter are constantly updated The graph plots in blue the current average value estimated by the simulator and in red the confidence intervals Confidence intervals appear in the graph when the simulator has gather sufficient samples to compute a reasonably accurate confidence interval note that the number of samples required for the confidence intervals to appear is not constant and depends also on other factors such as the degree of fluctuation of the average value estimate Simulation Arsita ege Length Queue Time Response Time Ubkcabon Throughout Queue Length Average number of customers fo ach chosen clas al aach chosen tation Stati
88. b ID defined Class ID Interarrival time of same class Interarrival time of any class These fields are found in the next section e Logfile Options Browse button allows changing the directory where logfiles are stored Overwrite method to use when the logfile exists and a new simulation needs to overwrite the file Replace overwrites the file append adds data to the end of the file Delimiter chooses the character to separate between e Status displays the path and file status of the logfile that is going to be written As messages flow through the Logger from one station to another the following information can be logged e Logger Name the name of the logger where the message occured e g Logger0 e Job arrival time this timestamp marks the current simulation time from start of simulation not seconds e Job ID the auto generated unique sequence number of the message e g 1 2 3 e Class ID the name of customer class of message e g Class0 e Interarrival time same class is a time difference between customer of the same class that passes through the logger e Interarrival time any class isa time difference between customers of any class that passes through the logger Once a Logger is configured running a simulation produces a logfile with the chosen fields An example of logfile output is LOGGERNAME TIMESTAMP JOBID JOBCLASS TIMEELAPSED_SAMECLASS TIMEELAPSED_ANYCLASS Lo
89. be defined Define What if analysis parameters 9 2 ae What if analysis l l l l Enable what if analysis Define the type of what if analysis to be performed and modify parameter options Parameter selection for the control of repeated executions Arrival rates pType of arrival rate growth 7 Description Repeat the simulation with different arrival rate for all Change arrival rates of all open classes open classes 0 Change the arrival rate of one open class i The To value represents the percentage of the final From 2 Fak arrival rate with respect to the initial value To 26 1505 St A y C a This option will not be available if there is at least one SERBS Uh BE SEE LAA A open class with an interarrival time distribution with infinite or null mean value Class Figure 3 31 The window for What If Analysis definition Activating the What If Analysis After completing the definition of the model and selecting the What If Analysis tab check the Enable what if analysis checkbox to activate it Selecting the What If Analysis After enabling the What If Analysis it is possible to select the parameter to control the sequence of simulation runs using the menu of Figure 3 32 When you select a What If Analysis parameter the bottom section of Parameter selection for the control of repeated executions umber of customers Number of customers Type of populatio
90. ber indicates a lower priority Default value is 0 and it can be changed by double clicking on the corresponding area Defining the Class Type Open Classes After adding a class and possibly changing its name and priority you must choose the type of customers comprising the class Classes are created Closed by default so if you want an Open class select the type Open in the menu The class characteristics looks like this now i Closed Population Arrival Time Distribution D expt Open classes describe customer populations that vary during time therefore they are best characterized by the probability distribution of the interarrival time rather than by a constant number of customers The default Interarrival Time Distribution is exp 1 Exponential Distribution with A 1 To change the Interarrival Time Distribution click the Edit button 84 Arrival Time Distribution A The following window will appear Te Editing Class1 distribution Selected Distribution Erlang Erlang erl a r Fiz iS P t Eulerofunction Cancel CHAPTER 4 JSIMWIZ Click on the Selected Distribution drop down menu to choose from any of the following distributions see section 3 4 Burst General Burst MMPP2 Constant Erlang Exponential Gamma Hyperexponential Normal Pareto Poisson Replayer StudentT Uniform In each case it is possible to configure the distribution parameters as you wish o
91. ber of steps must be specified The initial arrival rate is specified in the Arrival Rate section of the Classes tab and it is not modifiable here If the arrival rate is to be changed for all classes the final value is expressed as a percentage which is applied to all classes Change arrival rates of all open classes O Change the arrival rate of one open class From So To at 1502 Steps n of exec Class The figure above shows the settings for a what if analysis on the arrival rate of all the open classes The To field is seto to 150 which means that for each class the final arrival rate will be one and a half times the initial value 10 runs will be exectued with equally spaced in percentage intermediate values Service time for all types of classes Service Time is the time required by a customer class at each visit at a station In this case besides the final value and the number of runs to be executed the station and the customer class or all the classes whose service time will be varied must be specified From is To s Steps in of exec Station Server 1 Class The figure above shows the settings for a what if analysis of the service time of class Class1 at station Serverl The service time distribution will not change Only its average will be modified to span the range defined by the intial value specified in the Station Parameters tab and the final value specified here in the To fie
92. bs are routed to the station a lass haroct C ype te with the smallest queue Shortest Tate length number of jobs current value Routing Options No options available for this routing strategy Figure 3 85 Edit Loadbalancer properties Define performance indices Performance Indices Define system performance indices to be collected and plotted by the simulation engine Add selected index Performance Index Station Region Confidence Interval Max Relative Error 0 IM System Response Time 0 99 0 05 x System Response Time 0 99 Figure 3 86 Definition of the performance indices Confidence Interval and Max Relative Error 18 CHAPTER 3 JSIMGRAPH EN Define What if analysis parameters What if analysis Enable what if analysis Define the type of what if analysis to be performed and modify parameter options Parameter selection for the control of repeated executions Service times Type of service time growth Description Repeat the simulation with different service times of a a Change service time of all classes i 7 station for the jobs of all the classes Change service time of one class The To value represents the proportion of the final From 7a service time with respect to the initial value To o O Steps n of exec SSCS The all class proportionally option will not be enabled for those stations where at least one of the Station WebServ
93. button on the starting screen Figure 4 1 window shows up Three main areas are shown ea ISM Queue Network Models Simulator File Action Simulation Define 7 iF fr Doh A gt n Y o Reference Stations A Finite Capacity Regions i Simulation what if analysis K Classes Y Stations Connections Station Parameters Performance Indices Classes Characteristics Add Class Define type name and parameters for each customer class Classes Name Type Priority Population Arrival Time Distribution Figure 4 1 The home window of JSIM wiz simulator Menu it is organized into three groups of functions To use a menu click on the menu heading and choose the appropriate option For the description of menu entries see section 2 3 Toolbar contains some buttons to speed up access to JSIM functions e g New model Open Save If you move the mouse pointer over a button a tooltip will be shown up Page Area this is the core of the window All JSIM parameters are grouped in different tabs You can modify only a subset of them by selecting the right tab as will be shown later 4 2 Defining a new model To define a new model select the New command from the File menu or the button or use the shortcut CTRL N A new model is automatically created every time JSIM is started The following parameters must be defined in order to complete the new model e Classes e Stations e Connections e Stati
94. ccess request 195 655E 9 717 968E 14 904 537E 8 716 559E 11 Result status code 124 3595E 7 497 647E 12 904 537E 8 156 254E 8 Bytes transferred 1191 049E 10 Feo 4556 15 16 559E 11 156 254E 8 Figure 6 21 Correlation coefficients of the variables The univariate panel shows also the following two types of graphs e a histogram or frequency graph preview for each variable that can be magnified with a double click on the preview Figure 6 22 e a preview of the QQ plot graph of the variable quantiles compared with the normal distribution quantiles with the same average and variance or the exponential distribution with the same average Also this preview can be magnified with a double click Figure 6 23 Both magnified graphs can be saved in eps Encapsulated PostScript and png Portable Network Graphics formats Transformations and sample extraction The panel of univariate statistics allows also to perform some variables transformations To apply a transforma tion select the variable in the table of Figure 6 20 if it is of a numeric type the panel of Figure 6 24 that allows the selection of the type of transformation logarithmic min max and standard deviation will be shown and press the Apply transformation button It is possible to undo the last transformation by pressing the Undo transformation button The list of the variables with the transformations applied is reported in the table If the selected variable
95. ce issue can accept globally a limited number of customers in concurrent execution 1 e they are allocated in a Finite Capacity Region with the maximum number of customers MaxClients 100 A load balancer split the requests among them according to policies described later TO CHAPTER 3 JSIMGRAPH JSIMgraph Advanced queuing network design tool Editing Users Properties Station Name Station Name Users Users Parameters Definiton Service Section Routing Section J l r Number of Servers Number Service Time Distributions Class i Strategy Service Time Distribution Class0 Load Independent xi exp 0 062 Figure 3 74 The Users properties window The customers are subdivided into two open classes Class0 and Classi the first class access only the Apache server while the customers of the second class visit either the storage or the Apache server according to a probabilistic algorithm All Class0 customers go to the Load Balancer and their interarrival times are hyperex ponentially distributed with parameters p A1 A2 0 291 0 182 0 442 see Figure 3 82 resulting in a mean value equal to 3 2 sec and coefficient of variation equal to 1 192 The interarrival times of Classl customers are exponentially distributed with mean 5 sec In order to model the RAIDO striping algorithm a Fork station is used When a request arrive at the Fork stat
96. cept for fork and sink stations In the routing section for every class defined you may decide how the completed jobs are routed to the other devices connected to station for which the routing strategy is defined Routing Strategies Description Routing Strategy Jobs are routed randomly to one of the stations connected SS to the current one All routes have the same probability to be selected Routing Options No options available For this routing strategy For each class the routing algorithm to be used on the outgoing links of the station is selected from this menu Routing Strategy Shortest Q Length Shortest A Time Least Utilization Fastest Service By clicking an algorithm a brief explanation of the selected algorithm is shown and routing options can be specified where necessary Routing Strategies Description Routing Strategy It is possible to define the routing probability For each gt class connected station IF the sum lin angan of the probabilities is different From 1 all the values will be scaled to sum 1 Routing Options Destination Probability You can choose among the following algorithms NOTE in each of the pictures illustrating the algorithms the blue station implements the routing strategy to the other devices Random with this strategy jobs are routed randomly to one of the stations connected to the routing device The outgoing links are selected with the same probabil
97. ck using the left button of the mouse on the point and additional information will appear after the point s name If the clicked point is a dominated one then it will be possible to see by which point there could be more than one it is dominated 5 2 MODEL DEFINITION 115 Classi Class2 Figure 5 11 Convex Hull Graphic Disk2 Disk 18 53 13 18 Dominating en ak Fa CAU ago 2007 Figure 5 12 Convex Hull Graphic while CPU is selected Determining heavy load throughputs and bottlenecks under a certain workload mix Clicking left button on the line that it connects two bottleneck stations you can obtain information about the saturation sector such as the interval of mix population that make possible the bottleneck and also the throughput of the two classes Disko Class1 46 92 75 75 Class2 50 08 24 25 Class1 0 0303 job sec Class2 0 0379 job sec Figure 5 13 Convex Hull Graphic while saturation sector is selected Move a station to another point Now suppose that we have to analyze the upgrade of the station Station4 the new Station4 will have half demand for both the customer s classes compared to the old one In order to do this we can change the value in the demand s table of JABA or click on the point left button and drag it in the new position While dragging the point temporary co ordinates are shown and when the point is released all data are update and a new graph is created 1
98. class customers can be routed from source stations Setting or changing the properties Double click on the station icon to open the properties panel of Figure 3 40 There is only one section Routing Section Editing SourceO Properties Station Name Station Name Source Source0 Parameters Definiton Routing Section Routing Strategies Description Routing Strategy It is possible to define the routing we probability for each connected station Round Robin o e If the sum of the probabilities is different from 1 all the values will be scaled to sum 1 Routing Options Destination Probability LoadBalancer RAIDO Figure 3 40 Window for the Editing of the properties of a Source station 3 9 DEFINING NETWORK TOPOLOGY 49 Routing Section In the routing section for each class the generated customers are routed to the devices connected to the analyzed station according to various routing strategies The following algorithms are available e Random Customers are routed randomly to one of the stations connected in output to the considered station The outgoing links are selected with the same probability Figure 3 41 illustrates the routing strategy with 3 output links For each link the probability to be selected is 1 3 Input job p2 p1 p2 p3 1 3 Figure 3 41 Routing with Random algorithm e Round Robin Customers are cyclically routed to the outgoing links according to a circular
99. ction of within cluster variance between partitions in k and in k 1 clusters and the ratio of the variance among the clusters and the within cluster variance have been used Large values of the OMSR justify increasing the number of clusters from k to k 1 An optimal partition should also be characterized by values greater than 1 of the ratios of the variances among the clusters and within the clusters for each variable A visual indication of the goodness of a partition is given with the icons D and Y representing good and bad results respectively The values of OMSR and of the ratio are also reported in the table By selecting one of the rows of the table in Figure 6 36 the panel is updated and in the right side a tabs structure concerning the visualization of the results is shown Three main panels are available Figure 6 37 Num of clusters Figure 6 36 Indicators of the goodness of a partition Overall Mean Square Ratio and ratio indices for the K Means algorithm e Clustering Info It shows some statistical information concerning the clusters For each cluster the number of its components and its weight with respect to the total population are reported Pie charts are also used to visualize these data The panel at the bottom shows for each variable the distribution in of its values among the clusters Clustering Info i Cluster Info i Dispersion Matrix Y General information on clustering v Omsr value overall Mean Square
100. d Visits Tabs In the former tab you can insert the Service Times S for each pair station k class c in the model in the latter you can enter the visits number V See Figure 5 8 The layout of these tabs is similar to the one of the Service Demand Tab described in the previous para graph The default value for each element of the Service Times S matrix is zero while it s one for Visits matrix elements 5 2 5 Comment Tab In this Tab a short optional comment about the model can be inserted it will be saved with the other model parameters 5 2 6 Saturaction Sector Graphic Using the Solve command the Saturaction Sector graphic appears 5 2 MODEL DEFINITION 113 Tapa alla File Action Help Dra RAS Saturation Sectors Text Classes Stations Service Times isits Comment Saturation Sectors Graphics 4 i Convex Hull Graphics Visits Classi Class2 Average number of accesses of CPU 1 00 each class to the station Diski 1 00 Disk 1 00 Shation 1 00 Figure 5 8 Visits Tab Two Classes graphic We indicate a certain mix population with the couple N1 N2 where N1 is the percentage of the customers belong to classl and N2 is the percentage of the customers of class2 Because the sum of N1 and N2 must be 100 we will only consider N1 N2 can be calculated subtrahend N1 at 100 In the hypothesis that the number of customers in the system is constant and high it
101. d by double clicking on the c form For example in Figure 3 52 two distributions are defined when there is only one customer in the station the service times are generated according to an Erlang distribution with 92 CHAPTER 3 JSIMGRAPH ne Editing ClassO distribution Selected Distribution Normal Normal norm j c 1 pj Zu Figure 3 51 Editing of the parameters of a distribution np Editing Class0 Load Dependent service strategy FA Edt Help Load Dependent Service Time Distribution Define the distribution and the values of service times for a range of number of jobs inside the station Mean value of the distribution can be specified with an arithmetic expression as a function of the current value of n see Help for operators Ranges From To Distribution Erlang l Figure 3 52 Window for editing a load dependent service strategy mean 1 and c 0 5 For any number of customers greater than 1 in the station the service times are generated according to an Hyperexponential distribution with mean 1 and c 1 19 To delete a range click on the delete icon X at the end of the correspondent row Routing Section In the routing section for every class defined you can decide how the completed jobs are routed to the other devices connected to station for which the routing strategy is defined For each class the user should select the Routing Stra
102. del Solution progress window Es MVA Solutions Graphical Results Textual Results 1 Synopsis Graphical Results Select performance indices to be plotted Left click and drag on the graph to zoom it right click to save it in EPS or PNG format Performance index Residence Times cass m Aggregate Aggregate m A E a Fr _ E nm HEM Station SOS co o W Residence Times 0 2 0 4 0 6 0 8 Population mix Bi for Class Figure 2 18 Model Solution Graphical Results Tab CHAPTER 2 JMVA 2 2 MODEL DEFINITION 13 System Throughput Number of Customers This system indices can be easily obtained by selecting the spe cial Aggregate value for both Class and Station columns of the corresponding center indices see Appendix A for the definition of the performance indices but they were provided here as a shortcut As we are referring to aggregate measures the selection of reference class and station is not significant and in this case the table in the left of Figure 2 18 will not be shown On the bottom left corner of the window users can modify minimum and maximum value of both the horizontal and vertical axes of the plot JMVA is designed to automatically best fit the plot in the window but this controls allow the user to specify a custom range or zoom on the plot Another fast method to perform a zoom operation is to left click and drag a rectangle on the graphic window see Figu
103. distribution A hyperexponential distribution describes a random variable characterized by a variability higher with respect to an exponential one with the same mean It is the result of a weighted sum of two independent exponentially distributed random variables with parameters A and Ag respectively The weight p is the probability that the random variable behaves like the exponential variable with parameter A and 1 p that it behaves like the exponential variable with parameter Aj The probability density function is f z pAje 1 p Ae 4 When this distribution is used to model customer interarrival time or a station service time with probability p Figure 3 17 Generation of the values of an hyperexponential function through two exponential stages in parallel the next interval before a new arrival or the next service time is distributed like the upper server in Figure 3 17 the figure above while with probability 1 p it will be distributed like the lower server A family of hyperexponential density functions is shown in Figure 3 18 Note that when A A2 the hyperexponential reduces to a simple exponential 4 0 1 0 6 0 0 22 6 0 Figure 3 18 Family of hyperexponential density functions Normal norm 0 distribution The Normal distribution is also called Gaussian since its probability density function is the Gaussian function It is well known for its bell shaped density function The two parameters are y
104. ds A large value will make the simulation to proceed slower as the graphs are updated less often Small values will provide an impression of better responsiveness from the simulation as graphs are updated more frequently Animation checkbox is used to enable or disable queue animation during the simulation process Initial state of a simulation The Initial state is the model state at time 0 typically described by the number of customers in each station at the beginning of the simulation For closed customer classes all customers are allocated by default to their reference stations You can 44 CHAPTER 3 JSIMGRAPH modify this allocation as long as the total number of customers remains the one defined in the Classes tab For open customer classes it is possible to initialize each station with any desired number of customers In Figure 3 30 the initial state of a model with four stations and two classes ClosedClass with 3 customers in the CPU station and Class0 with 10 customers in the Users station is shown 3 7 What If Analysis A What If Analysis consists of a series of simulations in which one or more control parameters are varied over a specified range This allows the observation of system behavior under a spectrum of conditions unlike the single simulation run where the system is observed under a fixed set of parameters By default the What If Analysis is not enabled It must be activated explicitly and its parameters should
105. e number of customers the arrival rate can be changed for one specific open class or for all the open classes in the model If the option Change the arrival rate of one open class is selected the final arrival rate and the number of steps must be specified The initial arrival rate is specified in the Arrival Rate section of the Classes tab and it is not modifiable here If the option Change arrival rates for all open classes is selected the final value is expressed as 46 CHAPTER 3 JSIMGRAPH a percentage of increase with respect to the actual value that is applied to the arrival rates of all the classes Figure 3 31 shows the settings for a What If Analysis of the arrival rate of all the open classes The To field is set to 150 which means that for each class the final arrival rate will be 1 5 times greater than the initial value 10 runs will be executed with equally spaced in percentage intermediate values of arrival rates e Service time for all types of classes Service Time is the time required by a customer at each visit of a station In this case besides the final value and the number of runs to be executed the station and the customer s class or all the classes whose service time will be varied must be specified Figure 3 34 shows the settings for a What If Analysis From s To s 0 415 Steps n of exec 103 Station Serverl br Class Class1 y Figure 3
106. e Times and visits Figure 2 42 Example 5 Service Demands Tab 2 4 EXAMPLES 27 Classes Stations Service Demands What if Comment What if analysis Control Parameter Population Mix x Solve models with diferent proportion of jobs between two closed classes keeping constant the total number of oe jobs W Bi Ni Mi It is required that i Mi gt D From B 0 05 Since only integer Ni values are alowed the number of models To Bi 10 95 executed can be very small Class1 Class N job 10 10 Bi 0 5 0 5 Figure 2 43 Example 5 What if Tab value of System Throughput 0 32 job s and the minimum value of System Response Time 62 50 s They both corresponds to the execution with population mix 3 0 40 for Class1 which means that the optimal population values are Ny 8 and No 12 Graphical Results i Textual Results i Synopsis Graphical Results Select performance indices to be plotted Left click and drag on the graph to zoom it right click to save it in EPS or PNG format Performance index System Response Time co oo co nm a cn co System Response Time J a Co cn tmini oos max oss 0102 03 04 05 06 07 08 059 min Ymax Population mix Bi for Class Figure 2 44 Example 5 System Response Time 28 CHAPTER 2 JMVA Graphical Results 1 Textual Results i Synopsis i graphical Results Select performance indices to be plotted Left click and drag on the graph to zoom
107. e any of the stations select the target and press the corresponding X delete button Stations are name Station1 Station2 and so on by default If you want to assign model relevant names left clik on a name to change and replace it Similarly if the default station type Server is not what you need select from the drop down menu of each station the correct type 86 CHAPTER 4 JSIMWIZ station o F LoadSplitter You can choose among the following types of station 1 Delay station Customers that arrive at this station are delayed for the amount of time that defines the station service time They do not experience any queueing since a delay station is modelled as a station with an infinite number of servers with identical service time Because customers never have to wait for service response time at delay stations is equal to service time R S Furthermore the queue length corresponds in this case to the number of jobs receiving service since there is no waiting in queue Q Ri X Si X Uj The utilization of the delay center represents the average number of jobs receiving service i e in think state Delay centers are used when it is necessary to reproduce some known average delay with the selected distribution In the Station Parameters tab menu page you can modify Service Section in this section you can choose the service time distribution for the station For more information see Service sec
108. e parallel topology is derived from number of visits at each station and generated model is equivalent to original one Shortcut on Toolbar Accelerator Key CTRL G 2 3 3 Help JMVA Help Use this command to display application help From the initial window you can jump to step by step instruc tions that show how use JMVA and consult various types of reference information Once you open Help you can click the Content button whenever you want to return to initial help window Shortcut on Toolbar 2 Accelerator Key CTRL Q About Use it in order to display information about JMVA version and credits 2 4 Examples In this section we will describe some examples of model parametrization and solution using MVA exact solver Step by step instructions are provided in five examples 1 A single class closed model with three load independent stations and a delay service center subsec tion 2 4 1 A multiclass open model with two classes and three load independent stations subsection 2 4 2 A single class closed model with a load dependent station and a delay subsection 2 4 3 A multiclass mixed model with three stations subsection 2 4 4 Oo A W N A multiclass closed model where a what if analysis is used to find optimal Population Mix values sub section 2 4 5 2 4 1 Example 1 A model with a single closed class Solve the single class model specified in Figure 2 21 The customer class named ClosedClass has a popula
109. e provided JMCH it applies a simulation technique to solve a single station model with finite M M 1 k or infinite queue M M 1 and shows the underlying Markov Chain It is possible to dynamically change the arrival rate and service time of the system aA JABA for the identification of bottlenecks in multiclass closed product form networks using efficient convex hull algorithms Up to three customer classes are supported It is possible to identify potential bottlenecks corresponding to the different mixes of customer classes in execution Models with thousands of queues can be analyzed efficiently Optimization studies e g throughput maximization minimization of response time identification of the optimal load can be performed through the identification of the saturation sectors i e the mixes of customer classes in execution that saturate more than one resource simultaneously JWAT supports the workload characterization process Some standard formats for input file are provided e g Apache HTTP and IIS log files customized formats may also be specified The imported data can initially be analyzed using descriptive statistical techniques e g means correlations histograms boxplots scatterplots either for univariate or multivariate data Algorithms for data scaling sample extraction outlier filtering k means and fuzzy k means clustering for identifying similarities in the input data are provided These 2 CHAPTER 1 INTRO
110. e time indicates that the amount of time the server spends with each customer depends upon the current number of customers in the station A set of intervals for the number for jobs in the station is specified either by adding one range at a time via the Add Range button or by specifying the total number at once For each range its lower From button value must be specified Automatically its upper value To field is computed Each range of values can be associated with different service times distribution mean and coefficient of variation or a subset of them To set the parameters of a Load Dependent service time click the Edit button to edit the Service Time Distribution The panel of Figure 3 52 appears then specify the parameters for each range For each range of the number of customers the following parameters must be described Distribution you can choose among Burst General Burst MMPP2 Pareto Erlang Exponen tial Hyperexponential Poisson Uniform Constant Gamma and Normal distribution Mean the mean value of each distribution is specified in the Mean form by double clicking on it Insert a number or an arithmetic expression that will be evaluated with JFEP Java Fast Expression Parser For a complete list of the command supported by JFEP you can read the Help tab or see the JFEP web site at http jfep sourceforge net c The coefficient of variation of each distribution when c exists can be specifie
111. ection section 6 2 Input file selection To select the input file use the panel shown in Figure 6 6 The Browse option for the selection of the input file is available Figure 6 6 Once a file has been selected its name is added to the list of the files available for following analyses A panel showing the number of observations loaded and the file name will automatically Input file Load file Figure 6 6 Panel for the selection of the input file appears Figure 6 7 Number of observations 153817 File information File name 16 12 2001 outlogfile txt Figure 6 7 Panel with information about the selected file 6 1 WORKLOAD ANALYSIS 129 Format definition The next operation consists of the definition of the data format The format of the input data is required by the application e to recognize the number of variables that belongs to each observation e to recognize the type string numeric or data of each variable e to the right interpretation of the meaning of each data element that belong to a single observation For the definition of the elements regular expressions Perl5 Section section 6 2 are used The defined formats are stored in a library and can be browsed and reused e to select a subset of the variables of the observations that are in the original input file We will describe a very simple example of the format definition of an observation i e
112. ed with the following algorithm Vo 1 if Dr gt 0 i 0 if Di 0 She Dee if Dke gt O 0 if Dke 0 Service Demands Tab In this tab you can insert directly Service Demands Dj for each pair station k class c in the model In Figure 2 9 a reference screenshot can be seen notice that a value for every Dy element of the D matrix has already been specified because default value assigned to newly created stations is zero In the example of Figure 2 9 each job of type ClosedClass requires an average service demand time of 6 sec to CPU 10 sec to Disk1 8 sec to Disk and 2 5 sec to Station4 On the other hand a job of type OpenClass requires on average 0 1 sec of CPU time 0 3 sec of Disk1 time 0 2 sec of Disk2 time and 0 15 sec of Stations time to be processed by the system If the model contains any load dependent station the behavior of Figure 2 10 will be shown By double clicking on LD Settings button a window will show up and that can be used to insert the values of the service demands for each possible number of customer inside the station That values can be computed by evaluating an analytic function as shown in Figure 2 11 The list of supported operators and more details are reported in subsection 2 2 7 Service Times and Visits Tabs In the former tab you can insert the Service Times Ske for each pair station k class c in the model in the latter you can enter the visits number V e See Figure 2 12
113. een selected together with the following options number of clusters 6 interactions 20 fuzziness level 2 0 144 Maximum 124 600E1 i24 600E1 100 842E10 477 690E5 232 000E1 232 000E1 199 800E2 199 800E2 Minimum 000 000E0 100 837E10 Coeff of w 742 098E 3 163 276E 7 143 6 7E 2 142 211E 2 Variable Variance IP SI3 059E0 144 963E3 100 840E10 271 088E12 Access request 389 184E0 312 667E3 Bytes transferred 241 119E1 117 579E5 330 40E0 164 647E5 559 166E0 342 398E 1 Timestamp 000 000E0 000 000E0 Figure 6 47 Descriptive statistics of the original data after applying variable Access request pa dae Ped LS es ES f EUN 33 Frits SAA N mt CHAPTER 6 JWAT WORKLOAD ANALYZER TOOL Skewness 326 854E 3 351 270E2 628 080E 3 351 270E2 179 578E 2 351 270E2 237 149E 2 351 270E2 Kurbosis slza VEE 125 431E 2 201 294E 2 610 155E 2 466 000E0 100 841E10 141 000E0 100 200E1 the filter on the Bytes transferred Bytes transferred Figure 6 48 Scatters matrix on the data set after applying the filter on the Bytes transferred variable Step 4 Results panel The results concerning the goodness of the partitions obtained with the two clustering algorithms are reported in the following tables Clustering k Means 7 6 X Fuzzy k Mears 4 173 6735E2 SW 151 157E2 238 12 Clustering algorithms k Means Entropy 2 200 614E 3 3
114. efine correctly the regular expression for each variable In the specific of regular expressions in Perl 5 there are some characters that are considered metacharacters Some of them are the same operators defined before In this case to use such characters as elements in the expression is enough to precede them with the character The delimiter identifies one or more characters that delimit the value of a variable In the log file of the Apache format the page URL requested by the user contains characters and spaces and is delimited by A simple definition of the w type regular expression could produce a wrong result because the value recovered by application would finish at the first met space and not at the closure To avoid this problem it is possible to utilize the delimiters so that by using the expression and specifying as delimiter the result will be correct Concerning the Apache log file and more precisely the timestamp field it is possible to show another use of the delimiter The value is contained between characters e e g 12 Dec 2001 00 00 038 0100 and by using the field delimiter it is possible to specify as regular expression the following d d w w w d d d d d d d d d d This expression doesn t specify the last part of the field 0100 but it is correct in any case because specifying the delimiters it is possible to define the regular expression in order to match only a part of the var
115. el 3 11 Error and Warning Messages JSIMgraph analyzes the network before starting the simulation If errors or warnings are found a window reporting the description of the errors like the one of Figure 3 67 is shown Click on an error or warning message to open the panel where you can fix it modifying the wrong parameters or changing the network In the following table the diagnostic messages of the most common errors and the suggested actions to fix them are shown 3 11 ERROR AND WARNING MESSAGES 63 Station X is not forward linked Station X is not backward linked No reference station de fined for Class X Vo performance indices de ned Fork found but no join Join without fork Source X without open classes associated No classes defined A performance index is de fined more than once Closed class Class X routed to a station linked only to sink Undefined station in per formance index No station defined Open class found but no source defined Closed class ClassX at sta tion ServerO is routed to a sink with p 1 Onen classes were but no sink have been de ned Sink without open classes Vore than one sink de fined measures may not be qd Lrate What if analysis model modified unite Capacity Region khe gionX 1s empty Preloading of stations in side a finite capacity region 1s not supported This error occurs when the station source or join
116. el rr 0 970 1 gt 0 7 Samples 4 2 3 K min 100 oJ 6 wm S X max 1505 505 i a O o de 100 105 1 10 145 1 20 125 130 135 140 145 1 50 Ratio beteen assumed serice time at CPU and the initial one ro Simulation results table 100 0 116 67 133 33 150 00 Mean value 1 0 365 0 488 0 607 0 787 Max 3 0 383 0 535 1 663 0 843 Min 1 0 341 0 441 0 552 0 731 The values in red could not be computed wath the requested precision Figure 3 70 Results of a What If Analysis e The first part consists of the names of the index of the station and of the Class the number of samples executed the confidence interval and the maximum relative error and the minimum and maximum values of the index e The second part is represented by a graph with a grid to facilitate the reading and the X and Y axes with their measure unit and scale By default on the graph are plotted the confidence interval range for all the executions with different values of the What if analysis control variable that can disabled through the checkbox e The third part consists of a table showing the results of each simulation run The number of columns of the table corresponds to the number of steps executed When the simulation engine cannot compute the confidence interval or the max relative error with the required probabilities the values are written in red The size of each plot can be magnified double clicking on it
117. en assumed service time atWebServerl and the initial one 9 x10 2 Simulation results table bad 100 00 105 56 11111 116 67 122 22 127 78 133 33 138 89 144 44 150 00 Mean value s 1 066 1 122 1 136 1 194 1 206 1 258 1 259 1 310 1 338 1 380 Max 5 1 112 1 163 1 176 1 235 1 264 1 303 1 319 1 367 1 397 1 434 Min 5 1 021 1 081 1 097 1 153 1147 1 213 1 199 1 253 1 279 1 327 The values in red could not be computed with the requested precision Figure 3 89 Behavior of System Response Time for ClassO customers Description Plot Show confidence interval range Station Name Network Class Name Class1 No o Conf Int Max Rel Err 0 1 0 99 0 05 ystem Response Time s co mm Samples 10 X min wj 51 90 X max 1 88 wo Y min imi 1 80 Y max Mer E e E a a a a E asek ela El An ee aek ee 150 hse Ratio between assumed service time at WWebServer1 and the initial one x1 o Simulation results table ked 100 00 105 56 111 11 116 67 122 22 127 78 133 33 138 89 144 44 150 00 Mean value 5 1 871 1 920 1 952 1 844 1 873 1 899 1 885 1 888 1 878 1 881 Max 5 1 946 1 999 2 035 1 910 1 957 1 967 1 951 1 942 1 944 1 954 Min s 1 795 1 840 1 869 1 778 1 789 1 830 1 819 1 833 1 811 1 808 The values in red could not be computed with the requested precision Figure 3 90 Behavior of System Response Time for Class1 customers 80 CHAPTER 8 JSIMGRAPH Chapter 4 JSIM wiz
118. er applying the filter on the input data are shown respectively Scatter plot matrix of the filtered data are shown in Figure 6 48 Variable Variance Std Dew Coeff of v Minimum Maximum Median Kurtosis Skewness Mum Obs IP 516 05fED 144 58563 Se0 744E0 F7356 B25E 3 OOO 000E0 1 4 80061 124 80061 473 000E0 123 437E 2 312 164E 3 376 140E2 Timestamp 100 840E10 21 2 8El2 164 705E5 163 333E 7 100 837E10 100 8642E10 477 690E5 100 841E10 123 961E 2 2 748E 3 376 140E2 Access request 304 799E0 S12 024E5 S59 506E0 145 35DE 2 OOO 000E0 232 000E 232 000E1 131 000E0 212 949E 2 152 649E 2 376 140E2 Bytes transferred 397 872E1 465 577E5 682 532E1 171 495E 2 OO0 000E0 S398 790E2 S98 790E2 111 100E1 S98 435E 2 255 522E 2 376 140E2 Figure 6 46 Descriptive statistics of the original data before applying the filter on the Bytes transferred variable About 2500 observations have been dropped due to the filtering action reducing considerably the variance Step 3 Clustering panel The k Means algorithm and the variables timestamp and Bytes transferred have been selected in the clustering panel together with the following options number of clusters 7 interactions 50 and transformation Maz Min The clustering results panel is opened automatically Through the Back button we went back to the previous panel to execute a new clustering algorithm The fuzzy k Means algorithm and the variables timestamp and Bytes transferred have b
119. ering requested execution number in the spinner or using the up and down arrows user can cycle between all the computed 14 CHAPTER 2 JMVA performance indices for each execution Just below the spinner a label gives information on the value of the control parameter for the currently selected execution 2 2 10 Modification of a model To modify system parameters return to the main window and enter new data After the modifications if you use Solve command a new window with model result will show You can save this new model with the previous name overwriting the previous one or save it with a different name or in a different directory 2 3 Menu entries 2 3 1 File New Use this command in order to create a new JMVA model Shortcut on Toolbar Accelerator Key CTRL N Open Use this command to open an existing model You can only open one model at time to edit two or more models start more than one instance of JMVA If current model was modified since its creation or last save action a popup window will be shown for confirmation It is possible to open not only models saved with JMVA jmva but also with other programs of the suite for example JABA jaba JSIM jsim and JMODEL jmodel Whenever a data file of another tool is opened a conversion is performed and error warnings occurred during conversion will be reported in a window Models are stored in XML format see JMT system manual for a detailed description
120. erl 3 two following conditions is true there is at least one class with a service time distribution with infinite or null mean value there is at least one load dependent class Class Figure 3 87 Setting the What If Analysis parameters PE EPE Station Name WebServerl Class Name All classes Conf Int Max Rel Err 0 1 0 9 0 1 Samples X min X max hroughput js Show confidence interval range 0 98 1 00 1 02 1 04 1 06 1 08 1 10 112 1 14 116 1 16 1 20 1 22 1 24 1 26 1 28 1 30 1 32 134 1 36 1 38 1 40 1 42 1 44 1 46 1 48 1 50 1 52 x10 Ratio between assumed service time at WebServer1 and the initial one Simulation results table be 100 00 105 56 111 11 116 67 122 22 127 78 133 33 138 89 144 44 150 00 Mean value j s 0 238 0 249 0 252 0 164 0 167 0 177 0 168 0 163 0 163 0 161 Max j s 0 255 0 269 0 270 0 174 0 180 0 188 0 185 0 172 0 173 0 176 Min j s 0 223 0 232 0 236 0 155 0 155 0 168 0 153 0 155 0 154 0 148 The values in red could not be computed with the requested precision Figure 3 88 Throughput of the station WebServer1 for all the classes of customers 2 3 13 EXAMPLES 19 Show confidence interval range Station Name Class Name Conf Int Max Rel Err 0 1 Samples X min X max Y min Y max 0 98 1 00 1 02 1 04 1 06 1 08 110 112 1 14 116 118 120 1 22 1 24 126 128 1 30 132 134 136 138 140 142 144 146 148 1 50 1 52 Ratio betwe
121. ervers provides for equal average response time for all jobs as no job waits in queue for service In this section the load dependent or independent nature of the service time is also specified for each class in server stations Sumber of Servers Mumber Service Time Distributions Load Dependency Service Time Distribution i Classi Load Indepe expli a Class Load Indepe expt The number of servers in a server station can be modified using the corresponding input area Mumber For each class you must specify whether the service time is Load Dependent or Load Independent using this menu Load Dependency oad Independent pe Load Independent Load Dependent A load independent service indicates that regardless of the number of jobs that are in the station the system will serve all jobs following a fixed policy modelled by the chosen statistical distribution For each class the Service Time Distribution is set to Exponential with average equal to 1 It can be modified by clicking the button and inserting all the required parameters from this window 4 2 DEFINING A NEW MODEL 93 ty Editing Class1 distribution Selected Distribution Erlang e Erlang erl a r a r L 0r f x e e P t Eulerofunction Click the drop down menu and choose the service time distribution among the following e Burst General e Burst MMPP2 e Constant
122. ervice Times and visits Figure 2 36 Example 4 Service Demands Tab 24 CHAPTER 2 JMVA DA _ Di ClosedClass 20s 1 A Di OpenGtass DSI _ Da ClosedClass 20s 1 Ax Do OpenClass DS D3 ClosedClass 905 1 A x Ds On nCiass MVA algorithm is used to solve the equivalent closed model The number of customers of the closed class is 57 and the exact MVA technique should require the solution of other 56 models with smaller population In this particular case the formula used to compute the throughput can be simplified because the Service Demands are all equals N X N 3 eq 3 eq eq pga Tra Wr Oe N B N o 3 e 60 20 7 QUN 1 B N 60 20 N 1 X 2 57 0 048305 job s So the throughput measure for the closed class is XClosedClass X 0 048305 job s while the throughput for the open class coincide with its arrival rate XopenClass A AS visits were not specified they have been considered equal to one that s why throughput is equal at each station for each class see Figure 2 37 i e the solved model consists of 3 stations that are sequentially connected with feedback Throughput i Queue length it Residence Times Utilization A Synopsis ii Throughput Throughput for each class at each station 1 048305 1000000 0 048305 Station 1 048305 1000000 0 048305 Station 1 043305 LOOOO00 0 046305 Station 1 048305 1000000 0 048305 Figure 2 37 Example 4 throughput Queue lenghts can
123. es the default value is FCFS and can be changed to LCFS In both cases a priority version of the discipline is also available Service Distribution this parameter applies only to Queueing Stations the default value is Exponential It can be changed to any of the available distributions if most of the devices modelled are non exponential Delay Service Distribution this parameter applies only to Delay stations the default value is Exponential but i can be changed to any of the distributions available Routing Strategy this parameter applies only to Delay Queueing Join and Routing stations the default value is Random and it can be changed to any of the available routing strategies namely Random Round robin Probabilities Join the Shortest Queue Shortest Response time Least utilization and Fastest service Drop Rule this parameter applies only to Fork stations When a finite capacity is defined the default value of the Drop Rule is Drop i e all customers exceeding the station capacity are discarded Two other policies are possible When the capacity is infinite the Drop Rule is disabled by default Fork Capacity this parameter applies only to Fork stations the default value is infinite i e no limit on the number of customers entering a Fork station exists It can be changed to finite by checking the blocking checkbox and a finite number must then be specified Forking Degree this parameter applies only to Fork stations
124. es of customers may have different policies associated with them gt Editing ForkO Properties Station Name Station Name ForkD Fork0 Parameters Definiton Fork Section Qu ue Section Capacity Queue Policy Gass Queue Poly J IC dass0 FCPS w Waiting Queue no dop w Figure 3 56 Window for the editing of the Fork properties e Capacity a station can accept any customer and let them wait in queue in which case its capacity is considered infinite or it can only accept a finite number of customers In this case its capacity is finite the max number of customers is to be specified in the field length Queue policy it is the algorithm used to decide which customer to serve next A variety of factors can contribute to the order in which customers are served such as arrival order priorities associated with a class the amount of service already provided to customers etc In JSIM queuing disciplines based on arrival order and priority are the only available namely FCFS under the First Come First Served queuing discipline customers are served in the order in which they arrive at the station If the model is exported to MVA the following constraint is enforced in the exported model Since all customer classes must have the same average service time at a FCFS station the total number of visits to the station Vz k is adjusted in order to comply with the constraint and at the same
125. est m The resulting 5 il d The number of iit d The referring p s LA ag 5 fal 4 IP Username etc Timestamp Access request Result status code Bytes transferred tring The referring p tring The user agent A ee a a a T Cc yc cu 2 fa 2 2 a e 2 a 4 4 4 4 4 4 KI KI K ElK K amp K KI KI The referring p Click or drag to select classes to edit data single click and start typing Right click For a list of available operations Figure 6 11 Format definition table variables to load Methods for extracting a sample In order to process the data from real log files that usually are constituted by a very large number of observations e g several Gigabytes by a cluster algorithm with a reasonable amount of processing time and storage dimensions the size of the original data set has to be reduced Thus only a sample drawn from the original set of data is often submitted as input to the clustering algorithm After the definition of the data format it is possible through the panel Workload sampling method of Figure 6 12 to select one of the following extraction criteria Workload sampling method Choose sampling method omplete File Le e Mie Random Sampling By interval Figure 6 12 Extraction criteria for the sample construction 6 1 WORKLOAD ANALYSIS 131 e Complete file all the observations of the input file are considered e R
126. evaluated on the stations connected in output to the considered one These strategies can be further combined among themselves through the use of a routing station Other peculiar features of the simulator are e Load dependent service time strategies e Fork and join stations to model parallelism e Simulation of complex traffic pattern and service times e g burst Blocking regions in which the number of customer is limited e What if analysis with various control parameters Customization of default values 29 30 CHAPTER 3 JSIMGRAPH e Import Export of the model from to JMVA the exact solver when the required analytic assumptions are satisfied e Logging of the data flowing in any part of the model Logger station e Graphical visualization of the evaluated performance indices together with their confidence intervals e automatic transient detection and removal e automatic stop of the simulation when all performance metrics can be estimated with the required accu racy JSIMgraph has a modular Java based architecture that allows the introduction of new Java classes in the simulation engine without any modification to the source codes of the other classes 3 2 The home window In the initial window of the JSIMgraph Figure 3 1 all the icons in the toolbar except the first two Create a new model and Open a previously saved model are inactive Choosing Create a new model from the toolbar or New from the File menu bar activates
127. f the MMPP 2 is used as a service process while with probability o9 Ao co without any job arrival or service completion the case of state 1 is similar A MMPP 2 can be parameterized to have a predefined mean c skewness decay rate of the autocorrelation Given these four parameters there are closed form formulas to obtain the corresponding values of oo 01 Ao and A For example the mean is related to the rates of the MMPP 2 by Oo 01 mean TA A001 00A1 while the decay rate of the autocorrelation that controls the burstiness is AoA decay rate lt Ao 1 Ap01 0041 In particular a large decay rate gt 0 9 creates large bursts of arrivals service completions The reader could find additional details on how to fit a MMPP 2 for example in CZS07 and references therein example 1 A 9 A 5 is an exponential distribution for all choices of co and 01 example 2 A9 1 4346 A 0 co 0 0139 0 0 0319 is an hyperexponential with mean 1 c 20 p 0 99 since the hyperexponential has no burstiness here the autocorrelation coefficients are equal to zero 36 CHAPTER 3 JSIMGRAPH example 3 Av 12 Az 0 0879 co 0 0010 c 0 0001 is a MMPP 2 with burstiness The mean is 1 c 20 skewness 7 31 lag 1 autocorrelation coefficient is 0 4745 Since for a MMPP 2 the autocorrelation is always less than 0 5 this is an example of a process with very large burstiness T
128. fault values Such values can be change to suit the user s most common modelling activities Defaults can be modified for the following sections e Class Parameters e Station Parameters e Simulation Parameters e Finite Capacity Region FCR Parameters Class Parameters These settings define the default class parameters used when a new class is created For detailed information about classes see subsection 4 2 1 Class parameters Mame Class Type Closed Priority Population closed classes Distribution open classes Exponential le ib Name the default name for each newly created class of customers is Class followed by a progressive integer starting from 1 indicating how many classes you have created so far It can be reset to any alphanumerical string which will be followed by the same numbering scheme Type the default class type is Closed If open classes are used more often you may want to change to Open as default so as to minimize the type changes in the class definition section Priority the default class priority is 0 Higher numbers correspond to higher priority Population this parameter applies only to closed classes the default value is 1 i e all closed classes are created with 1 customer in each of them Change the value if you want larger populations by default in each closed class Distribution this parameter applies only to jemjopen classes the default value is Exponential si
129. for any type of station see Figure 3 64 Station parameters Name Station Type Server y Queue Capacity Infinite Number of Servers o 1 Queue Strategy FCFS PA v Service Distribution Exponential v Delay Service Distribution Exponential nd Routing Strategy oT a OS J Fork Capacity v Infinite Drop Rule O Fork degree 1 a Figure 3 64 Station parameters modification window Name the default name of each newly created station is Station followed by a progressive integer starting from 1 indicating how many classes you have created so far It can be set to any alphanumerical string which will be followed by the same numbering scheme Type the default station type is Queueing sometimes referred to as Server since this is the most popular type of station in performance models Alternative types are Fork Join Routing Delay Logger Queue Capacity this parameter applies only to Queueing and Fork station types the default value is infinite i e an infinite number of customers can queue at such stations It can be set to finite with a finite value specified by checking out the Infinite checkbox Number of Servers this parameter applies only to Queueing stations the default value is 1 as most devices are single server It can be changed to any finite value Queue Strategy this parameter applies only to Queue and Fork station typ
130. fork station A job is removed from the queue and serviced i e split into tasks when a job is recomposed at the matching join station and leaves it Capacity is defined using the form below after checking the Finite capacity box nable Finite Capacity limit maximum number of jobs inside a Fork join section Capacity max number of jobs NOT tasks Queue section How to Define the Queue Strategy The Queue section is part of the Station Parameters definition page it is present only for server and fork stations The Queue section allows the specification of the queueing capacity whether finite or infinite and policy Different classes may have different policies associated with them Capacity Queue Policy 8 infinite i Finite length Capacity a station can accept any customer and let them wait in queue in which case its capacity is considered infinite or it can only accept a finite number of customers In this case its capacity is finite with a length to be specified in the form Pret afz Queue policy it is the algorithm used to decide which customer to serve next A variety of factors can contribute to the order in which customers are served such as arrival order priorities associated with a class the amount of service already provided to customers etc In JSIM queueing disciplines based on arrival order and priority are the only available namely FCFS under the First Come First Served queueing discip
131. formance indices The following list include the performance indices that can be obtained from a simulation run Queue Length of a station number of customers N at a station both waiting and receiving service Queue Time of a station average time spent by the customers waiting in a station queue It does not include the Service Time Residence Time of a station total time spent at a station by a customer both queueing and receiving service considering all the visits at the station performed during its complete execution Response Time of a station average time spent in a station by a customer for a single visit sum of Queue time and Service time Utilization of a station percentage of time a station is used i e busy evaluated over all the simulation run It ranges from 0 0 when the station is always idle to a maximum of 1 100 when the station is constantly busy servicing customers for the entire simulation run Queueing stations may have more than one server their number is a parameter to be specified default is 1 It is important to point out that the utilization U of a queueing station with a single server is given by U AS and in a station with mservers the utilization of any individual server is given by U AS m In delay stations for consistency with Little s law the utilization is computed as the average number of customers in the station and thus it may be greater than 1 Throughput of a sta
132. g the default value to 10 all classes are represented in most models Graph animation is enabled by default but can be disabled Finite Capacity Region FCR Parameters These parameters define the default values for newly cre ated Finite Capacity regions For information about Finite Capacity Regions see subsection 4 2 1 Name the default name of each newly created Finite Capacity Region is FCRegion followed by a progressive integer starting from 1 indicating how many classes you have created so far It can be reset to any alphanu merical string which will be followed by the same numbering scheme Global Region Capacity the default value of this parameter is infinite i e there is no upper limit to the total number of customers allowed in the region the value can be changed to finite and a number must be specified Region Capacity per Class the default value of this parameter is infinite i e there is no upper limit to the per class total number of customers allowed in the region the value can be changed to finite and a number must be specified Drop the default value of this parameter is False i e no customer is ever discarded when arriving at the region it can be changed to True in which case customers in excess of the region capacity are discarded 4 5 Modify the Current Model After creating a model and possibly running a simulation you can go back to the model and modify it To modify the current model para
133. gger0 0 199 1 Class0 0 000 0 199 Logger0 0 559 2 Class0 0 341 0 341 Routing Section For each class of customers the user should select the algorithm that want to apply in order to determine the outgoing connection i e the routing strategy followed by a customer that completed its service in the current station The following algorithms are available Random Round Robin Probabilities Join the Shortest Queue JSQ Shortest Response Time Least Utilization Fastest Service To know details about these algorithms please refer to the Routing Section of subsection 3 9 1 Source Station 3 10 Modification of the Parameters 3 10 1 Modifying Simulation Parameters To modify the simulation or initial state parameters the user has to select Simulation Parameters icon 2 from the Define menu and change the values From Simulation Parameters the user can change the Initial state i e the location of the customers at the beginning of the simulation change or confirm the seed of the random number algorithm in order to have different run of the simulation Change the maximum number of samples change the time interval used in the graphical representation of the indices oF W N e change or confirm the maximum duration of the simulation For more details about these parameters see the Section Simulation Parameters of subsection 3 10 3 3 10 MODIFICATION OF THE PARAMETERS 99 3 10 2 Modifying station para
134. h Number of customers at a station both waiting and receiving service Queue Time Average time spent by the customers waiting in a station queue It does not include the Service Time Residence Time Total time spent at a station by a customer both queueing and receiving service considering all the visits at the station Response Time Average time spent in a station by a customer for a single request it is the sum of Queueing time and Service time System Response Time Average time a customer spends in the system in order to receive service from the various stations it visits It corresponds to the intuitive notion of response time as the interval between the submission of a request and the reception of the response Utilization Percentage of time a resource is used w r t the system lifetime it varies from 0 0 when the station is always idle to a maximum of 1 100 when the station is constantly busy serving customers for the entire system lifetime Utilization may be greater than 1 if a station has more than one server Throughput Rate at which customers departs from a station 1 e the number of services completed in a time unit System Throughput Rate at which customers departs from the system Customer Number Average number of customers in the system If the index is associated with a closed class then it is equal to the number of customers in the class Each index is associated with a class and a station and will be computed
135. h two large disks arrays The user requirements are homogeneous and the workload generated may be considered as a single class The layout of the digital infrastructure is shown in Figure 3 71 The customer class referred to as ClosedClass has a population of N 3 customers There are four stations CPU Disk1 and Disk2 three Figure 3 71 The system of Example 1 are of queueing type load independent and one is of delay type Users Users delay station represents user s think time Z 16s between interaction with the system Service times distributed exponentially and the visits at the stations are reported in Table 3 1 Drawing the graph e Select File gt New or click on the icon from the first toolbar hb e Insert a Queueing station in the drawing window by at first clicking the icon and then clicking on the drawing window Perform this task 3 times in order to add 3 stations e Double click on a Queueing station You will find a textbox to modify Station Name By clicking each of the queueing stations rename Station Names as CPU Disk1 and Disk2 e Insert a Delay Station by selecting the E icon from the toolbar Double click on it and rename the Station Name as Users e By selecting the y icon connect the queueing stations and the delay station as given in the problem The graph should look like Figure 3 72 Now we have to describe the values of the parameters Defining customer class e Select Define gt
136. has not outgoing or mate system throughput and response time Click on this error to open and set the missing reference station mance index is defined l l together in the model have inserted only one of the two stations when the simulation is run JSIM will show a diagnostic message Having a Fork without a Join is possible although it may lead the system to saturate quickly Having a Join without a Fork is a mistake hence the Error message The missing station must be added with the corresponding links a source only if you have an open class you have only a closed class the source cannot be defined But if you have open and closed classes you have to define a Source and a Sink in the network This error appears when you have built a model with a source but without open customer classes e definition of at least one class of customers 1s required in order to solve a model Customer classes are a mandatory parameter of any Error Error Warning Error Error Error definition of the model output the same index has been addec Error more than once for the same station and class Multiple occurrences not visit a Sink station or a station that is connected on the outgoing link only to the Sink since this would cause them to leave the system The station connections must be changed When a new performance index is defined a connected station should Error Error also be selected Click on Performa
137. hat if analysis Define the type of what if analysis to be performed and modify parameter options Parameter selection for the control of repeated executions r Number of customers v Type of population growth Description Repeat the simulation with different number of jobs in each iteration starting from the current number of jobs in the closed class and increasing the number of jobs of selected class only e Increase number of jobs of one closed class From N To N m ksal La iel eh Steps n of exec Class ClosedClass_ Population mix ye ClosedClass _Ni_ 10 Bi 1 00 Figure 3 33 Selection of the Type of population growth in a What If Analysis The option Increase number of jobs of one closed class has been selected The initial value of the number of customers is not modifiable from this window as it is part of the Classes tab The final value should be specified in the field To N In this case with a final value of 20 and 6 Steps simulations are run for 10 12 14 16 18 and 20 customers respectively Only the customer number in the class selected in the Class ClosedClass in the picture will be changed The remaining classes if they are present will keep their initial number of customers The simulator control that the sum of the percentages of jobs of the various classes represented by the components PB of vector 3 e
138. he following Add a routing station Y among Z s output stations and define random routing for the three of them A B Y Then connect Y to C and D and define Join the Shortest Queue routing to C and D In the Station Parameters tab menu page you can modify Routing Section in this section you can specify how serviced customers should be routed to the next station they will visit in the model For more information see Routing section section 4 2 2 1 6 Source station 51 If the model comprises at least an open class a sink and a source stations are created by default as they are necessary for the simulation and cannot be removed Name Type Source Ei Source Sink Sink Open classes are characterized by an infinite stream of jobs that can enter the system Source stations are used to introduce jobs in the model Their service time is the interarrival time of each customer class and as such it is defined as a parameter of the class the job belongs to The routing strategy defines the first station a newly created job will visit Only open class jobs can be routed from source stations In the Station Parameters tab menu page you can modify Routing Section in this section you can specify how newly created customers should be routed to the next station they will visit in the model For more information see Routing section section 4 2 2 7 Sink Station Open class customers leave the system once they have received all the service
139. he help Suggestions concerning the single tab in the application are also available by using the Help button in the buttons bar of application Shortcut on Toolbar 2 Accelerator Key CTRL Q About Use this command to visualize information concerning JWAT application 6 2 FORMAT DEFINITION 147 6 2 Format definition In this section we will describe the format definition of the file in input to the application We will introduce the basic concepts on which the format specific is based and then we will describe some examples with different files The application allows by using regular expression to utilize as input either log files of standard formats as Apache and IIS or log files modified by the user The only important requirement on the input file structure is that every observation i e the set of the variables that refer to one element item considered must end with n character new line To allow the application to be able to process correctly a log file the user must describe e the observation structure that is the number of variables that compose it e and for each variable the name the type and the structure These information are specified by the user through the input panel described in section 6 1 2 Regarding the number of variables it is enough to insert in the format table a number of rows equal to the number of elements that compose the observation see section 6 1 2 In Figure 6 51 t
140. he observation is composed of 6 variables Comment Perl5 Reg Exp d 0 Jd 0 0 d d 0 d 2 d 0 d id d 04 d Figure 6 51 Format table after the insertion of the number of variables The definition of the single variable requires in addition to the name a comment its selection in order to be considered in the analysis or not its type the description of the possible delimiter Separator and of the regular expression that characterizes it The type has to be chosen among the numeric string o data The delimiter defines if it exists the character or the characters that delimit the variable s value The regular expression Perl 5 defines the format with which the variable value is recorded in the log file A concise description of the format used for the regular expressions Perl 5 follows The purpose of the definition of the regular expression is to specify the pattern that the variable values must have and therefore together with selected type to allow the application to process correctly its value For a complete description of the regular expressions see a Mastering regular expressions book In this section we will describe some options useful to define in a simple way the pattern of the variables values A list of operators follows it indicates that there are one or more instances of the preceding character a gt a aa aaa it defines a pattern that allows to
141. heckmark sign see e g Figure 3 68 In case of errors or of early termination the sign indicates that the results obtained are not within the requested confidence interval In case of a syntactically correct network with some connections that make no sense from a modelling point of view e g a station that is never visited by any customer a question mark indicates that the simulator could not compute the index for lack of measurements 3 12 RESULTS OF SIMULATION 65 Simulation Results Queue Length Average number of customers for each chosen class at each chosen station Station Name cl Class Name All Conf Int Max Rel Err 0 9 0 1 Analyzed samples 163840 Min 0 0818 Max Average value 0 0888 A dd ii ii interval red lines and the requested maximum relative error Station Name Diski Class Name All ConfInt Max Rel Err 0 9 0 1 Analyzed samples 163840 Min 0 3754 Max 1 Average value 0 4109 Abort Measure A dd REE ES SSEREL RETR SEP ENTE ee Ver siewe sie interval red lines and the requested maximum relative error Figure 3 68 Results of a single simulation run Values are available for the following parameters e Station Name This is the name of the station for which the index is computed e Class Name This is the name of the class for which the index is computed at the station it could be All
142. hroughput for each class at each station 0 143961 0 143961 CPU 14 540104 14 540104 Diski Bodf6s6 8 697656 Disk o E Users 0 143961 0 143961 Figure 2 26 Example 1 output data Throughput Tab Since we are considering a single class model all results in the column Aggregate correspond to the results in the ClosedClass column JMVA computes Residence Times Wg Throughputs Xy Queue lengths QQ and Utilizations Uz for all stations The algorithm begins with the known solution for the network with zero customers and iterates on N that in this example is three Note that the aggregate Residence Time is the System Response Time measure and the aggregate Queue Length is the average number of customers in the system Using tab selector you can change tab and see Queue length Residence Times Utilizations and a synopsis panel with a schematic report of the model Figure 2 27 The computed performance indices are shown in Table 2 4 Aggregate CPU Disk1 Disk2 Users Throughput job s Queue Length job Residence Time s Utilization Table 2 4 Example 1 model outputs 2 4 EXAMPLES 19 Throughput Queue length Residence Times Utilization Synopsis A MVA Model Details Classes Name Type Population Arrival Rate ClosedClass clased 3 stations CPU Load Independent Disk1 Load Independent Disk Load Independent Lisers Delay Infinite Server Service Demands ClosedClass Figure 2
143. iable value 6 2 1 Example of a format definition Let s consider a file to be analyzed with the following structure of the observations String without spaces 1000 0 0876 12 668 String with spaces 12 Dec 2001 00 00 03 0100 The variables are 6 and their definition Figure 6 52 is the following String without spaces we can define the regular expression in different ways as for example a zA Z if the string doesn t contain numbers or w to indicate whichever string of numbers and characters Integer number we define the regular expression as a sequence of one or more numbers and therefore as d Positive decimal in this case there is the possibility to have decimal digits so that we define the regular expression as a sequence of one or more digits d that may have the decimal separator and a further succession of one or more digits The result is therefore d d Decimal with sign in this case in comparison to the previous case there is the possibility that at the beginning of the number there is a sign or no sign Therefore it is enough to add at the beginning of the regular expression String with spaces if we utilize the regular expression previously defined w we would have a problem because the value recovered from the log file would be String that is not correct The best solution is to utilize the delimiter in this case and to utilize therefore the definit
144. ibed either probabilistically or according to the following strategies Fastest service Least utilization Random Round robin Join the Shortest Queue Shortest response time the values of the control parameters are evaluated on the stations connected in output to the considered one These strategies can be further combined among themselves through the use of a routing station Other peculiar features of the simulator are e Load dependent service time strategies Sl 82 CHAPTER 4 JSIMWIZ e Fork and join stations to model parallelism e Simulation of complex traffic pattern and service times e g burst e Blocking regions in which the number of customer is limited e What if analysis with various control parameters e Customization of default values e Import Export of the model from to JMVA the exact solver when the required analytic assumptions are satisfied e Logging of the job flows in any part of the model Logger station e Graphical visualization of the evaluated performance indices together with their confidence intervals e automatic transient detection and removal e automatic stop of the simulation when all performance metrics can be estimated with the required accu racy JSIMwiz has a modular Java based architecture that allows the introduction of new Java classes in the simu lation engine without any modification to the source codes of the other classes 4 1 1 Starting the discrete event simulator Selecting
145. ice demands or service times of a load dependent station It allows to specify times as an analytic function of n where n is the number of customer inside the station Expression are evaluated using JFEP Java Fast Expression Parser package which supports all operators enumerated in Table 2 1 and all functions enumerated in Table 2 2 Operator Power Unary Plus Unary Minus Modulus Division Multiplication Addition Subtraction Function Sine Cosine Tangent Arc Sine Arc Cosine Arc Tangent Hyperbolic Sine Hyperbolic Cosine Hyperbolic Tangent Inverse Hyperbolic Sine Inverse Hyperbolic Cosine Inverse Hyperbolic Tangent Natural Logarithm Logarithm base 10 Absolute Value Magnitude Random number 0 1 Square Root Sum Table 2 2 List of supported functions for the load dependent service times 2 2 8 Model Solution Use Solve command to solve the model If the model specifies a what if analysis please refer to subsection 2 2 9 Model results will be shown on a separate window like the one of Figure 2 15 3http jfep sourceforge net 2 2 MODEL DEFINITION 11 a MVA Solutions Throughpu ii Queue length i Residence Times Y Utilization i Synopsis i Throughput Throughput for each class and each station Aggregate ClosedClass OpenClass Class3 3 146376 0 003494 3 140000 0 002882 CPU 3 146376 0 003494 3 140000 0 002882 Disk 1 3 146376 0 003494 3 140000 0 002882 Disk 3 146376 0 003494 3 14000
146. idtilh d ee Cider diddi did did Figure 6 8 Format table Comment Perl5 Reg Exp IP Address YAH tdt dti d Only relevant IF Username etc String Timestamp Time stamp of The request m Access request String Result status code Numeric Bytes transferred Mumeric e Referrer URL 1 Figure 6 le al al Ea al al ix Deletion of selected variables Once the correct number of variables in a observation is defined the next step is their description The columns of the format table have the following meaning e Name as default to each new added variable it is assigned the standard name Variable X In order to facilitate the analysis of the results it is recommended to change these names with new ones related with the meaning of the variables e Type it identifies the type of the variable Possible choices are number string and data The type definition is fundamental for the right interpretation of the results 130 CHAPTER 6 JWAT WORKLOAD ANALYZER TOOL e Selection it allows to specify which of the variables of the observations registered in the input file will be effectively loaded In any case it is necessary to define all the variables of each observation also if some of them will not be selected for the statistical analysis e Comment it is allowed to add a string of comment to each variable e Delimiter Sep it identifies the character used if it exists in the inpu
147. ing that has to be contained in the selected observations Sampling options Minimum value Maximum value 15 664 Do Sampling Undo Sampling Figure 6 27 Filter on the values of a numeric variable Sampling options From date 15 12 2001 00 00 04 To date 15 12 2001 00 00 31 Do Sampling Undo Sampling Figure 6 28 Filter on the values of a data variable The operation of Undo sampling is available Graphs The last two panels of the statistics tab concern a preview of QQ plot graphs and of scatter plots for all the variables respectively Both allow to save graphs in the most common formats png eps Previews can be magnified with a left double click of the mouse Several functions are available for the graphs portions zoom points dimension by clicking the right button of the mouse on a graph various formats are available for export the graph as image 6 1 4 Clustering algorithms The next step of the characterization process is the choice of the clustering algorithm to be used ad of the options available Two clustering algorithms are actually implemented in the tool k Means and Fuzzy k Means see Figure 6 31 Depending on the selected algorithm in the right panel of tab the available options are listed The execution of a clustering algorithm will start when the buttons Solve or are pressed During the execution the window of
148. initon Routing Section i Routing Strategies Description Routing Strategy Jobs are routed randomly to ENE one of the stations connected to the current Class2 one All routes have the same probability to be selected 2 Stations Routing Options 1 Mo options available For this routing strategy Example with a server station Server a station with multiple parameters type Ej Source Sink Stationi sub tabs menu parameters pages Station Paramet Queue Section Service Section i Routing Section 4 Capacity Queue Policy ig infinite 2 Station a Class FCFS i i Finite length NOTE You can find detailed information about station parameters subsection 4 2 2 4 2 5 Define Performance Indices Performance Indices are selected using the Performance Indices tab 96 CHAPTER 4 JSIMWIZ La JSIM Queue Network Models Simulator Fille Action Simulation Define 7 he E Pn Q y 2 Reference Stations Finite Capacity Regions Simulation what if analysis Classes Stations Connections Station Parameters Performance Indices Performance Indices Define system performance indices ta be collected and plotted by the simulation engine lt Back Next Solve Cancel Help You can choose any subset of indices from the list below to be plotted as the model output Queue Lengt
149. into stations number textbox or select number 4 using spin controls or push New Station button three times Now your model has four Load Independent stations with a default name e if you want you can change station names Substitute CPU for default name Station1 substitute Disk for default name Station2 substitute Disk2 for default name Station3 and substitute Users for default name Stations e change the type of last inserted station Users station is a Delay Infinite Server At the end of this step the Stations Tab should look like Figure 2 23 Step 3 Service Times and Visits Tabs e use Next gt command to switch to Service Demands Tab e press Service Time and Visit button as you don t know the Service Demands of the three stations in this case Service Times and number of Visits should be typed After button pressure the Service Demands Tab will be hidden and Service times Tab and Visit Tab will appear e you can input all Service Times in the table Remember that Service Time of the Users station of delay type is think time Z in this case 16 s At this point the Service Times Tab should look like Figure 2 24 2 4 EXAMPLES 17 Classes Stations Service Demands Comment i Stations characteristics Rumaa E Number customized name and type of stations ou can add stations one by one or define total number at once New Station Load Independent Load Independent Load Independent Delay Infinite Server Figure
150. ion Date even in this case by using the delimiter we can define the following regular expression d d w w w d d d d d d d d d d that may be used to recover the only information 12 Dec 2001 00 00 03 leaving out the remaining part Comment Perl5 Reg Exp Walt 1d rdt d d 0 Md 2 Cuts ide orhwiuaftdydichdshayds dd i PA btringa senza spazi umera intero umero Reale Reale con segno Gtringa con spazi Figure 6 52 Example of the definition of a file format 6 2 FORMAT DEFINITION 149 6 2 2 Example of the definition of the Apache log Now we will describe the format of the Apache log Each observation has the following structure 151 29 12 105 12 Dec 2001 00 00 10 0100 GET mappe HTTP 1 1 200 318 www polimi it http www polimi it Mozilla 4 0 compatible MSIE 5 0 Windows 98 DigExt A brief explanation of the regular expressions used Figure 6 53 follows 1 these last three strings are all delimited by the character for the Ip address of the request we define a sequence of one or more digits separated by a point and therefore the regular expression is d d d d in most cases no value is set and therefore it is possible to define exactly the string that we want to recover from the file through it is advisable not to select this variable at the moment of loading for the date we use the same definition desc
151. ion RAIDO it is splitted in three requests sent in parallel to all the disks of the storage server Fork degree at RAIDO station is 3 that is for each incoming request three requests are generated in each outgoing link Service times for all the disks Disk1 Disk2 and Disk3 are 5 for ClassO and 0 5 for Class1 customers respectively An FCR is used in order to model the Apache server which contains two web servers Web Server 1 and Web Server 2 that accept a maximum number of requests equal to 100 The load balancer station in this FCR split the load among the two web servers with the following algorithms ClassO customers with Join the Shortest Queue and Class1 customers with Shortest Response Time The service times for both Web Servers are 1 sec for Queue length Residence time Utilization Throughput it ea 0 080 0 076 0 096 0 089 0 088 0 082 2 157 2 157 2 463 2 463 2 310 2 310 0 373 0 276 0 434 0 318 0 297 0 159 0 185 0 172 Table 3 2 The results of the simulation at the stations level 3 13 EXAMPLES 71 JSiMgraph Advanced queuing network design tool Editing CPU Properties Station Name CPU Parameters Definiton Queue Section Service Section y Routing Section Routing Strategies Description Routing Strategy Itis possible to define the routing probability for each connected station If the sum of the probabilities is different from 1 all the values will be scaled to sum 1
152. ion where A gt 0 is the distribution parameter often called the rate parameter the distribution is defined in the interval 0 00 The probability density function is je r 2 gt 0 fa 4 4 x lt 0 3 4 DISTRIBUTIONS 37 0 2 4 6 8 10 12 14 16 Figure 3 14 A family of Erlang distributions with different values of the parameters a r The exponential distribution is used to model Poisson processes The time interval between two consecutive events generated by a Poisson process can be described by an exponential random variable with parameter A The parameter A is a real number the mean value is given by 1 A the variance is given by 1 A A family of exponential density functions with different values of A is shown in Figure 3 15 0 2 3 4 5 6 Figure 3 15 Exponential density functions with different mean 1 A values Gamma gam a A distribution The Gamma is a continuous probability distribution with two parameters the shape a and the scale A both real numbers The probability density function is a 1 fe Taye oo where T t is the Eulero function When the Gamma distribution is selected the user can either provide a and A or the distribution mean equal to aX and the variance aA A family of probability density functions is shown in Figure 3 16 for a set of and A values Figure 3 16 Gamma density functions for different values of a and A 38 CHAPTER 3 JSIMGRAPH Hyperexponential hyp p A1 A2
153. ion1 Station2 StationN In order to personalize your model you can change and give names other than default ones In Figure 5 6 there is only one station with default name Station4 and there are three stations with person alized names CPU Disk1 and Disk2 dl JABA E leg File Action Help Nba gt SU ai gt Saturation Sectors Text Classes Stations Service Demands Comment Saturation Sectors Graphics E Convex Hull Graphics Stations characteristics namber na Number customized name and type of stations You can add stations one by one or define total number at once New Station 4 Station lt Back Mext gt Solve Exit Help Figure 5 6 Defining the stations name 5 2 4 Service Demands Service Times and Visits Tabs Service Demands can be defined in two ways e directly by entering Service Demands Dy 112 CHAPTER 5 JABA ASYMPTOTIC BOUND ANALYSIS e indirectly by entering Service Times Ske and Visits Vic Service demand Dj is the total service requirement that is the average amount of time that a customer of class c spends in service at station k during one interaction with the system i e it s complete execution Service time Sy is the average time spent by a customer of class c at station k for a single visit at that station while V is the average number of visits at that resource for each interaction with the system Remember
154. ions to include in the region with the mouse left click with the mouse and hold it pressed until all the elements are included The selected stations are framed with green dashed lines as shown in Figure 3 36 3 9 DEFINING NETWORK TOPOLOGY A7 OA AAA SM Figure 3 36 Selection of the stations to be included in a FCR 2 Select the icon MA and the Finite Capacity Region will appear with a blue background see Figure 3 37 3 Double click on FCRegion to set the properties The properties panel will appear Figure 3 38 FCRegionO i I T Editing FCRegionO Properties Global FCRegion0 Properties Region name FCRegion Region capacity Class specific FCRegionO Properties Class Capacity co az ClassO as Classi Figure 3 38 Window for the definition of the FCRegion properties Global Properties Region Name the name of the region created Region Capacity max number of customers that can be in the region Enable Infinite if you don t want a bound Class Specific Properties In the bottom part of the panel the class specific properties can be defined Here you can define each class capacity as infinite or as defined in same way stated above for FCR capacity and choose the dropping property of the class Capacity maximum number of customers of that class into the FCR Drop when the FCR is busy and Drop is false the incoming jobs are not dropped but are put into a temporary queue until the FCR can accept
155. is not numeric the following message is shown This variable could not be transformed since it is not numeric To extract a sample from the original input file press on tab Sample construction The panel of Figure 6 25 shows the possible criteria that can be applied to the loaded variables that depends on the selected method and on the type of the variables e Random and Obsev interval methods are similar to those available in input window and allow to select randomly n observations from the input file or to extract the observations whose numerical identifiers are included into the interval defined by the user 134 CHAPTER 6 JWAT WORKLOAD ANALYZER TOOL x10 2 2 2 0 1 8 r 1 6 1 4 u 1 2 1 0 c 0 8 0 6 s 0 4 0 2 0 0 00 05 10 15 20 25 30 35 4 0 Variable Bytes transferred x1 o Figure 6 22 Histogram or frequency graph of the variable Bytes transferred Graphs Frequencies G0 Plot i Double click to enlarge this graph Normal distribution Actual quantile distribution versus normal or exponential Figure 6 23 QQ plot preview for the comparison of a given distribution with an exponential or a normal ones Apply to Result status code Type Numeric Transformations Mix Max Standard Deviation Apply transformation Undo transformation Transformations applied to variable Result status code Logi SD xy Figure 6 24 Selection of the transformation to apply to the origi
156. is possible to find an interval N1 to N1 where the same two stations are bottleneck We define this interval saturation sector and its extremity switching points that are the value in with the station change from non bottleneck to bottleneck or viceversa It is possible to represent a saturation sector and the switching points using a bidimentional graphic Fig ure 5 9 oa eT i lassa 1 000 Disk 4 501 A a m aS Disk Disk2 0 243 rerrrrconnananannnnnn nana pare i Disk Ran 0 499 i 1 000 Classi 0 000 0 757 Figure 5 9 Saturation Sector Graphic In this example we can observe that Disk1 is a bottleneck for a mix population among 0 1 and 0 499 0 501 At the point 0 499 0 501 color switches from green to blue because this point is a switching point In fact for a mix population from 0 499 0 501 to 0 757 0 243 Disk1 and Disk2 are both bottleneck After the point 0 757 0 243 that is a swiching point too only Disk2 is a bottleneck Three Classes graphic Suppose we can split the customers of our system in 3 class of customers a specific population mix could be represented by a point whose coordinates are the percentage of customers of a specific class on a triangle that has the vertex in the points 1 0 0 0 1 0 e 0 0 1 The triangle area represent every possible population mix So we can divide the triangle in different sub areas and each area rapresent a population mix range where one two or more statio
157. ite checkbox and set Region Capacity as 100 Click Done From the menu bar choose Define gt Customer Classes Add two open customer classes Class0 and Class1 Class0 is hyperexponentially distributed with p A1 A2 0 291 0 182 0 442 Class1 is exponentially distributed with mean value 5 Double click on Requests Set routing strategy for both Class0 and Classi as Probabilities Since all Class0 customers go to the LoadBalancer set Probability of the LoadBalancer as 1 Whereas since the ClassO customers may go either to the LoadBalancer or to the RAIDO station set the Probability 12 CHAPTER 3 JSIMGRAPH 0 a E JSIMgraph Advanced queuing network design tool n File Editing Disk1 Properties k Station Name A Station Name Diski Diski Parameters Definiton Queue Section 1 Service Section i Routing Section Routing Strategies Description Class Routing Strategy It is possible to define the E a routing probability for each connected station If the sum of the probabilities is different from 1 all the values will be scaled to sum 1 Routing Options Destination Probability Figure 3 76 Setting the routing probabilities or the visits in output of Disk1 station of both LoadBalancer and RAIDO as 0 5 Then Click on Done see Figure 3 83 e Double click on RAIDO and set Fork degree at 3 see Figure 3 84 e Double click on the disks the
158. ity The figure illustrates the routing strategy with 3 output links For each link the probability to be selected is 1 3 4 2 DEFINING A NEW MODEL 91 Input job pl p2 p3 1 3 Round Robin with this algorithm jobs are cyclically routed to the outgoing links according to a circular routing As the figure shows the first job is sent to the top station the second job is sent to the central station and the third job is sent to the bottom station The next job would be sent to the top station again and so on Input jobs p y Probabilities with this algorithm you can define the routing probability for each outgoing link The sum of all probabilities must equal 1 If the values provided do not satisfy the constraint JSIM automatically normalizes the values before the simulation starts Input job p1 0 2 p2 0 4 p3 0 4 p1 p2 p3 1 always This strategy requires that you define the probability for each output link via the panel on the bottom right of the window Routing Options Probability Join the Shortest Queue with this strategy each job is routed to the device that has the smallest queue length i e number of jobs waiting at the time the job leaves the routing station The figure shows a case where the queue lengths at the devices are 3 2 and 1 jobs respectively from top to bottom The exiting job will be routed to the bottom station since its queue is the shortest 1 job q1 3 jobs
159. k CPU Class A Class B Figure 5 27 Example 2 Saturation Sectors Graphics This graphic show the range of mix population where two or more stations are both bottleneck For example the orange area is a renge of mix population in which Disk1 and Disk2 are both bottlenek Step 5 Saturation Sectors Text If you use Next gt command again you will see the Saturation Sectors Text a simple textual report about the Saturation Sectors 124 CHAPTER 5 JABA ASYMPTOTIC BOUND ANALYSIS Chapter 6 JWAT Workload Analyzer Tool A computer system can be viewed as a set of hardware and software resources that are used in a time variant fashion by the processing requests generated by the user During any given time interval the users submit their processing requests to the systems by inputting sets of programs data commands requests for web sites or file downloads etc All this input requests are usually designated by the collective term of workload Every time the value of a system or network performance index is given the workload under which that values obtained must be reported or at any rate known since performance cannot be expressed by quantities independent of the system s workload Thus no evaluation problem can be adequately solved if the workloads to be processed by the systems or transmitted over a network are not specified The quantitative description of a workload s characteristics is commonly called workload charac
160. l distribution is used As soon as the interval ends a new interval is chosen based on the given probability as before Figure 3 10 shows the concept idea of the Burst General distribution clarifying the role of the occurrence probability and the role of the interval length random number probability A probability B A interval A interval B P p Interval Length A Interval Length B Figure 3 10 Main structure of the Burst General distribution consisting of two type of intervals with inde pendent statistical characteristics Burst MMPP2 mmpp2 09 01 o 1 distribution A MMPP 2 is a continuous time Markov chain that jumps between two states and the active state determines the current rate of service For example one state may be associated with slow inter arrival times state 0 the other may have fast inter arrival times state 1 As time passes the MMPP 2 jumps several times between the slow state 0 and the fast state 1 In JMT the MMPP 2 is parameterized by four rates oo 01 Ao and A see Figure 3 11 While in state 0 the MMPP 2 generates arrivals with rate Ay or jumps to state 1 with rate oo in state 1 the arrival and jump rates are A and oj respectively This can be equivalently stated as follows in state O a random number with exponential distribution having rate Ay go is drawn then with probability Ao Ao go is the arrival of a new job or equivalently the completion of its service i
161. ld If the All classes option is selected the range of service time to explore is expressed in percetange starting from the initial value specified at model definition 100 The station where the service time change is applied must be specified 4 3 IMPORT IN JMVA 101 Seed for all types of classes Steps fn of exec j Unlike the previous cases where the analysis is performed for a range of values of one of the model parameters in order to investigate the system behavior under a variety of conditions a what if analysis on the seed aims at evaluating the sensitivity of the simulation engine to numerical conditions in particular to the initial value fed to the pseudo random number generator i e the seed The Simulation engine uses a pseudo random number generator to generate the sequence of values used in each execution By changing the seed a different sequence of values is produced thus leading to different numerical results The first value is the one defined in the Simulation Parameters tab In this panel the number of executions is specified and the simulation engine generates as many pseudo random seeds to be used in the executions 4 3 Import in JMVA After creating a simulation model you can export it to the analytic solver component of the JMT suite namely JMVA In the Action menu click Export to MVA File Mis Simulation Define F E Ct Ciestra i z a ChH Siniskra Clase Ctrl ers Perf
162. lgorithms are available Random Round Robin Probabilities Join the Shortest Queue JSQ Shortest Response time Least Utilization Fastest Service To know details about these algorithms please refer to the subsection 3 9 1 Source Station 3 9 7 Queueing Station The Queueing Station is one of the most important components in a queueing network model A queueing station consists of two main components a queue and a server one or more to execute the requests If all the servers of the station are busy when a new customer arrives at the station the arriving customer join the queue and waits its turn to receive service from the first idle server The queueing discipline determine which customer is served next when a server becomes free The response time at queueing stations includes service time and queueing time Queueing stations may have more than one server their number is a parameter to be specified default is 1 It is important to point out that the utilization U of a queueing station with a single a ServerD Figure 3 59 The Queueing Station icon server i e the fraction of time in which the server is busy is given by U AS and in a station with mservers the utilization of any individual server is given by U AS m Set or change of the properties Double click on the Queueing Station icon and the Editing Server Properties window will open see Fig ure 3 60 Station name is the name of the s
163. lies only to jemjServer stations the default value is 1 as most de vices are single server It can be changed to any finite value Queue Strategy this parameter applies only to jemjServer and jemjFork station types the default value is FCFS and can be changed to LCFS In both cases a priority version of the discipline is also available Service Distribution this parameter applies only to jemjServer stations the default value is Exponential as it is the most popular when modelling device service time It can be changed to any of the available distri butions if most of the devices modelled are non exponential Delay Service Distribution this parameter applies only to Delay stations the default value is Exponential but i can be changed to any of the distributions available Routing Strategy this parameter applies only to jemjDelay Server Join and Routing stations the default value is Random and it can be changed to any of the available routing strategies namely Random Round robin Probabilities Join the Shortest Queue Shortest R time Least utilization and Fastest service Drop Rule this parameter applies only to Fork stations When a finite capacity is defined the default value of the Drop Rule is Drop i e all customers exceeding the station capacity are discarded Two other policies are possible When the capacity is infinite the Drop Rule is disabled by default Fork Capacity this parameter applies only to Fork statio
164. line customers are served in the order in which they arrive at the station If the model is exported to MVA the following constraint is enforced in the exported model Since all customer classes must have the same average service time at a FCFS station the total number of visits to the station Vc k is adjusted in order to comply with the constraint and at the same time allow for distinct service demands Dc k 90 CHAPTER 4 JSIMWIZ FCFS Priority under this policy customers are ordered according to their arrival time but customers with higher priority jump ahead of customers with lower priority conventionally a small priority number low priority Customers with the same priority are served FCFS LCFS under the Last Come First Served queueing discipline an arriving job jumps ahead of the queue and will be served first unless other jobs arrive before the one currently in service finishes The LCFS discipline implemented in JSIM is not the preemptive resume type LCES Priority under this policy the next customer to be served is one with the highest priority conven tionally a small priority number low priority so an arriving customer can only jump ahead of the queue of the other jobs with the equal or smaller priority Customers with the same priority are served LCES Routing section How to Define the Routing Strategy The Routing section is part of the Station Parameters definition page defined for all stations ex
165. mber of customers in the station and thus it may be greater than 1 Dominated Stations A station P is dominated if exist al least one station Q whose service demands for each class of customer are highest or equal but at least one highest than those of P Interactive workload terminal workload Its intensity is specified by two parameters the number of active terminals customers and the average length of time that customers use terminals think time between interactions Load Dependent Resource station A load dependent service station can be thought of as a service station whose service rate the reciprocal of its service time is a function of the customer population in its queue Masked off Stations a station that is not a Potential Bottleneck or a Dominated station A Masked off station may exhibit the largest queue length and hence the highest response time Mean Value Analysis MVA Iterative technique used to evaluate closed queuing networks Multiple class models Models with several customer classes each of which has its own workload intensity and its own service demand at each center Within each class the customers are indistinguishable Number of customers at a resource i Q The average queue length at station 7 include all customers at that center whether waiting in queue or receiving service Number of customers in the system It is the aggregate measure of Queue Length over all stations Numbe
166. me S Average service requirement of a request of a given class per visit at resource k Station or Service Center or Resource It represents a unit of the network Customers arrive at the station and then if necessary wait in queue receive service from server and eventually depart from the station System Response Time R Correspond to the intuitive notion of response time perceived by users that is the time interval between the instant of the submission of a request to a system and the instant the corresponding reply arrives completely at the user It is the aggregate measure of Residence Times R We System Throughput X Rate at which customers perform an entire interaction with the system It is the throughput observed at a user defined reference station Throughput X Rate at which customers are executed by station k accounting also periods where the server is idle That is X is the mean number of completions in a time unit Utilization U Proportion of time in which the station k is busy or in the case of a delay center For single server stations it may be interpreted as the average number of customers in the station see Little Law Lit61 Visit number of V Average number of visits that a customer makes at station k during a complete execution it is computed as the ratio of the number of completions at resource k to the number of system completions as observed at a user defined reference station
167. meric JABA solver Selecting button on the starting screen Figure 5 1 the JABA window shows up E JABA Sele File Action Help D gt El gt RO Classes Stations Service Demands Comment Saturation Sectors Graphics Convex Hull Graphics Saturation Sectors Text Classes characteristics Number customized name typeof classes and number of customers fclosed class or Number Max 3 EI z arrival rate open class New Class New Class You can add classes one by one or define total number at once Class1 E z Class Mesck Solve Exit Help Figure 5 1 Classes tab Three main areas are shown 109 110 CHAPTER 5 JABA ASYMPTOTIC BOUND ANALYSIS Menu it is organized into three groups of functions To use a menu click on the menu heading and choose the appropriate option For the description of menu entries see section 5 3 Toolbar contains some buttons to speed up access to JABA functions e g New model Open Save See section 5 3 for details If you move the mouse pointer over a button a tooltip will be shown up Page Area this is the core of the window All JABA parameters are grouped in different tabs You can modify only a subset of them by selecting the proper tab as will be shown later 5 2 Model definition Models with two or three customer classes provide estimates of wich stations are potential bottleneck For a brief description of basic terminology plea
168. meters To modify the parameters of a station select the icon x and double click on the station to modify The properties panel of a station will be opened and the modifications could be applied To see a complete list of properties of each station see section 3 9 Defining Network Topology 3 10 3 Modifying the default values of parameters The simulator default settings for Class Station Simulation and Finite Capacity Region parameters can be changed from the Define menu in the menu bar At first the user need to select Default parameters from the Define menu Alternatively the user can select the Y Define default values of model parameters JSIMgraph Advanced queuing network design tool File Edit ENS sv Help D f id 29 Customer classes f 4 a JS es Performance indices a3 Simulation parameters yur What if analysis 1 e Default parameters Define default value of model s parameters Figure 3 62 Selection of the Default parameters from the Define menu button In JSIMgraph all the parameters have default values Such values can be changed to suit the user s most common modelling activities The default values of Class Station Simulation Finite Capacity Region FCR and their possible modifications are described in the following sections Class Parameters These settings define the default values of class parameters assigned to a new class see Figure 3 63
169. meters By default the what if analysis is not enabled It must be activated explicitly and its parameters defined Activating the What If Analysis After completing the definition of the model and selecting the What if analysis tab check the Enable what if analysis checkbox to activate it What if analysis Define the type of what if analysis to be Enable what if analysis performed and modify parameter options Selecting the What If Analysis Parameter After enabling the what if analysis it is possible to select the parameter to control the series of simulation runs using the menu below Parameter selection for the control of repeated executions umber of customers Number of customers Type of population growth ERAES Arrival rate Seed a I Teereses mimhar af inh af ane eacad elare Description Repeat the simulation with When you select a what if analysis parameter the bottom section of the window will change depending upon the parameter In the right portion a description is provided of the selected parameter and of the impact of its variation In the left portion the details of the parameter range From and To fields and the number of executions Steps on the range are provided The set of modifiable parameters depends upon the number and type of classes in the model e In a single class model you simply select the parameters you want to change during simulation e In a multiclass model you select the parameter
170. meters after a simulation close the simulation windows with the button and select the tab of the feature you wish to modify No constraints on the order apply in this case since all the model parameters are already defined If no simulation was run simply select the tab of interest Reference Stations Finite Capacity Regions Simulation what if analysis i 1 Classes Stations Connections Station Parameters Performance Indices Parameters are changed the same way they were set when creating the model the first time section 4 2 4 6 Error and warning messages When you start the simulation JSIM analyzes the model and if there are errors or inconsistencies a diagnostic window will pop up describing the problems found 4 6 ERROR AND WARNING MESSAGES 105 Simulation diagnostic E Problems found Click on an element to solve the problem Description a Error Sinki is not backward linked a Error Preloading of stations inside a blocking region is not supported In what follows a list of common problems and the respective solutions are presented o Y Error Sourced is not Forward linked This error occurs when the station source or join has not outgoing or forward links to any other station in the model Only Sink stations do not have forward links To see how to connect two stations see subsection 4 2 3 o Y Error Sink0 is nok backward linked Each sink station must have at least an incoming or backward
171. n clicking Edit in the Service Section tab set the mean values for all the disks Disk1 Disk2 and Disk3 as 5 for Class0 and 0 5 for Class1 e Double click on the LoadBalancer Set the Routing Strategy of Class to Shortest Queue length and that of Class1 to Shortest Response Time see Figure 3 85 e By double clicking on the Web Servers then under the Service Section tab by clicking Edit set the mean values for all the web servers WebServer1 and WebServer2 as 1 for both the classes e From the menu bar Define gt Performance Indices add the index System Response Time twice the first one for ClassO and the second one for Class1 Change the Confidence Interval to 0 99 and Maximum Relative Error to 0 05 Then add the index Throughput Set its Station Region as WebServer1 see Figure 3 86 e From the menu bar choose Define gt What if analysis Check the checkbox Enable What if analysis Select the Service Times parameter Set To as 150 Steps n of exec as 10 and Station as WebServer1 Keep the values of the Arrival Rates parameter as it is To should be 150 and Steps should be 10 Steps in the Seed parameter should remain 10 by default Click Done see Figure 3 87 e To run the simulator press Alt s or select Simulate from the Solve menu or press from the toolbar Note that if you had run the simulation for the same program before JSIMgraph asks for your confirmation whether you want to replace the previous simula
172. n case of syntactically correct components that make no sense from a modelling point of view e g a station that is never visited by any customer a question mark on a yellow bullet indicates that the simulator could not compute the index for lack of measurements Values are available for e Station Name This is the name of the station for which the index is computed e Class Name This is the name of the class for which the index is computed at the station it could be All to mean All Classes e Conf In Max Rel Err This is the Confidence Interval and Maximum Relative Error of the computed index e Analyzed Samples This is the number of samples used to compute the performance index e Min This is the minimum value observed for the index e Max This is the maximum value observed for the index e Average Value This is the computed average value of the index usually the value of greater interest 4 8 Start Simulation When a model is complete and the Simulation Parameters have been defined you can start the simulation clicking the button or selecting Start Simulation from the Simulation menu ls JSIMwiz Queue Network Models Simulator File Action MEE Define Help ye Start Simulation Ctd Performance Indices R Stark Simulation Sheree Alaro If there are errors and or potentially critical conditions error and or warning messages will appear see In case of errors the simulation m
173. n growth Begs Arrival rate Seed E a Tarro aca Mi mahar oF ink oF one Fm Place Figure 3 32 Selection of the parameter for the control of a What If Analysis Description Repeat the simulation with the window of Figure 3 31 will change depending upon the parameter In the right portion a Description is provided of the selected parameter and of the impact of its variation In the left portion the details of the pa rameter range From and To fields and the number of executions Steps on the range are provided The set of modifiable parameters depends upon the number and type of classes in the model in a single class model you simply select the parameters you want to change during simulation while in a multiclass model you must select the parameter and specify whether you want to apply the variation to all the classes or just to one specific class The parameters that may be used to control the sequence of executions in a What If Analysis are 3 7 WHAT IF ANALYSIS 45 e Number of Customers only for models with closed classes JSIM repeats the simulation changing the number of customers in each run starting from the number inserted in the From N field to the value inserted in the To N field The simulation is repeated Steps n of exec number of times In Figure 3 33 a What If Analysis is planned on a single closed class model Define What if analysis parameters NES What if analysis v Enable w
174. n units unique Job ID defined Class ID Interarrival time of same class Interarrival time of any class These fields are found in the next section e Logfile Options Browse button allows changing the directory where logfiles are stored Overwrite method to use when the logfile exists and a new simulation needs to overwrite the file Replace overwrites the file append adds data to the end of the file Delimiter chooses the character to separate between e Status displays the path and file status of the logfile that is going to be written As messages flow through the Logger from one station to another the following information can be logged e Logger Name the name of the logger where the message occured e g Logger0 e Job arrival time this timestamp marks the current simulation time from start of simulation not seconds Job ID the auto generated unique sequence number of the message e g 1 2 3 e Class ID the name of customer class of message e g Class0 e Interarrival time same class is a time difference between customer of the same class that passes through the logger e Interarrival time any class is a time difference between customers of any class that passes through the logger Once a Logger is configured running a simulation produces a logfile with the chosen fields An example of logfile output is LOGGERNAME TIMESTAMP JOBID JOBCLASS TIMEELAPSED_SAMECLASS TIMEELAPSED
175. nal data Sampling methods Variables Observ interval Interval Access request Result status code Bytes transferred Referrer URL 1 Referrer URL 2 User Agent Referrer URL 3 Figure 6 25 Sampling extraction criteria that can be applied on the selected variables Sampling options Percentile EY Percentile MESE Dx lt Precentile Dx gt Precentile Perc lt x lt Prec Do Sampling Undo Sampling Figure 6 26 Filter of the percentiles of a variable trimming of the distribution 6 1 WORKLOAD ANALYSIS 135 e Trimming the outliers i e those values of a variable that are too distant from the other values of the same variable may distort the transformation and the statistical analysis by causing the other observations to be assigned too much or too little weight should be removed To filter a variable distribution trimming operation the percentiles that should be removed can be specified Figure 6 26 e Interval operation applies a filter on a variable s values Depending on the type of the variable different options panels will be shown If the selected variable is numeric the panel is similar to that of Figure 6 27 the minimum and maximum values of the variable should be specified If the selected variable is of data type the panel is similar to that of Figure 6 28 the dates of start and end of observations should be specified If the variable is of string type it is possible to specify a substr
176. nce Index from Define menu and ele he corre ion Error You have to insert at least one station in the model l When an open customer class is defined added to the network to generate and collect the jobs Add a source Error VOLK In the routing section of station closed class job to a sink is one This is an error because jobs cannot Paes leave a closed model Add another link to connect the station with other components of the network and set the new routing probabilities When an open customer class is defined a Source and a Sink must be added to the network to generate and collect the jobs Add a sink to the network l gt is only used to collect customers of open classes This means that a sink without any closed class is useless Warnin The evaluation of System Throughput performance index may be inac curate with multiple sinks We recommend to use one sink only O Error Error Warning Error stations in the Finite Capacity Region All Stations in a FCR must have initial state equal to O otherwise this error will appear Preloading is not supported in FCR Error When you try to Export model defined with JSIM to JMVA some additional errors can appear due to the assumptions that must hold in order to apply the MVA algorithm 64 CHAPTER 3 JSIMGRAPH Simulation diagnostic E Problems found Click on an element to solve the problern Type Description y Error SinkO is
177. nce it is the most popular distribution that characterizes customer interarrival times at a system Change it to any of the distributions available if most of your customer interarrival times follow a non exponential pattern Station Parameters These settings are general parameters for every type of station For a detailed de scription of station types see subsection 4 2 2 Station parameters Mame Station Type Server Queue Capacity Iw Infinite Number of Servers 1 Queue Strategy FFS 7 Service Distribution Exponential Delay Service Distribution Exponential Routing Strategy Random Y Fork Capacity e Infinite Drop Rule Drop hd Fork degree i Name the default name of each newly created station is Station followed by a progressive integer starting from 1 indicating how many classes you have created so far It can be reset to any alphanumerical string which will be followed by the same numbering scheme 4 4 MODIFY DEFAULT PARAMETERS 103 Type the default station type is Server since this is the most popular type of station in performance models Alternative types are Server Fork Join Routing Delay Queue Capacity this parameter applies only to Server and Fork station types the default value is infinite i e an infinite number can queue at such stations It can be reset to finite with a finite value specified by checking out the Infinite checkbox Number of Servers this parameter app
178. ne doesn t match Format element 8 not Found Line doesn t match Format element 8 not Found Error in row 125 Line doesn t match Format element 8 not Found Line doesn t match Format element amp not Found Line doesn t match format element 8 not found Line doesn t match Format element 8 not Found Line doesn t match Format element 8 not Found Line doesn t match Format element 8 not Found Line doesn t match Format felement amp not Found Line doesn t match Format element amp not Found Line doesn t match Format element 8 not Found Line doesn t match Format elerment 8 not Found Line doesn t match Format element amp not Found Line doesn t match Format element 8 not Found Line doesn t match Format element 8 not Found Line doesn t match format element 8 not found Line doesn t match Format element 8 not Found Line doesn t match Format element 8 not Found Line doesn t match Format element 8 not Found Line doesn t match format element 8 not found Line doesn t match Format element 8 not Found Figure 6 18 Example of error log in the loading phase 6 1 WORKLOAD ANALYSIS 133 Bivariate bivariate statistics QQ plot matrix QQ plots of the variables for comparison with normal and exponential distributions Scatter plot matrix Scatter plots of all the variables Input Statistics Clustering i Clustering Information y Univariate Sampling Construction Bivari
179. ne the default values for newly created Finite Capacity Regions Finite Capacity Region Parameters Name FCRegion 7 7 Global Region Capacity Infinite Region Capacity per Class Infinite Drop False M Figure 3 66 Parameters of a Finite Capacity Region e Name The default name of each newly created Finite Capacity Region is FCRegion followed by a progressive integer starting from 1 indicating how many classes you have created so far It can be reset to any alphanumerical string which will be followed by the same numbering scheme e Global Region Capacity The default value of this parameter is infinite i e there is no upper limit to the total number of customers allowed in the region the value can be changed to finite and a number must be specified Region Capacity per Class the default value of this parameter is infinite i e there is no upper limit to the per class total number of customers allowed in the region the value can be changed to finite and a number must be specified e Drop the default value of this parameter is False i e no customer is ever discarded when arriving at the region it can be changed to True in which case customers in excess of the region capacity are discarded 62 CHAPTER 3 JSIMGRAPH Reset to Default Parameters If you have modified the default parameter and you want to restore the original values press the Reset button at the bottom of the pan
180. ng the system as they enter the sink station but do not ever leave it Sink stations have no parameters only incoming connections from one or more stations depending upon the model 3 9 3 Delay Station Customers that arrive at this station are delayed for the amount of time that defines the station service time They do not experience any queuing since a delay station is modelled as a station with an infinite number of servers with the same service time Thus response time of delay stations is equal to the service time R Sj Furthermore the queue length corresponds in this case to the number of customers receiving service since there is no waiting Q RX S X U In delay stations for consistency with Little s law the utilization is computed as the average number of customers in the station and thus it may be greater than 1 Delay stations are used when it is necessary to produce some known average delay A common application of delay stations is to model transmission time download upload of large amounts of data over a network Internet lans or to model users think time at the browsers Setting or changing the properties Double click on the icon representing the delay station to see the property panel Service Section Delay stations are infinite servers with the same service time characteristics the service time distribution should be defined The infinite numbers of servers provide the same average respo
181. nk station may have only incoming links Source Statianl Station Source Sink Station O O O Station2 O Ol O To define a consistent model a Source station must have at least one outgoing connection and a Sink station must have an incoming connection Example 1 if you want to connect stationl to station in this way you must check this box 4 2 DEFINING A NEW MODEL 95 5Skationl Station Station Station Es Example2 if you want to connect stationl to station2 in this way you must check this box 5Skationl Station Station Station E Example3 if you want to connect stationl to itself with a feedback loop you must check this box Stationl Station Station Statione O LJ NOTE if connections among the stations are inconsistent the system displays error warning messages For more information about connection errors read ref 4 2 4 Station Parameters The Station Parameters tab allows you to define the characteristic parameters of each station For each station a different menu is presented depending upon the station type Queuing service routing and forking or subsets thereof are the characteristics to be defined through a series of tabs Default settings are provided that can be modified at the user s need The Sink station does not have any parameter Station Parameters For each station in the list define the requested parameters source Parameters Def
182. nly if there will be only one class closed or open On the contrary multiple class models will have at least two classes closed and or open The number of classes in the model can be specified in the corresponding input area shown in Figure 2 4 and can be modified using the keyboard or using the spin controls Number Figure 2 4 Number of classes Using the delete button X associated to a specific class a class can be removed provided that there will be at least one class after the deletion Similar result may be obtained using spin controls decreasing classes number in this case last inserted class will be removed Default class names are Class1 Class2 ClassN A model can be customized by changing these names this can be done by clicking directly on the name that should be changed In Figure 2 5 there are three classes of customers two closed and one open The third class has the default name Class3 while the other two classes have customized names namely ClosedClass and OpenClass Mo of Customers Arrival Rate 4 5 1 ClosedClass E opencless EO ca E O Figure 2 5 Defining the classes types A class type can be Open or Closed It is important to define each class type because a closed class workload is described by a constant number of customers in each class while the open classes workload is described by the customer arrival rate for each class which does not imply limits on the maximum number of customers
183. not backward linked y Error Preloading of stations inside a blocking region is mot supported Figure 3 67 Window with some diagnostic errors found by the simulator routing strategy in ew constraints apply as for the admissible routing strategies ClassX for Source is not al Warnin Robin routing is not implemented in JMVA so it will be automatically lowed This was considered 6 transformed into Random if you click the Continue button Other as RandomRouting ou can change it following the link a Routing strategy that doesn t match the one of the A state dependent routing Worn BCMP theorem Click on the warning message and choose if you want to strategy was found S convert all non state independent routing strategies to Random routing manually ServerX with non valid ser Warnin ify the service time distribution to an exponential one If Continue vice time distribution S button is pressed this distribution is considered as an Exponential with e same mean value of the original one What If Analysis W you want to export the model in WIA not available Warning A this error appears because the JMVA can t support WIA If Continue button is pressed WIA is ignored Different per class queue for the stationX a queue strategy different for the various classes To ing strategy found at Sta Warning export in JMVA all queue strategies must be equal for all the classes tionX If Continue button is
184. ns the default value is infinite i e no limit on the number of customers entering a Fork station exists It can be changed to finite by checking the blocking checkbox and a finite number must then be specified Forking Degree this parameter applies only to Fork stations the default value is 1 i e one task is gen erated for each outgoing link of the Fork station It can be changed to any finite value thus increasing the degree of parallelism a job has and the number of tasks it is split into Simulation Parameters These parameters define the simulation behavior from a statistical point of view For more information see subsection 4 2 8 for simulation parameters or subsection 4 2 8 for Confidence Interval and Max Relative Error Simulation parameters Confidence Interval Measure 0 1 E Max Relative Error Measure 0 1 Simulation seed 23 000 Maximum duration sec Infinite Maximum number of samples 500 000 Animation update interval sec a Number of classes in queue animation Animation Confidence Interval Measure this parameter is set by default at 90 a commonly used value as it provides a good trade off between results accuracy and simulation time larger values will lead to more accurate results at the expenses of an increase in the time the simulation takes to complete smaller values will achieve the opposite effect Maz Relative Error Measure this parameter is set by default at 10 sm
185. ns are bottleneck at the same time It is clearly understandable that we have no more a switching point such as in the two classes graph but a switching segment 114 CHAPTER 5 JABA ASYMPTOTIC BOUND ANALYSIS Station4 Disk Stationd Diski Stationd Cisk1 Disk Station4 Disk DA Diski Disk Diski Classi Class Figure 5 10 Saturation Sector Graphic In this example Figure 5 10 we can observe a big area on the top of the triangle that rapresents the range of mix population where Station is a bottleneck In the center of the triangle there is a little red area that rapresent the range of mix population where Disk1 Disk2 and Stations are all bottleneck This graph is useful for understanding what station begin bottlenek and when but it is not simple to recornize the exat value of the swiching segment In order to obtain the exact value select the Saturation Sector Text tab subsection 5 2 8 5 2 7 Convex Hull Graphic Using the Solve command and selecting the Convex Hull Graphic tab the Convex Hull graphic is show Overview The Convex Hull graphic implements the polyhedral analysis technique The polyhedral analysis technique implemented in JABA is limited to queueing networks with customers grouped in two classes The points in the graph are obtained from the service demand matrix as follows Each station corresponds to a point on the graph whose co ordinates are represented by the service dem
186. nse time for all jobs as no job waits 3 9 DEFINING NETWORK TOPOLOGY ol 1 Input job 2 3 1 0 34 s S2 0 89s S3 1 02s Figure 3 48 Routing according to the Fastest Service algorithm val diting Delay0 Properties Station Nome Station Name DelayD DelayO0 Parameters Definiton Service Section Routing Section Number of Servers Service Time Distributions Gass Load Dependency Service Time Distribution IC Classo Load Dependent Load Dependent Service Strategy Classi Load Independent exp t Figure 3 49 Windows for the editing of delay properties in queue for service The load dependent or independent characteristic of the service time must be specified for each class of customers through the menus of Figure 3 49 and Figure 3 50 Load Dependency Load Independent Figure 3 50 Selecting load dependency e Load Independent A load independent service indicates that regardless of the number of customers that are in the station the system will serve all the customers following a fixed policy modelled by the chosen statistical distribution To choose the Distribution press the Edit button and insert all the parameters from the window of Figure 3 51 The following service time distributions see section 3 4 are supported Burst General Constant Erlang Exponential Gamma Hyperexponential Normal Pareto Poisson Student T Uniform e Load Dependent A load dependent servic
187. nt routing strategies user defined general distributions import and reuse of log data A module for What If Analysis where a sequence of simulations is run for different values of control parameters particularly useful in capacity planning tuning and optimization studies is also provided The simulation engine performs on line the statistical analysis of measured performance indices plots the collected values discards the initial transient periods and computes the confidence intervals Network topologies implemented and solved using JSIMgraph can be exported in vector e g eps pdf or raster e g jpeg png image formats Main Features Arrival rates for open classes of customers generated by Source stations and station service times for any type of station in open and closed models can be generated according to the following distributions Burst Gen eral Constant Erlang Exponential Gamma Hyperexponential Normal Pareto Poisson Student T Uniform Queueing discipline the following strategies are available First Come First Served FCFS with priority Last Come First Served LCFS with priority Routing of the customers in the network i e the path followed by the requests among the resources can be described either probabilistically or according to the following strategies Fastest service Least utilization Random Round robin Join the Shortest Queue Shortest response time the values of the control parameters are
188. nt to learn details on internal data structures computational engines and XML interfaces should refer to JMT system manual Several other documents related to JMT description and applications are provided with the suite Click on Online Documentation button to access the library An exercise book is also available Chapter 2 JMVA 2 1 Overview JMVA solves open closed and mixed product form BCMP75 queueing networks with the exact MVA algorithm RL80 In order to avoid fluctuations of the solutions when the model contains load dependent stations the implemented algorithm is a stabilized version BBC 81 of the classic MVA algorithm Resources may be of two types queueing either with load independent or load dependent service times and delay The model is described in alphanumeric way user is guided through the definition process by steps of a wizard interface 5 or 6 steps What if analyses where a sequence of model are solved for different values of parameters are also possible see subsection 2 2 5 A graphical interface to describe the model in a user friendly environment is also available see JSIMgraph for details 2 1 1 Starting the alphanumeric MVA solver Selecting button on the starting screen Figure 2 1 window shows up T hree main areas are shown Ls JMVA PFON exact solver File Action Help Dee gt Bee Classes Stations Service Demands Comment Classes characteristics Number customized name
189. ntary to fork stations In classical queueing network theory a task arrives at a join station from the corresponding Fork station In JSIM a Join station may have incoming links from stations other than the corresponding Fork one A Join station has no service time as it is only used to recombine the tasks a job had been previously split into and then route the job to some other station s When a task arrives at a join station it waits until all its sibling tasks have arrived At this time the original job is recomposed and routed to the next station If a job arrives from a station other than the corresponding Fork i e a job that was not split it is simply routed to the next station In this case the Join station operates as a routing station In the Station Parameters tab menu page you can modify Routing Section in this section you can specify how serviced customers should be routed to the next station they will visit in the model For more information see Routing section section 4 2 2 5 Routing station S A routing station is a dummy station with service time equal 0 that is used to create more complex and sophisticated routing strategies by sending jobs through one or more such stations For example if we wanted two thirds of the incoming traffic at station Z to be randomly routed to either station A or B and the remaining third to go either to station C or D depending on the shortest queue at the two stations we could implement t
190. o compute system throughput for that class For open classes there is only one possible reference station that is the Source station Such an association is done by the system automatically each time an open class is created and cannot be modified Class Reference Station classi E Source For each closed class any of the existing stations can be selected using the scroll menu below Reference Station Classe oe Station me Station iE Station2 3 Stations NOTE if a reference station is missing for any of the classes an error message is returned when the simulation will start 4 2 7 Finite Capacity Regions The Finite Capacity Regions tab allows you to define Finite Capacity Regions in the model Finite Capacity Regions can either be added one at a time by clicking the Add Region button or all at once by selecting the desired number in the Regions selector Add Region When a new region is created two new sub areas devoted to the parameters of the region namely the stations involved and class properties when in the region appear on the screen on the right Capacity En Stations in FCRegiona co IES Add Station Stations mae P FCRegion4 E FcRegionS i Class For each region define first the capacity infinite by default If the check in the Infinity box is removed the desidered number can be input in the Capacity field F FCRegion4 E FcRegionS Xx 98 CHAPTER 4 JSIMWIZ Then f
191. o solve different models in a selected range Five choices are possible 2 2 MODEL DEFINITION 9 Disabled disables what if analysis so only a single queueing network model specified in the previous steps will be solved This is the default option Customer Numbers different models will be executed by changing the number of customers of a single closed class or of every closed class proportionally This option is available only when current model has at least one closed class Arrival Rates different models will be executed by changing arrival rate of a single open class or of every open class proportionally This option is available only when current model has at least one open class Population Mix the total number of customers will be kept constant but the population mix i e the ratio between number of customers of selected closed class 7 and the total number of customers in the system bi Ni gt 1 Nx This option is available only when current model has two closed classes Service Demands different models will be solved changing the service demand value of a given station for a given class or for all classes proportionally This option is available only for load independent and delay stations Whenever a control parameter is selected the window layout will be changed to allow the selection of a valid range of values for it For example in Figure 2 14 Service Demands control parameter was selected On the bottom of
192. o this field acts as a reminder The only exception is when Population Mix is changed in that case it is allowed to modify this value too To the final value of what if analysis Please notice that this value can be greater or smaller than From value and is expressed in the same measure unit Whenever All classes proportionally option is selected both From and To values are expressed as percentages of initial values specified in the previous steps for example in a model with two closed classes with population vector 2 6 the following models can be executed 1 3 2 6 3 9 4 12 10 CHAPTER 2 JMVA and reminded in the table at the bottom of the panel see Figure 2 14 in the other situations they are considered as absolute values for the chosen parameter Steps this is chosen number of executions i e the number of different models that will be solved When control parameter is Customer Numbers or Population Mix the model can be correctly specified only for integer values of population JMVA will perform a fast computation to find the maximum allowed number of executions given current From and To values if user specifies a value bigger than that JMVA will use the computed value 2 2 6 Comment Tab In this Tab a short optional comment about the model can be inserted it will be saved with the other model parameters 2 2 7 Expression Evaluator An expression evaluator is used for the definition of serv
193. of the number of interactions for each partition Experiences suggest the value of 4 interactions as a reasonable choice the results are obtained in a short time and are enough accurate To obtain more accurate results higher values should be used this involves a higher computation time the transformation type to apply to selected variables if needed Transformations of the values are applied before the execution of the algorithm and at the end of the execution the results can be transformed back to their original values The transformation of the values is often required since the variables are usually expressed in different units and their ranges are very different Since the algorithm uses the Euclidean distance function as comparison metric to determine if an observation belongs to a cluster the results could be not reliable if the values differ of one or more order of magnitude Clustering options k Means Clustering Specify maximum number of clusters and maximum number of iterations Clusters Clustering iteration number of clusters number of iterations Select maxsimum number of Select maximum number of Clusters that the algorithm has iterations that the algorithm has to produce to perform to find solutions Transformations Transformations 8 none Specify the transformation to apply to selected variables considered by the algorithm 2 value mean std dev C value
194. on Mame CPU Class Hemet Classi Cont ities Beles 0 9 Gud Analyzed samples 154330 Y Min 2 0591 Pase 2 3955 Average value 2 3753 Fs Teen are CONTADO MAT Ce ACA CONE ribe yii red ines and Cha requested maximum rative error Station Nara cru Class Hama Cal Conf int Rel Em 0 9 0 1 Analyzed samples 136738 8 Min 1 3166 Wiar 1 6448 Average value 1487 Aok maania Simulator is phil computing hhe maare miiia ei gt ma An hourglass indicates that the computation of that index is not finished yet A checkmark in a green bullet indi cates that the computation of that index has successfully terminated In this case the minimum and maximum average are reported as well At the bottom of the result window are the simulation control buttons namely the pause button double bar the start button right pointing triangle and the stop button square The status bar indicates the percentage of simulation executed so far both graphically and numerically 108 CHAPTER 4 JSIMWIZ Chapter 5 JABA Asymptotic Bound Analysis 5 1 Overview Product form queueing network models are used for modelling the performance of many type of systems from large computing infrastructures to distributed applications The complexity of modern systems makes the ap plication of exact solution techniques such as the convolution algorithm or the MVA prohibitively expensive in terms of computational resource requirements Also approximate
195. on parameters 4 2 DEFINING A NEW MODEL 83 e Performance indices e Reference stations e Finite capacity regions e Simulation To set each parameter follow the user manual step by step NOTE if no values are provided for the parameters marked with default values will be used and the simulation will run anyway 4 2 1 Define Classes Customer classes identify different customer behavior and characteristics such as the type closed or open the size of the customer population for closed classes or the interarrival time distribution for open classes They can be set using the Classes tab during the creation of a new model e SIM Queue Network Models Simulator File Action Simulation Define he amp gt ne y oe Reference Stations Y Finite Capacity Regions i Simulation i what if analysis r Classes Y Stations Connections Station Parameters Performance Indices Classes Characteristics Define type name and parameters for each ue P Classes oof customer class Name Type Priority Population Arrival Time Distribution Adding a Class Classes must be explicitly added to the model either one at a time by clicking the button or by selecting directly the final number of classes desired in the form lesses of The newly added classes will be listed with deafult parameters Double click on the default name ClassN to change it Each new class has a priority in the system A smaller num
196. only be an integer number only the population vectors with integer components can be considered Therefore the actual number of executions may be smaller than the one specified Population Mix only for models with two closed classes The population mix describes the way the popula tion is divided between the two class i e the percentage of customers in each class over the total population Because of the complexity of the underlying modelling this type of analysis is possible only for models with two closed classes Mixed class models can be analyzed too as long as there are two closed classes Only the closed classes will be considered Initial Final DL ok Steps n of exec po sH Class In order to allow for a complete analysis of the population mix in this case the initial value of the percentage of customers in one of the two classes the one selected through the Class field can be modified Its default value is the ratio of the class population to the total population of closed customers defined in the Class tab Both the final and the initial beta are numbers on the range 0 1 Arrival Rate only if there are open classes Arrival rate is the frequency at which jobs arrive at a sta tion during a period of time Similarly to the number of customers the arrival rate can be changed for one specific open class or for all the open classes in the model If a single class is selected the final arrival rate and the num
197. only used to recombine the tasks a job had been previously split into and then route the job to some other station s When a task arrives at a join station it waits until all its sibling tasks have arrived At this time the original job is recomposed and routed to the next station If a job arrives from a station other than the corresponding Fork i e a job that was not split it is simply routed to the next station In this case the Join station operates as a routing station 3 9 DEFINING NETWORK TOPOLOGY Set or change of properties It has only the Routing section Editing JoinO Properties Tr wa Station Name Station Name Joind Join0 Parameters Definiton i Routing Section Routing Strategies Routing Strategy andom Description Jobs are routed randomly to one of the stations connected to the current one All routes have the same probability to be selected Routing Options No options available for this routing strategy Figure 3 57 Editing of the Routing Strategy Routing Section 59 In the routing section for each class defined you can decide how the completed jobs are routed to the other devices connected to the station for which the routing strategy is defined For each class the user should select the algorithm applied to determine the path followed by the outgoing customers The following algorithms are available Random Round Robin
198. or each region define which stations are part of that region Stations are added in alphabetical order on their names If the model has more than one station a drop down menu from the station name allows you to change the station to add Stations in FCRegion4 Station name 2 Stationl Stations Finally in the bottom right panel you can define class specific properties for the finite capacity region selected Region capacity for that class finite or infinite the default value and the dropping characteristic true or false in case the capacity is exceeded are defined here Class specific FCRegiond Properties Capacity amp Classi C class 4 2 8 Define Simulation Parameters The Simulation Parameters and Initial State of the model are defined using the Simulation tab Finite Capacity Regions Simulation what if analysis A Classes i Stations Y Connections Station Parameters Performance Indices A Reference Stati Simulation parameters In the top section of this windows you can edit general simulation parameters Simulation Seed The simulation seed is a number used by the simulation engine to generate pseudo random numbers As this numbers are pseudo random if you change the seed you will obtain a different sequence of pseudo random numbers If a simulation is repeated using the same seed the same sequence of pseudo random numbers will be generated thus leading to identical results The default
199. or networks with very general characteristics usually referred to as non product form networks like fork and join of customers blocking mechanisms regions with capacity constraints on population state dependent routing strategies user defined general distributions import and reuse of log data A module for What If Analysis where a sequence of simulations is run for different values of control parameters particularly useful in capacity planning tuning and optimization studies is also provided The simulation engine performs on line the statistical analysis of measured performance indices plots the collected values discards the initial transient periods and computes the confidence intervals All the plots generated by a simulation can be exported in vector e g eps pdf or raster e g jpeg png image formats Main Features Arrival rates for open classes of customers generated by Source stations and station service times for any type of station in open and closed models can be generated according to the following distributions Burst general Burst MMPP2 Constant Erlang Exponential Gamma Hyperexponential Normal Pareto Pois son Student T Uniform Queueing discipline the following strategies are available First Come First Served FCFS with priority Last Come First Served LCFS with priority Routing of the customers in the network i e the path followed by the requests among the resources can be descr
200. ormance Indic Import current model into JMYA If there are errors in the model i e conditions not allowed in models with analytical solution a dialog window with information about such errors appears See section 4 6 If you want to continue with the analytical solution you must corret the errors When the model satisfies all the constraints for analytical solution a JMVA window appears on the screen and the model can be solved with JMVA TI JMVA PFQN exact solver AE File Action Help Doe gt Bes O Classes Stations Service Times visits what if Comment Classes characteristics Number customized name type of classes and lore number of customers closed class or arrival rate fopen class Add classes one by one or define New Class total number at once Class1 Class Refer to JMVA user s guide chapter 2 for specific help on JMVA functionalities 4 4 Modify default parameters The simulator default settings as for Class Station Simulation and Finite Capacity Region parameters may be changed using the Define menu in the menu bar Click the Default parameters ls JSIMwiz Queue Network Models Simulator File Action Simulation e Default parameters Classes Stations Connections station Parameters Performance Indices F 102 CHAPTER 4 JSIMWIZ or the Y Define default values of model parameters button In JSIM all parameters have predefined or de
201. pecified JSIMwiz sup ports state independent routing strategies e g Markovian or round robin as well as state dependent strate gies e g routing to the server with minimum utilization or with the shortest response time or with minimum queue length The simulation engine supports several extended features not allowed in product form models namely finite capacity regions i e blocking fork join servers i e parallelism and priority classes The JSIM performs automatically the transient detection based on spectral analysis computes and plots on line the estimated values within the confidence intervals What if analyses where a sequence of simulations is run for different values of control parameters are also supported si E JSIMgraph a graphical user friendly interface for the same simulator engine JSIM used by JSIM wiz It integrates the same functionalities of JSIMwiz with an intuitive graphical workspace This allows an easy description of network structure as well as a simplified definition of the input and execution parameters Network topologies can be exported in vectorial or raster image formats JMVA for the exact analysis of single class or multiclass product form queueing networks processing open closed or mixed workloads A stabilized version of the Mean Value Analysis MVA algorithm is used Network structure is specified by textual wizards What if analyses and graphical representation of the results ar
202. pressed each queue strategy is considered as Processor Sharing N l l a ew constraints apply as for the admissible service time distributions on a eee E B i Warnin A FCFS station must have exponentially distributed service time with da EE A the same mean for all the classes of customers that visit the station If StationX i i ou click the N tal ew constraints apply as ISS distributions ES et Ore A FCFS station must have exponentially distributed service time with time inside FCFS station Warning E Station X the same mean for all the classes of customers that visit the station If me ou click the Continue button this issue is ignored 3 12 Results of simulation Two types of results are generated depending on the type of simulation executed single simulation run and What If Analysis run 3 12 1 Results from a single simulation run At the end of a simulation a panel with several tabs corresponding to the performance indices previously selected is shown see Figure 3 68 If there are more indices of the same type for example one index is referred by two or more different stations or different classes you can see the graphs under the same tab In each window results for all the stations for which the performance index is specified are listed Numerical values and graphs are given Successful results i e if the confidence interval has been computed with the precision set by the user are indicated by the c
203. r E Accelerator Key CTRL O Save Use this command in order to save the active document with its current name in the selected directory When you save a document for the first time JABA displays the Save As dialog box so you can rename your document If you save a model after its resolution results are stored with model definition data Shortcut on Toolbar E Accelerator Key CTRL S Exit Use this command in order to end a JABA session You can also use the Close command on the application Control menu If current model was modified since its creation or last save action a popup window will be shown for confirmation Accelerator Key CTRL Q 118 CHAPTER 5 JABA ASYMPTOTIC BOUND ANALYSIS 5 3 2 Action Solve Use this command when model description is terminated and you want to start the solution of the model At the end of the process the Saturation Sector Graphic subsection 5 2 6 will show Shortcut on Toolbar Fa Accelerator Key CTRL L Randomize Use this command in order to insert random values into Service Demands or Service Times table Shortcut on Toolbar E Accelerator Key CTRL R 5 3 3 Help JABA Help Not still avaiable 5 4 Examples In this section we will describe some examples of model parametrization and solution using JABA exact solver Step by step instructions are provided in two examples 1 A two class model subsection 5 4 1 2 A three class model subsection 5 4 2 5 4 1 Example 1
204. r each partition identified is shown Figure 6 36 The number of clusters the Entropy index and the ratio are shown By selecting one of the rows of table in Figure 6 40 the panel is updated and appears in the right side a tabs structure that permits to visualize information concerning results by grouping them in three main panels Num of clusters eae les 3435 116E 3 1 1 294E 2 140 278E 2 120 25E 2 123 819E 2 i 111 252E 2 a 108 480E 2 106 8 2E 2 Figure 6 40 Results of a fuzzy k Means algorithm execution e Clustering Info It shows the clusters that have been identified and the entropy values Figure 6 41 The error value used to identify a partition should be set by the user and can be easily changed error setting information are reported on the right Pressing the Apply error button the assignment of the observations in the current partitions will be changed according to the new error value and the table at the bottom showing the composition of each cluster and the statistical and graphic information of the following panels will be updated Note that the sum of the percentages could be greater than 100 because of the multiple assignments of the fuzzy algorithm Clustering Info Y Cluster Info i Dispersion Matrix CLUSTERING INFORMATION This clustering has been performed searching 4 clusters and the entropy for this result is 610 374E 3 a ERROR SETTING INFORMATION Sorc no 0 5 9 You can select which erro
205. r of visits The average number of visits that a customer makes to each resource during a complete execution Open Class or Transaction Workload Workload class in which there is an external source with an arbitrary number of customers that are sent to the system according to a given distribution The number of customers in the model varies over time and can be arbitrarily large depending on the congestion level of the resources and on the arrival process Global Population N Constant number of requests belonging to a closed class Population Mix The ratio between N the number of customers of closed class i and the total number of customers in the system 6 N gt Nx 151 152 APPENDIX A BASIC DEFINITIONS Potential Bottleneck Station a station that can become bottleneck for some feasible combination of pop ulation Queue length Q also referred to as Customer number average number of customers at station k either waiting in queue and receiving service Queueing network model A network of queues is a collection of service resources which represent system resources and customers which represent users or transactions Queueing station A resource consisting of two components queue and server Customers at a queueing resource compete for the use of the server The time spent by a customer at a queueing resource has two components time spent waiting in queue and time spent receiving service Reference Station User
206. r to use to create each single cluster according to Fuzzy K Means Clustering results Cluster Num observations Percentage 13 916 ES FAO 71 055 4 53 Figure 6 41 Results of a fuzzy k means algorithm execution e Clusters Info It shows statistical information concerning the selected cluster Figure 6 42 See the comments reported above for the cluster info of the k means algorithm e Dispersion Matrix this last panel shows the matrix of all the possible variable vs variable scatter plots Figure 6 43 See the comments reported above for the dispersion matrix of the k means algorithm 142 CHAPTER 6 JWAT WORKLOAD ANALYZER TOOL Clustering Info Cluster Info f Dispersion Matrix i Cluster Information Select a clustering then choose Cluster 2 4 has 8620 observations 9E10 251 542E5 263 FDEZ 751 041E 3 Access request 196 799E1 306 707E1 546 72DE 2 247 3946 2 Result status code 201 620E0 158 153E 1 96 125 997E0 109 275E 1 Bytes transferred 696 41 7E1 206 55462 111 079E0 924 994E 2 IS gt J t my 165 0 1 008374691E12 4167 0 200 0 6358 0 165 0 1 008374691612 4169 0 200 0 6358 0 165 0 1 008374691 12 4175 0 200 0 6358 0 165 0 1 0083746989E12 4251 0 200 0 6929 0 1165 0 1 009374699 12 4255 0 200 0 7077 0 165 0 1 008374608E12 4259 0 200 0 7303 999990000009 165 0 1 00837 4699E12 4262 0 200 0 8363 0 x 165 0 1 008374608E12 4269 0 200 0 9302 0 Y Bytes tra
207. r use the default values Parameters that are related each other are automatically adjusted if one is modified for example the figure shows how for an Erlang distribution if you set the a r pair the mean c pair is automatically adjusted to the correct value The Replayer distribution allows you to provide data traces from files Click OK when you are done to return to Class parameters definition The final step in defining a class is the definition of the Reference Station i e that station in the model with respect to which the performance indices will be computed For Open classes there is no choice since the Source station is the unchangeable default Reference Station used to compute System Throughput for all the Open classes Classes if Stations AN Connections x Station Parameters Reference Station Define reference station for each closed class This is used to calculate system throughput for that class Reference Station Ei Source 4 2 DEFINING A NEW MODEL 9 Defining the Class Type Closed Classes Population Arrival Time Distribution 0 1 Classes are created Closed by default so there is not need to change the Type Priority can be changed as in the Open class case The population size is the parameter that characterizes a Closed class It is fixed and does not change for the entire life of the system By default is 1 and it can be changed by clicking on the corresponding area in the class properties ma
208. re 2 19 or right click on it and select Zoom in or Zoom out options To automatically reset the best fit scale users can right click on the graphic window and select Original view option Throughput Oo o tk m o 0 0 0 2 0 4 0 6 0 8 1 0 Population mix Bi for Class Figure 2 19 Zoom operation on the plot The graphic window allows to export plots as image to be included in documents and presentations To save current graph as image right click on the graphic and select Save as option A dialog will be shown to request the name of the file and the format Currently supported format are Portable Network Graphics PNG raster and Encapsulated PostScript EPS vectorial currently only black and white The second tab of the solution window shown in Figure 2 20 is used to display the solutions of each execution of the analytic algorithm ls MVA Solutions Graphical Results Textual Results Y Synopsis Execution number Number of customers For Class Mi 26 Throughput Queue length i Residence Times Y Utilization i Throughput Throughput for each class at each station Class1 Class 0 695178 Station 1 781795 Station 0 695176 Stations 0026726 Figure 2 20 Model Solution Textual Results Tab This Tab has the same structure of the results window without What if analysis described in subsec tion 2 2 8 but allows to select the execution to be shown in the field Execution Number By ent
209. ribed in the previous example or more simply by selecting the date type in the concerning box the application supplies a default definition that is correct too it is a string delimited by that can contains within some spaces characters and numbers The best definition uses the delimiter and the regular expression it is an integer number and as we have seen before we can utilize a more simple regular expression d o d d even in this case it is an integer number and as we have seen before we can utilize the regular expression d o A d d in this case the string is not delimited by any particular character and it doesn t contain any spaces so that we can utilize a simple regular expression w or ones little bit different as s and they can contain some spaces characters or numbers and therefore we must utilize the regular expression Comment Perl5 Reg Exp IF Address 10 1 40 1 14d 1 1d Only relevant Time stamp of dd tad did idid Wd The request The resulting i padt d 72 The number of 4 20 d The referring p 5 The referring p 4 sername etc imestamp Access request String Result status code Numeric Bytes transferred Numeric e Referrer URL 1 String Referrer URL 2 String ser Agent String Referrer URL 3 g The user agent Es 5 K Es 5 8 8 E E e 4 The referring p
210. routing As shown in Figure 3 42 the first customer is sent to the top station the second customer is sent to the central station and the third customers is sent to the bottom station The next customers would be sent to the top station again and so on Input jobs Figure 3 42 Routing with Round Robin algorithm e Probabilities The routing probability for each outgoing link must be defined The sum of all probabil ities must be equal 1 Figure 3 43 and Figure 3 44 If the values provided do not satisfy the constraint JSIM automatically normalizes the values before the simulation starts The probability for each output link may be set in the panel on the bottom right of the window shown in Figure 3 40 Routing Options Destination Probabiity Figure 3 43 Definition of the probability of the outgoing links p1 Input job p2 p p1 0 2 p2 0 4 p3 0 4 p1 p2 p3 1 always Figure 3 44 Routing according to the Probability algorithm e Join the Shortest Queue JSQ sometimes referred to as Shortest Queue Length Each customer is routed to the station connected in output that has the smallest number of customers either in queue and in service at the time the customer leaves the routing station Figure 3 45 shows a case where the number of customers in queue and in service at the devices are 3 2 and 1 job respectively from top to bottom The exiting customer will be routed to the bottom station since its
211. s used to initialize the pseudo random number generator It should be changed very cautiously since the statistical quality of the sequence of pseudo randomly generated numbers is affected by the seed choice e Maximum Duration This parameter is set to infinite by default so that even lengthy simulations can complete and satisfy even narrow confidence intervals finite values in seconds may force termination before the end of the simulation e Maximum Number of Samples this parameter is set by default to 500 000 With a smaller number of samples it may not be possible to achieve the requested confidence interval a larger number may not necessarily increase the results accuracy and simply extend the simulation time It should be tuned depending on the objectives of the simulation study performed e Animation Update Interval this parameter indicates the time interval between consecutive graph updates on the screen the default value is 2 sec as it provides for a smooth progression of the graphs on the screen Larger values will make the evolution of the simulation appear jerky e Number of classes in queue animation this parameter controls the number of classes for which graphs will be plotted for the selected performance indices By setting the default value to 10 all classes are represented in most models Graph animation is enabled by default but can be disabled Finite Capacity Region FCR Parameters These parameters defi
212. screen i e the time interval before a new point is added to the graphs as the simulation proceeds A large value will make the simulation to proceed slower as the graphs are updated less often Small values will provide an impression of better responsiveness from the simulation as graphs are updated more frequently Initial state Initial state is the model situation at time 0 typically expressed by the number of customers in each station before starting the simulation For closed customer classes all jobs are initially allocated to their reference station You can modify this allocation as long as the total number of jobs remains the one defined in the Classes subsection 4 2 1 tab For open customer classes it is possible to initialize each station with any desired number of jobs The following table represents an example of an initial state of a model with three stations and two classes 4 2 DEFINING A NEW MODEL 99 Station Stationz Stations Class Ni 6 Class a a a 4 2 9 Define what if analysis The parameters of a what if analysis are defined using the What if analysis tab 1s Simulation En analysis i A What If Analysis consists of a series of simulations in which one or more parameters are varied over a specified range This allows the observation of system behavior under a spectrum of conditions unlike the single JSIM simulation run where the system is observed under a specific set of configuration para
213. se Time Figure 3 25 The drop down list for the selection of the performance indices 2 Select Add Selected Index and the index will be added to the panel Then the index must be set 3 Select from the Class menu a Single class or All Classes for which the index must be computed 4 Select the Station for which the index must be computed from Station menu In case of system wide indices namely System Throughput and System Response Time this option is not available 5 Double click to modify the default values for the Confidence Interval size of the solution and for the Maz Relative Error of the greatest sample error if you want more less accurate results 42 CHAPTER 3 JSIMGRAPH Class E classo y All Classes O Class2 Figure 3 26 The drop down list for the selection of the Class Staton jo ServerO v SeryverO r Server Figure 3 27 The drop down list for the selection of the Station Confidence Interval Max Relative Error a 0 9 0 1 X Figure 3 28 Definition of the Confidence Interval and Max Relative Error 6 Repeat these steps for all the indices you want to include in the model output NOTE Errors in parameter settings will be detected only when the simulation is started raising a warning or an error message 3 5 1 Confidence Intervals The confidence interval shown at the end of a simulation run contains the true value of the estimated inde
214. se refer to Appendix A The workload is characterized for each station by the service demands of every customer class Al least JABA works with 2 classes of custumers therefore a matrix of service demands is required LZGS84 5 2 1 Defining a new model To define a new model select toolbar button L or the New command from File menu The following parameters must be defined Classes Stations service centers Service demands or Service Times and Visits Aa CW N HE Optional short Comment The execution of JABA produces the following graph e Saturation Sector Graphics e Convex Hull Graphics And a textual report about the saturation sectors e Saturation Sectors Text Input tabs As shown in Figure 5 1 the parameters that must be entered in order to define a new model are divided in four tabs Classes Stations Service Demands and Comment The number of tabs become five if you click Service Times and Visits button in Service Demands Tab As will be discussed in subsection 5 2 4 the Service Demands Tab will be hidden and it will appear Service Times Tab and Visit Tab You can navigate across tabs e using sequential wizard buttons if enabled at the bottom of the window Figure 5 2 e using sequential buttons located in menu e using the tab selector clicking on the corresponding tab Figure 5 3 Figure 5 2 Wizard buttons Classes Stations Service Demands Comment Saturation Sectors Graphics Con
215. section you can specify how serviced customers should be routed to the next station they will visit in the model For more information see Routing section section 4 2 2 3 Fork station O A JSIM Fork station is simply a station where jobs are split into tasks No service is provided therefore there is no service time specification Tasks are then routed along the Fork station outgoing links Unlike classical queueing theory fork join queues a JSIM Fork station is not associated with a join station automatically Any combination of server stations finite regions fork join routing stations etc is possibile after a Fork station This feature allows the modeling of very general parallel behaviors of which the traditional Fork Join one is a special case In JSIM the classical queueing theory Fork Join queue behavior is obtained by connecting the Fork station to as many Server stations as the degree of parallelism requested with one task per outgoing link Each Server station is then connected to a Join station where the job is recomposed A Fork station is characterized by the forking degree i e the number of tasks routed on each one of its outgoing links and the capacity 1 e the maximum number of jobs that can be served by the station simultaneously Therefore the number of sibling tasks a job is split into is given by the product of the number of outgoing links from the Fork station times the forking degree Note that a finite station capacit
216. solution techniques become less accurate or more expensive with the growing complexity of the models The alternative is represented by asymptotic techniques that can efficiently determine asymptotic values for several performance indices such as throughput response time and queue lengths The asymptotic techniques are particularly useful in tuning studies where one needs to evaluate the performance gains of different tuning alternatives The key to determine the asymp totic performances is the knowledge of the queueing center s with the highest utilization i e the bottleneck station s Multiclass models can exhibit multiple simultaneous bottlenecks depending of the population mix While identifying the bottleneck stations under a single class workload is a well established practice no simple methodology for multiclass models has yet been found JABA provides such a technique called Polyhedral Analysis using convex polytopes based approach presented in CS04 Among the no bottleneck station we distinguish two different centers dominated and masked off stations This distinction is important since the masked off stations despite having lower utilization than the bottleneck center s may still exhibit the largest queue length and hence the highest response times Dominated sta tions instead typically play a marginal role in determining system performance and have always the smallest utilization and queue lengths 5 1 1 Starting the alphanu
217. specified station where a customer flow through when it has completed its execution i e it has performed an entire cycle of service in the system The system throughput system response time and the visits V are computed with respect to the visits at the reference station usually assumed as 1 Residence Time Wp Average time that a customer spent at station k during its complete execution It includes time spent queueing and time spent receiving service It does not correspond to Response Time Ry of a station since W Ry Vp Response Time R Average time required by a customer to flow through a station k includes queue time and service time Saturated Resource When the arrival rate at a resource is greater than or equal to the maximum service rate the resource is said to be saturated i e its utilization is equal to 1 Saturation Sector a interval of Population Mix in witch one two ore more stations are both bottleneck Server Utilization U The utilization of a queuing center is the proportion of time the resource is busy or equivalently the average number of customers in service there definition valid also for delay centers Service Demand D average service requirement of a customer that is the total amount of service required by a complete execution at resource k In the model it is necessary to provide separate service demand for each pair service center class It is given by Dk Vp Sp Service Ti
218. ss has a priority in the system A smaller number indicates a lower priority Default value is 0 it can be changed by double clicking on the corresponding area In this panel you can insert either one or multiple customer classes Defining Open Classes After adding a class and set its name and priority you must select the type of the class Classes are created Closed by default so if you want an Open class select the type Open from the Type menu Type E Closed _w Figure 3 3 Selection of the type of the class Now the class characteristics should look like Figure 3 4 Color Name Type _ Priority Population Arrival Time Distribution Reference Station MU cos Open 2 expt Edt E Source Figure 3 4 Class characteristics window Open classes describe customer populations that vary over time They are characterized by the probability distribution of the interarrival time of customers arriving at the system The default Interarrival Time Distri bution is exp 1 Exponential Distribution with A 1 To change the Interarrival Time Distribution click the Edit button Arrival Time Distribution EN Figure 3 5 Definition of the interarrival time distribution and its parameters Edit button The following window will appear Editing class distribution Selected Distribution Exponential Exponential exp A f x A As Figure 3 6 Window for the editing of the distribution of inter
219. structions of Step 2 in the previous examples in this case the model has three Load Independent stations see Figure 2 41 Step 3 Service Demands Tab Follow the instructions of Step 3 in the previous examples and define service demands for both classes as illustrated in Table 2 11 see Figure 2 42 Step 4 What if Tab 1 use Next gt command to switch to What if Tab 2 Select Population Mix as a control parameter of the analysis in the combo box several fields will be shown below 3 Classi is already selected by default as reference class for the what if analysis This means that 0 values in From and To fields are referred to Class1 4 By default JMVA suggests the minimum allowed value of 3 in the From field and its the maximum value in the To field Since we want to find the optimal value in the entire interval we leave this unchanged 5 we want to perform the maximum number of allowed executions so we enter a big number in the Steps field 100 for example JMVA will automatically calculate the maximum number of allowed executions provided that number of customers for each class must be an integer and will report 19 At the end of this phase the What if Tab will look like Figure 2 43 Step 5 Model Solution Use Solve command In the Graphical Results Tab select System Response Time and System Throughput as Performance Index Figure 2 44 and Figure 2 45 Zooming on the plot allows to identify the maximum Since
220. t Solve Exit Help lt Back Next gt sowe ext Hep Figure 2 12 Visits Tab CHAPTER 2 JMVA The layout of these tabs is similar to the one of the Service Demand Tab described in the previous para graph The default value for each element of the Service Times S matrix is zero while it is one for Visits matrix elements In current model contains load dependent stations the behavior of Service Times Tab for their parametriza tion will be identical to the one described on the previous paragraph for Service Demands Tab On the other hand Visits Tab behavior will not change as load dependency is a property of service times and not of visits 2 2 5 What if Tab This Tab is used to perform a what if analysis i e solve multiple models changing the value of a control parameter In Figure 2 13 is shown this panel when what if analysis is disabled Ls JMVA PFON exact solver File Action Help bo gt wes Classes Stations Y Service Demands What if Y Comment Y What if analysis Select a control parameter if you want to solve several models with its values changing in the selected range The performance indices will be shown in a graph Control Parameter Disabled lt Back Mext gt Solve Exit Help lt Back next gt sowe ext Hep Figure 2 13 What if Tab Disabled analysis The first parameter to be set is the control parameter i e the parameter that will be changed t
221. t file to delimit the field identified by the current variable For example in the Apache server log file the variable timestamp is contained within square brackets e Regular Expression definition of regular expression Perl 5 that defines the variable For example in case of IP variables a possible regular expression is d d d d e Delete the corresponding variable will be deleted In order to help the users for each of the types the tool sets automatically some of the fields delimiter of field and regular expression supplying standard settings as shown in Figure 6 8 where for for the type string it is proposed as delimiter and w as regular expression A format definition may be saved by using the Save format button so that it may reused in the future Format loading If a standard log file Apache IIS is used it is possible to load the corresponding format by using the combobox in the panel of Figure 6 10 File format Load saved format Apache log file Format Frit Figure 6 10 Panel for the loading of standard and previously saved format For example by selecting the option Apache log file format the format definition table of Figure 6 11 is automatically loaded At this point the user can select through the format table selection field the subset of Comment Perl5 Reg Exp IP Address 10411041 dA d Only relevant Time stamp of Wd at ddd yids did yd 4 The requ
222. tage of utilization and queue length colored areas Simulation Results nonn m Queue Length Residence Time Utilization Throughput System Response Time Y System Throughput Customer Number Queue Length Average number of customers for each chosen class at each chosen station Station Name CPU Class Name Conf Int Max Rel Err Analyzed samples Min Max CONS CUCU te TOMS SUH ii SEF EIT IEA Versi es eee interval red lines and the requested maximum relative error Station Name Class Name Conf Int Max Rel Err Analyzed samples Min Max wisest OOD OF COTES Me COWS WWE ii SEP HS SHO CE Ee Werdet ewes tee interval red lines and the requested maximum relative error Figure 3 80 Progress of the simulation average values and confidence intervals 3 13 EXAMPLES 19 Requests Figure 3 81 Example 2 A system with a multiclass workload a RAIDO storage server modelled with Fork and Join Stations and a web server consisting of two systems used in parallel with a limited number of requests in execution modelled with a Finite Capacity Region Define customer classes a T j Add Class Classes Characteristics gy Editina Class distribution 7 l e Classes ais Define type name and parameti Selected Distribution Hyperexponential y aCe Hyperexponential hyp p A A2 Edit JLS Requests IX f x p Aje ur 1 p Aye 27 p 10 291317496907 Al 0 182073435567 A2
223. tation is characterized by the forking degree i e the number of tasks routed on each one of its outgoing links and the capacity i e the maximum number of jobs that can be served by the station simultaneously Therefore the number of sibling tasks a job is split into is given by the product of the number of outgoing links from the Fork station times the forking degree Note that a finite station capacity makes sense only when there is a Join station downstream from the Fork station that can recompose the split jobs Otherwise inconsistencies in the model and subsequent simulation error such as out of memory may occur No automatic checks to identify such critical conditions have been implemented since it may happen that users are required to simulate special conditions purposely Both the forking degree and the capacity are section parameters to be specified in the model As an example a Fork station with forking degree 1 connected to three queueing stations would split a job into 3 sibling tasks this is a traditional Fork Join like behavior If no Join station is connected to any of the three Servers a warning message is displayed since the model could quickly saturate due to the extra load 3 more customers created in addition to each job entering the Fork station Set or change of properties The station has two sections Fork Section and Queue Section Fork Section In this section the user can define the station forking degree i e
224. tation that the user like to assign There are three tabs Queue Section Service Section and Routing Section Queue Section Please refer to Queue Section of subsection 3 9 4 Fork Station Service Section The service time distribution and the number of servers default is 1 should be defined The load dependent or independent characteristic of the service times must be specified for each class of customers through the menus of Figure 3 49 and Figure 3 50 Please refer to Service Section of subsection 3 9 3 Delay Station Routing Section In the routing section for each class of customers you can decide the path followed by the completed jobs are routed to the devices connected to station for which the routing strategy is defined For each class the user should select the algorithm you want to use in order to determine the outgoing connection followed by a customer The following algorithms are available Random Round Robin Probabilities 3 9 DEFINING NETWORK TOPOLOGY ov o Editing Server0 Properties m gt 7 FF 7 sz Station Name Station Name Server Server0 Parameters Definiton 1 Queue Section Service Section 1 Routing Section Capacity Queue Policy Class Queue Policy Drop Rule Class0 FCFS Infinite Capacit infinite O finite length 1S Figure 3 60 Window for editing the Queueing server Station properties Join the Shortest Que
225. tegies Class Routing Strategy LO Classi Random x Figure 3 53 Selecting the Routing Strategy algorithm you want to use for outgoing connections The following algorithms are available Random Round Robin Probabilities Join the Shortest Queue Shortest Response time Least Utilization Fastest Service To know details about these algorithms please refer to subsection 3 9 1 of Source Station 3 9 DEFINING NETWORK TOPOLOGY 99 3 9 4 Fork Station A Fork station is a station where jobs are split into tasks No service is provided therefore there is no service time specification Tasks are then routed along the Fork station outgoing links see Figure 3 54 Unlike classical queueing theory fork join queues a JSIM Fork station is not associated with a join station ForkO Serverl Figure 3 54 The Fork and Join stations automatically Any combination of queueing stations Finite Capacity Regions fork join routing stations log gers etc is possible after a Fork station This feature allows the modelling of very general parallel behaviors of which the traditional Fork Join one is a special case In JSIM the classical queueing theory fork join queue behavior is obtained by connecting the Fork station to as many queueing stations as the degree of parallelism requested with one task per outgoing link Each queueing station is then connected to a Join station where the job is recomposed A Fork s
226. terization A characterization is usually done in terms of workload parameters that can affect system behavior and are defined in a form suitable for a desired use Thus a workload is characterized correctly if and only if its result is a set of quantitative parameters selected according to the goals of the characterization operation Workload characterization is fundamentally important in all performance evaluation studies and is indispensable for designing useful workload models A workload may be regarded as a set of vectors in a space with a number of dimensions equal to the number of the workload parameters used to describe each element considered Since the amount of resulting data is generally considerable their analysis for the purpose of identifying groups of components with similar characteristics will have to be performed by statistical techniques that can handle multidimensional samples that is techniques that deal with multiple factors The JWAT tool is based on the application of a set of statistical techniques oriented towards the charac terization of log data representing resource utilizations traffic of requests user web paths etc Its application provides the input data for the models to be used in all types of performance evaluation studies The main window of JWAT Figure 6 1 is opened pressing the wat button in the JMT suite main window Through this window it is possible to select one of the three main components of JWAT
227. the default value is 1 i e one task is generated for each outgoing link of the Fork station It can be changed to any finite value thus increasing the degree of parallelism a job has and the number of tasks it is split into Simulation Parameters These parameters define the simulation run from a statistical point of view More details on Confidence Interval and Max Relative Error are reported in subsection 3 5 1 and subsection 3 5 2 e Confidence Interval Measure This parameter is set by default at 90 a commonly used value as it provides a good trade off between results accuracy and simulation time Larger values will lead to more 3 10 MODIFICATION OF THE PARAMETERS 61 Simulation parameters Confidence Interval Measure 0 1 0 9 Max Relative Error Measure 0 1 a Od Simulation seed 23 000 Maximum duration sec Infinite Maximum number of samples 500 000 Animation update interval sec 2 gt Mumber of classes in queue animation ps v Animation Figure 3 65 Parameters for the control of the simulation accurate results at the expenses of an increase in the time the simulation takes to complete smaller values will achieve the opposite effect e Max Relative Error Measure This parameter is set by default at 10 smaller values will increase results accuracy while bigger values allow for larger errors in the samples e Simulation Seed This parameter i
228. the errors found in the data is shown A user may decide to stop the analysis and verify the input data or may continue with the following steps 2 Computation and visualization for each variable of the descriptive statistics univariate and bivariate of the frequency graphs of the scatter plots and of the QQ plot compared to a normal or exponential distribution section 6 1 3 It is important to observe that usually the variables are expressed in nonhomogeneous units To make them comparable a scale change must be performed The following statistical analysis of the original data especially of the histograms of their parameters allows us to determine when it would be useful to apply to them a logarithmic or another transformation Very often the density functions of some variables are highly positively skewed and have high values of kurtosis too Applying a logarithmic transformation of highly skewed variable densities it is possible to avoid or to reduce correlations among means and variances of the clusters that will be identified Several transformations may be applied to the numeric variables attention ONLY to the numeric variables A sample may be extracted from input file by using different criteria The distributions of two variables may be compared through QQ plots and scatter plots selected in the corresponding matrix 3 Selection of the clustering algorithm to apply and of the variables to be considered in the cluster analysis
229. the fuzzy exponent and Specify the fuzziness level range fram 2 to 100 1t determines the for the algorithm degree of fuzziness of the final solution Transformations Transformations Crate Specify the transformation to apply to CA value ming f max min selected variables 05 value mean std dev Figure 6 34 Parameters of the clustering algorithm Fuzzy k Means 6 1 5 The results of a clustering execution At the end of the execution of a clustering algorithm the tab that allows the analysis of the results is shown The main panel shows the table in Figure 6 35 that contains the algorithm s executed and the maximum number of clusters identified It is possible to delete the results of an execution by clicking the button in the last column Clusterings Clustering k Means 5 Fuzzy k Means 8 k Means 4 Figure 6 35 List of executed clustering algorithms Depending on the selected clustering algorithm different results panels are shown in the results table K Means algorithm results When the k Means algorithm results are selected a table reporting the indices concerning the goodness of the partitions is shown Figure 6 36 To estimate the optimal number k of clusters in which the given set of observations will be subdivided two indicators of the goodness of a partition are used For each variable the Overall Mean Square Ratio OMSR 6 1 WORKLOAD ANALYSIS 139 i e a measure of the redu
230. the number of tasks created for each job arriving at the fork station and its capacity 1 e the maximum number of jobs that can be in a fork join section when a join is present Fork degree Number of tasks to be generated on each output link for each input job E Fork join section capacity _ Enable Finite Capacity limit maximum number of jobs inside a fork join section Capacity max number of jobs NOT tasks Figure 3 55 Setting of the Fork degree and the Fork capacity e Forking degree It is the number of tasks that are routed on each outgoing link of the fork station Therefore each customer is split into forking degree x number of outgoing links tasks By default the forking degree is 1 it can be modified as shown in Figure 3 55 e Capacity It is the maximum number of customers jobs that can be served by a Fork Join section simultaneously It makes sense only if there is a Join station matching the Fork one It can be finite in this case when the limit is reached the jobs wait in the queue of the Fork station A job is removed from the queue and serviced i e split into tasks when a job is recomposed at the matching Join station and leaves it Capacity is defined using the form shown in Figure 3 56 after checking the Finite capacity box 54 CHAPTER 3 JSIMGRAPH Queue Section The Queue section allows the specification of the queueing capacity finite or infinite and policy Different class
231. the other icons in the toolbar From Figure 3 1 we can see that the As JSIMgraph Advanced queuing network design tool File Edit Define Solve Help be e ybh MENA META Go JEDIA TORALO Figure 3 1 The home window of JSIM graph home window has a menu bar and two toolbars The menu bar has 5 menus File Edit Define Solve Help The first toolbar has the following icons D Create a new model f gt Open a previously saved model El Save the current model e Cut D Copy i Paste Es Define customer classes Define the performance indices to be evaluated and plotted Sa Define simulation parameters Y Define What if analysis parameters Export the current model to JMVA gt Start simulation model 1 Pause simulation E Stop simulation 3 3 WORKING WITH THE GRAPHICAL INTERFACE 31 y Show simulation results window Y Define new default values of model parameters The second toolbar has the following icons X Select 51 Insert a source station Insert a sink station eS Insert a routing station k Insert a delay station 4 Insert a queueing station Insert a fork node Insert a join node 4 Insert a logger station Connect two elements ME Add selected stations to a new Finite Capacity Region Rotate the component SE Optimize the graph 3 3 Working with the graphical interface 3 3 1 Defining a new model To define a new model the following steps have to be performed Draw the network
232. them otherwise they are dropped from the network 3 9 Defining Network Topology To define a new model select New from File menu or click the icon and draw the network topology Selecting the stations From the second toolbar Figure 3 39 select a station and click on the model panel to insert it drag and drop The available stations are 48 CHAPTER 3 JSIMGRAPH DEL OO s m E Figure 3 39 The toolbar for the selection of the stations to be inserted in the network is J Insert a source station Insert a sink station Insert a routing station H Insert a delay station Insert a queueing station Insert a fork node W Insert a join node 4 Insert a logger station Add selected stations to a new Finite Capacity Region To rotate a component press the button To optimize the final layout of the network press the Press the dE button Connecting two elements To link two stations of the model 1 Select the icon 2 Select and hold the mouse pressed from one station to the other station to which you want to connect to 3 9 1 Source Station Setting station properties Open classes are characterized by an infinite stream of jobs that can enter the system Source stations are used to generate customers in the model The interarrival time of the customers of each class should be defined as a parameter of the class The routing strategy defines the first station a newly created customer will visit Only open
233. time interval when such events are independent of the amount of time elapsed and they occur at a fix rate It is a discrete probability distribution characterized by a single parameter A a positive real number which is the average number of events in a time interval and its variance The probability of having an arrival in a time interval t t At is At o At while the probability of more than one arrival in the same interval is o At For large time intervals T the distribution is near the mean value thus the number n of arrivals over the interval is given by n AT The time intervals between two consecutive events having a Poisson distribution are exponentially distributed with average value equal to 1 1 The probability mass function is Ha e a A family of Poisson probability mass functions is shown in Figure 3 21 Replayer replayer filename distribution When Replayer is chosen a trace of data provided by the users can be reused as interarrival times or service times The file format should be text binary with values separated by CR Carriage Return In order to use this user supplied file of data the user should provide in the input window the absolute path name of the file Student T studT v distribution The T distribution or StudentT distribution is a continuous distribution characterized by the single parameter v a real positive number It is used when the mean of a normally distributed population
234. tion Figure 2 21 Example 1 network topology of N 3 customers 16 CHAPTER 2 JMVA There are four stations three are of load independent type named CPU Disk1 and Disk2 and one is of delay type named Users Users delay station represents user s think time Z 16 s between interaction with the system Service times and visits for stations are reported in Table 2 3 Disk1 Disk2 Users Service Times s 7 nn 0 038 0 030 16 000 Visits 101 000 60 000 40 000 1 000 Table 2 3 Example 1 service times and visits Step 1 Classes Tab e use New command to create a new MVA document e by default you have already a Closed class e if you like substitute default Class1 name with a customized one ClosedClass in our example e complete the table with workload intensity number of customers Remember that intensity of a closed class N must be a positive integer number in this case 3 At the end of this step the Classes Tab should look like Figure 2 22 Classes El Stations A Service Demands i Comment A Classes characteristics Number customized name type of classes and number of customers closed Number class or arrival rate open class You can add classes one by one or define total number at once Mo oF Customers Arrival Rate 4 ClosedClass Figure 2 22 Example 1 input data Classes Tab Step 2 Stations Tab e use Next gt command to switch to Stations Tab e digit number 4
235. tion rate at which customers departs from a station i e the number of requests completed in a time unit System Throughput of the system rate at which customers departs from the system System Response Time of the system average time a customer spends in the system in order to receive service from the various stations it visits It corresponds to the intuitive notion of response time as the interval between the submission of a request and the reception of the response Customer Number of the system average number of customers in the system If the index is associated with a closed class then it is equal to the number of customers in the class Any subset of indices from the above list can be plotted as model output Each index is associated with a class a ws Define performance indices Performance Indices Queue Length Define system performance indices to be colected and plotted by the simulation engine Add selected index Performance Index Class Station Confidence Interval 0 1 Max Relative Error 0 1 BE jii Figure 3 24 The window for the selection of the performance indices and a station and will be computed within the given Confidence Interval and Maximum Relative Error both defined on the 0 1 range by performing the following steps 1 Select the index you want to add to the model from this menu Queue Length X Queue Length a Queue Time Throughput System Throughput EA System Respon
236. tion Sectors Text Classes Stations Service Demands Comment Saturation Sectors Graphics Service Demands FirstClass SecondClass Input service demands of each CPU 2 60 2 13 station for each class Diski 7 02 4 51 If station type is set to Load Disk2 4 31 5 70 Dependent vou can set values of service demands for each number of customers by double clicking on any button in station s row IF you whish to input service times and visits instead of service demands press Service Times and visits button Service Times and Visits Figure 5 21 Example 1 input data Service Demand Tab SecondClass 1 000 Diski 0455 A e a S a i Diski Disk Disk URNS 0 545 r 1 000 FirstClass 0 000 0 684 Figure 5 22 Example 1 Saturation Sectors Graphics 5 4 EXAMPLES 121 Potential FirstClass Bottleneck Stations z Wlaske d off 10 Stations Dominated Stations a y Masked off Ara Dominated g aire B a 10 secondClass Figure 5 23 Example 1 Convex Hull Graphics Step 5 Convex Hull Graphics Using Next gt command to switch to Convex Hull Graphics and a graphic like Figure 5 23 will be shown This graphic implements the polyhedra analysis technique The points on this graphic represent the stations Dominated stations are green masked off ones are blue and bottlenek ones are red If you click on a station additional information will be shown otherwise
237. tion results or not Choose yes to carry on If we look the drawing window of the Simulator we can see the simulation going on The windows of Figure 3 88 Figure 3 89 and Figure 3 90 show the results of the What If Analysis Note that the results of different simulation runs may slightly vary due to the differences in the sequence of random numbers generated with different seeds 3 13 EXAMPLES Performance Indices Queue Length v Define system performance indices to be collected and plotted by the simulation engine Add selected index Queue Length Queue Length All Classes Y SS 7 OEE Queue Length All Classes Y All Classes alm ona A 4 Performance Indices Define system performance indices to be collected and plotted by the simulation engine Add selected index Performance Index Confidence Interval 0 1 Max Relative Error 0 1 al Queue Length All Classes CPU Queue Length All lsses wll Dil Queue Length All Classes v Disk2 Queue Length Throughput Throughput Throughput Throughput Residence Time Residence Time Residence Time Residence Time Utilization Utilization Utilization Utilization Customer Number System Throughput System Response Time Figure 3 78 The Define Performance Indices window at the end of the selection of the indices 13 714 CHAPTER 3 JSIMGRAPH File Edit Define Solve Help Figure 3 79 Example 1 The layout of the model with the percen
238. tion section 4 2 2 Routing Section in this section you can specify how serviced customers should be routed to the next station they will visit in the model For more information see Routing section section 4 2 2 2 Server station The Server station is one of the most important components in a queuing network model Service sta tions represent the service facilities of the system being modelled A server station provides the required service to its customers Server stations may have any finite number of servers If all the servers in the service station are busy when a customer arrives at the station the arriving customer is put in a waiting queue until its turn to receive service from the first available server is up The queueing discipline decides which customer is served next when a server becomes free Therefore the response time at server stations includes service time and queuing time Server stations may have more than one server Their number is a parameter to be specified default is 1 In the Station Parameters tab menu page you can modify Queue Section in this section you can choose the type of queue finite or infinite and the policy used to select the next customer to be served For more information see Queue section section 4 2 2 Service Section in this section you can choose the service time distribution for the station For more information see Service section section 4 2 2 Routing Section in this
239. to different numerical results The first seed is the one defined in the Simulation Parameters tab The number of executions is specified in the panel of Figure 3 35 and the simulation engine generates as many pseudo random seeds to be used one for each execution 3 8 Finite Capacity Region FCR A Finite Capacity Region is a region of the model where the number of customers is controlled It is possible to define two types of FC region capacity constraints e Shared an upper bound for the number of customers that are in the region regardless of the classes they belongs to e Dedicated an upper bound for the number of jobs for a specific customer class in the region During the simulation the most restrictive constraint is applied For example consider a multiclass model with two classes Class1 and Class2 with a shared constraint of 100 customers a dedicated constraint of 30 customers for Class1 and no dedicated constraint for Class2 If during the simulation the queue contains 30 customers belonging to Class1 and 60 customers belonging to Class2 an incoming job of Class1 will be rejected as it s dedicated constraint is violated while an incoming job of Class2 will be accepted as it will not exceed the shared constraint If the initial state was 20 jobs of Class and 80 jobs of Class2 an incoming job will always be rejected despite of its class as it would violate the shared constraint How to define a FCR 1 Select the stat
240. total number of models to be solved and the elapsed time At the end of the solution results will be shown in a separate window see Figure 2 18 This tab allows to show in a plot the relation between the chosen control parameter see subsection 2 2 5 and the performance indices computed by the analytic engine The combo box Performance Index allows to select the performance index to be plotted in the graph while in the table below users can select the resource and the class considered e The first column is fixed and lists all available colors to be used in the graph e The second column named Class is used to select the class considered in the graph The special value Aggregate is used for the aggregate measure for all classes If input model is single class the class is selected by default for each row e The final column named Station is used to select the station considered in the graph The special value Aggregate is used for the aggregate measure for the entire network Note that the Aggregate value is not valid when the Utilization performance index is selected In addition to the center performance indices i e Throughput Queue length Residence Times Utilization three system performance indices are provided in the Performance Index combo box System Response Time 12 ita What if analysis progress What if analysis running please wait Elapsed time 00m 04s Solving model 24 of 110 Figure 2 17 Mo
241. trans yeyd tD Jad Ej Figure 6 45 Input format example Each observation consists of the values of 4 variables described in Figure 6 45 e IP String type variable that defines IP address of the request e Timestamp Date type variable that defines the timestamp of the request the regular expression d d w w w d d d d d d d d d d identifies that the data will be in the format dd mmm yyyy hh mmiss e g 12 Jun 2000 12 21 45 e Access request String type variable that identifies the object that is the target of the request The definition through delimiter and regular expression allows the reading of all the string that is contained between quotation marks if it is necessary it is possible to modify the expression to read only a part of the string between quotation marks e Bytes transferred Numeric type variable that identifies the quantity of bytes transferred due to the execution of the request submitted Step 2 Descriptive statistics and sample extraction Before the execution of the cluster analysis the size of the input data set has been reduced executing the filter Interval to the values of the variable Bytes transferred setting a maximum value of 20000 and a minimum value of 0 The purpose of this filtering operation is to obtain a data set more compact but still representative of the original one In Tables Figure 6 46 and Figure 6 47 the descriptive statistics before and aft
242. trix The final step is to define a Reference Station for the class that will be used to compute the performance indices selected for the class Use the Reference Station tab menu to select the Station All stations but the sink can be used as reference station for a closed class PEREA III IE ERLE Le AFL 1 Classes i Stations Y Connections Station Parameters Reference Station Define reference station for each closed class This is used to calculate system throughput for that class Reference Station oe Station le Station se Skation2 l Stations A Station Distributions See section 3 4 4 2 2 Define stations When you create a new model you must define the Stations from the Stations page of the tabs menu da JSIM Queue Network Models Simulator AE File Action Simulation Define beh A pun Y e Reference Stations Finite Capacity Regions Simulation What if analysis Classes Stations Connections Station Parameters Performance Indices i icti Add Stati Stations Characteristics Define type and names for each station Stations Mame lt Back Next Solve Cancel Help You can insert one station at a time by pressing the button or multiple stations all at once by choosing the desired number in the input form ts 02 The added stations will be listed in the page Various types of stations are available the default type being server If you want to remov
243. ue JSQ Shortest Response Time Least Utilization Fastest Service To know details about these algorithms please refer to the Routing Section of subsection 3 9 1 Source Station 3 9 8 Logger station A logging station i e logger reads information flowing through it and writes it to a file In the simplest way it is a tool to understand and debug the traffic flow moving through the interesting part s of the model Place the logger station into the model choose the parameters and trace the data as it passes through the model Set or change of the properties Double click on the Logger Station icon 4 to open the Editing Logger Properties station s configuration dialog see Figure 4 2 There are two sections Logger Section and Routing Section 5 Velie Copgerii Properties Ala Aa uain Para Legt vO Pee bere pimihan Logg See 1 Arabia hechan Litany nalima LiglRe Miimi Loria Logue cit Thage Fehi bet e Pir at Jobard rw we hb I Oeerarts se Claes I dread tine same cles Trieras Inercia alar Fle CL LL y cee nod e Figure 3 61 Window for the Logger Station configuration Logger Section The configuration properties of the Logger Section are e Logging Options 58 CHAPTER 3 JSIMGRAPH The Logfile s name to use either individual or merged Logger0 csv or global csv respectively The information to log fields Logger Name Job Arrival Time simulation units unique Jo
244. valuated over the global population N of the model add up to 1 as shown in the Population mix table on the bottom of the window of Figure 3 33 in the simple case of a single class model If the Increase number of jobs of all closed classes option is selected the overall population is increased keeping constant the relative proportion of jobs in the various classes i e the values 6 also referred to as population mix Because in the JSIM the number of customers in each class can only be integer numbers only the population vectors with all integer components can be considered Therefore the actual number of executions may be smaller than the one specified The population mix describes the way the global population is subdivided between the classes i e the percentage of customers in each class 8 values over the total population The population mix can be modified extensively selecting the way we want to change it with the increasing of the global population of customers all classes increase proportionally or only one class increases keeping constant the jobs of the other classes select the option Increase number of jobs of one closed class in this case Mixed models can be analyzed too Remember that only models with closed classes at least one will be considered in this What If Analysis e Arrival Rate only if there are open classes Arrival rate is the frequency at which jobs arrive at a station during a period of time Similarly to th
245. value is random which indicates that the simulation engine will pick a seed of its choice in a pseudo random fashion each time it is started deselect random and insert a number if you want a custom simulation Maximum duration sec It represents the maximum amount of time in seconds that the simulation will run If the simulation ends before the maximum duration the parameter is ignored and does not affect the results The default value is infinite deselect it and specify the preferred maximum time if you do not want the simulation to run for a possibly very long time In this case the simulation stops when the time limit is reached although a solution may not be available yet Maximum number of samples It is the greatest number of samples for each index that JSIM collects before ending the simulation During a simulation measurements can be stopped in case of e Success if the results have reached the required Confidence Interval and the Max Relative Error e Failure if the simulation has analyzed the maximum number of samples but has not reached the required Confidence Interval or Max Relative Error e Failure if timeout occurs before successfully calculating the final results The default value for the maximum number of samples is 500 000 you may increase it for a more accurate simulation o decrease it for a faster simulation Representation Interval sec This is the granularity at which results are plotted on the
246. vex Hull Graphics Saturation Sectors Text Figure 5 3 Tab selector 5 2 MODEL DEFINITION 111 Number Max 3 2 E Mew Class Figure 5 4 Number of classes 5 2 2 Classes Tab An example screenshot of this tab can be seen in Figure 5 1 This tab allows to set the number of custumer classes It s possible to set two or three clesses The number of classes in the model can be specified in the corresponding input area shown in Figure 5 4 and can be modified using the keyboard or the spin controls Using the delete button X associated to a specific class a class can be removed provided that there will be at least one class after the deletion Similar result may be obtained using spin controls decreasing classes number in this case last inserted class will be removed Default class names are Class1 Class2 ClassN The model can be personalized by changing these names 5 2 3 Stations Tab The number of stations of the model can be specified in the corresponding input area Figure 5 5 and can be modified using the keyboard or the spin controls Mumber New Station Figure 5 5 Number of stations Using the delete button associated to a specific station a station can be removed provided that there will be at least one station after the deletion Similar result may be obtained decreasing stations number using spin controls in this case last inserted station will be removed Default station names are Stat
247. x with the selected probability 1 a or equivalently if an experiment is repeated many times in 1 a 100 of cases Various difficulties in meeting theoretical assumptions can cause that the real percentage of the confidence intervals containing the true parameter differs significantly from 1 a The robustness of the above methods of data collection and analysis is usually measured by the coverage of confidence intervals defined as the frequency with which the intervals X n Az X n Ax contain the true parameter value ug at a given confidence level 1 a 0 lt a lt 1 The coverage analysis can be applied only to systems with a theoretical well known behavior since the value of uy has to be known Any analyzed method must be applied in a statistically significant number of repeated simulation experiments usually 200 or more replications to determine the fraction of experiments producing the final confidence intervals covering the true mean value of the estimated parameter 3 5 2 Max Relative Error Let x be the true value of a quantity and x be the measured or inferred value The relative error is defined by X Mr Eza k a X n Mol where X n Y where ug is the mean value The relative error is the sum of the deviations between the sample values and the mean value divided for the mean value 3 6 Simulation Parameters The Define Simulation Parameters window can be reached either by selecting Simulation Parameters ms
248. y makes sense only when there is a join station downstream from the fork station that can recompose the split jobs Otherwise inconsistencies in the model and subsequent simulation error such as out of memory may occur No automatic checks are available at the moment that can identify such critical conditions Both the forking degree and the capacity are section parameters to be specified in the model As an example a Fork station with forking degree 1 connected to three Server stations would split a job into 3 sibling tasks this is a traditional Fork Join like behavior If no Join station is connected to any of the three Servers a warning message is displayed since the model 4 2 DEFINING A NEW MODEL 87 could quickly saturate due to the extra load 3 more jobs created in addition to each job entering the Fork station In the Station Parameters page of the tabs menu you can modify Fork Section in this section you can choose the forking degree of a job on each outgoing link and the fork station capacity i e the maximum number of jobs that can be served in parallel by the station For more information see Fork section section 4 2 2 Queue Section in this section you can choose the type of queue finite or infinite of the fork station in case its capacity is finite and jobs must wait before proceeding through the fork station For more information see Queue section section 4 2 2 4 Join station QO oin stations are compleme
249. you can drag a station and see what will change in your model Step 6 Saturation Sectors Text If you use Next gt command again you will see the Saturation Sectors Text a simple textual report about the Saturation Sectors 5 4 2 Example 2 A three class model Solve the multiclass open model specified in Figure 5 24 The model is characterized by three A B and C X Disk Disk Disk 2 Figure 5 24 Example 2 network topology There are three stations identified with names CPU Disk1 and Disk2 Service times and visits for stations are shown in Table 5 2 and Table 5 3 CPU Disk1 Disk2 Class A s 0 38 0 30 Class B s 0 62 0 80 Class C s 0 42 0 50 Table 5 2 Example 2 service times 122 CHAPTER 5 JABA ASYMPTOTIC BOUND ANALYSIS CPU Disk1 Disk2 Class A Class B Class C Table 5 3 Example 2 number of visits Step 1 Classes Tab It is the same procedure of the Example 1 subsection 5 4 1 You have only to add one more class Step 2 Stations Tab It is the same procedure of the Example 1 subsection 5 4 1 Step 3 Service Times and Visits Tabs e use Next gt command to switch to Service Demands Tab e press Service Time and Visit button if you don t know the Service Demands of the three stations Now Service Times and number of Visits should be typed After button pressure the Service Demands Tab will be hidden and Service times Tab and Visit Tab will appear

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