A performance analysis tool of discrete
Contents
1. Transitory Plot click on the picture to obtain the time GE TF 00 37 74 11 1 148 18 5 22 2 25 8 295 33 2 369 406 44 3 48 0 51 7 55 4 59 1 62 8 665 702 73 8 77 5 Fig A 14 Number of entities processed in a system Once the plot is shown on the screen it is possible to click over it to obtain information about which time it matches Fig A 15 to help the user define the timing 46 0 54 0 60 0 66 0 72 0 78 0 84 0 90 0 36 0 102 0 108 0 114 0 120 0 126 0 Fig A 15 Window showing which time is for the selected point Software CASA User s manual Page 11 A 7 Calculate the number of replica The study that is done in this window consists in determining which is the number of replica needed in order to have the confidence interval of one of the results of the simulation equal to a selected 2 wide Regarding the graphic aspect and user interaction when beginning this analysis a panel similar to the previous is shown but with some differences The part designed to choose the text file is identical but in the part that uses the current SIMAN model a list appears with all the variables about which it is possible to obtain information through simulation Fig A 16 Text File Use a text file Choose file Current File Use current model There is a model opened ntity 1 TotalTime Entity 1 VVaitTime Entity 1 NumberOut Entity 1 VA Time Proceed Fig A 16 VVindovv to calculate the number of re2. Check the FreeHEP home page for more info Permission to use and or redistribute this work is granted under the terms of the LGPL License with the exception that any usage related to military applications is expressly forbidden The software and documentation made available under the terms of this license are provided with no warranty In order to use this software it is necessary to have at one s disposal the Rockwell Arena Software Fig A 28 Information Panel
3. 2 727896666666667 Standard Deviation 1 6516345439190436 Standard Error 0 6742769790260116 Real System Mean 4 75 TO 0 027189617773716535 alpha 0 05 T Student 0 025 5 2 5705818362903066 ITO lt T Student 0 025 5 Model is accepted as VALID Calculate Risk of accepting a non walid model Replication number 6 Lambda 0 8 Current Risk 0 6438261406288355 In order to hawe the Desired Risk 0 2 15 replications would be needed Fig A 20 Result screen of the model validation Finally the three results and a summary in a text field of all de detailed calculation process are presented In case of working with a text file entering the datum as the difference of results of the simulation with those of the real system and comparing with a u equal to 0 the case of a set of entrance exit datum can be calculated A 9 Comparison between two models Another interesting option is to be able to compare two different models In fact what it is needed is to determine the confidence interval of mean differences with a t Student statistic In case that this interval contains zero value the difference between the two models is not significative Before this however the test of hypothesis of the equality of the variances is carried out from the distribution of Fisher Snedecor in totally transparent way to the user In the upper part of the screen there is a field to choose a second model which will be compared with t
4. arenasimulation com must be available in order to use its SIMAN compiler linker and simulation programs The input SIMAN files can be either generated by the PIPE module described in the previous section or by the ARENA software The CASA software has the following options model simulation specification of the warm up period computation of the number of replications required model validation comparison between two models and factorial design Theoretical expressions used are obtained from Banks et al 1996 Model simulation Once the SIMAN model is loaded the simulation utility allows the simulation of the model A command window is opened where the different calls to the compilation linking and execution programs are automatically performed The output data is shown in text format Specifying the warm up period This option allows the determination of the warm up period The MOD file is shown to the user where he specifies the variable to be used for determining the warm up period It can either be a Window Sira ata Daviciinn a0 Moan wade Taansdary Pt clech on Ue pecbere bo atria the tie snr rors va 1 a a bits 1 Eli Figure 4 Warm up Period Panel variable computed at the exit of a block e g parts produced or a variable computed between to blocks e g time in queue or WIP In either case the software allows the use of the moving average method to filter the data using a chosen window size w Sa
5. corresponding panels are as follows 1 Open and Save files 2 Edit Modify Models 3 Compilation and simulation 4 Autocorrelation Analysis 5 Warm up Period Analysis 6 Calculate the number of replica in order to obtain a certain result 7 Validate the model with the real system 8 Comparison of two models 9 Factorial Analysis 10 Information Panel A 2 Open and Save files When the software is run the panel shown by default is the panel to open and save files as can be seen in Fig A 2 In this panel the user must select the folder where ARENA is installed if he has not done it before and using the three buttons below open a new model close the one in use without saving changes or save the model in use Open i Close Save as Fig A 2 Panel to open and save files Software CASA User s manual Page 3 Although some of the software s options can be used with text files containing numeric data the most useful and practical way to use CASA is through SIMAN code files These files are simulated using the Rockwell Automation software ARENA www arenasimulation com which has an educational version available To do this it is necessary to specify the folder where this software is installed which can be done using the Browse button in the Arena Path field The folder is stored in an internal file so that it won t be necessary to specify it again Once the folder is selected it is shown as in F
6. defined in the corresponding type D place Once the Petri net is defined the SIMAN code generation module can be executed Figure 2 The module first makes a validation of the net in order to avoid future parsing problems This validation consists in the following verifications 1 Type A places Existence of at least an input arc and initial marking set to zero 2 Type B places Non null initial marking 3 Type C places Specification of a family group and non null initial marking per group Figure 3 Example Net 4 Type D places Existence of at least one type D place existence of at least one output arc and either the existence of a non null initial marking or the specification of the time between arrivals 5 Non existence of isolated transitions or places 6 Non existence of repeated arcs 7 Non existence of multiple input arcs if there are non unitary weights 8 Non existence of multiple output arcs if there are non unitary weights Steps 1 to 5 are strictly necessary for the correct parsing to a SIMAN model Step 6 solves a PIPE bug and steps 7 and 8 greatly simplify the parsing process Whenever one of these steps fails the module warns the user indicating where the problem is located Figure 2 shows a case where there is a problem with the initial marking of type B places Once the problems are solved the Generate Code button is activated and when pressed the SIMAN code is generated and a window is opened with the c
7. drawing and analyzing Petri nets developed at the Department of Computing at Imperial College London Figure 1 Some of its available modules include invariant analysis simulation state space analysis and comparison and classification New modules can be developed and easily incorporated SIMAN is a general purpose simulation language vvhich incorporates special purpose features for modeling manufacturing systems Pedgen 1986 It is one of the best and first developed simulation languages extensively used Taking into account this and the use of the extensibility property of PIPE this paper will introduce both 1 The development of a PIPE module able to automatically generate SIMAN code from a Petri net model of a system 2 The development of a software tool to aid in the performance analysis of a system described with its SIMAN model The tool must help the user in the specification of the warm up period the computation of the number of replication required the validation process the comparison between models and the specification and execution of factorial designs As extra requirements the developed tools must be open source developed in Java and must provide the capability of executing the SIMAN models on a remote simulation server through the WEB This will allow the sharing of software and hardware resources over the Internet independent of the user s platform Guru et al 2000 After this introduction the paper is struct
8. in the currently open model Pressing Go Back returns to the previous window Fy Computer Aided Simulation Analysis Modify Experiment File Model statements for module Process 1 ASSIGN Process 1 NumberIn Process 1 NumberIn 1 Process 1 WIP Process 1 WIP 1 DELAY Triangular 5 1 1 5 VA ASSIGN Process 1 NumberOut Process 1 NumberOut 1 Process 1 WIP Process 1 WIP 1 NEXT 2 Model statements for module Dispose 1 ASSIGN Dispose 1 NumberOut Dispose 1 NumberOut 1 DISPOSE Yes Model statements for module Dispose 2 ASSIGN Dispose 2 NumberOut Dispose 2 NumberOut 1 DISPOSE Yes Store Changes Go back Fig A 6 mod and exp manually modifiing window Software CASA User s manual Page 5 If the user does not know how to modify SIMAN code directly the option Modify Experiment Parameters can be used to be assisted by the computer This option allows the user to modify failures resources and replication parameters in an easy way Fig A When this option is activated the computer shows the current experiment file information and modifies it It is necessary to save the changes every time that a line is modified to save them properly Finally with the store changes button all the changes are stored in the model in use Failures Count Time Count GAMMAC 3 20 Down Time GAMMACT 1 0 Save Failure Resources ResourceP5 Failure lt No Failure Replication P
9. incomplete beta function This value is computed graphically in Banks 1996 The user can specify a desired maximum risk f f and then the program outputs the number of replications required to achieve it Comparison between two models This option allows the comparison between the loaded SIMAN model and another one that is loaded when the comparison module is opened The comparison is done considering independent sampling The user specifies which variables are to be compared and then the simulation of the models is performed Then the confidence interval of the difference of means is computed 7 7 t se 5 Whenever this confidence interval contains zero there is not strong statistical evidence that one system design is better than the other To compute this confidence interval the test of equal variances is performed This test uses the Fisher Snedecor distribution 1 e 1f S IE lt FR Ra 6 Si then both variances are considered equal In this case the standard error of the difference is computed as follows R 1 S R 1 S Se a 7 R R 2 1 s e Sp La Es 8 R R And the degrees of freedom are v R R 2 1 alpha 95 Goback 90 95 100 Results Effect Results Effect 1 Cl 2 505 0 648 186 3 15 Effect 2 Cl 1 577 0 91 Effect 3 Cl 6 498 1 767 8 26 4 73 Figure 6 Detail of the Factorial Results Otherwise when variances are considered une
10. top The other area is needed to work with the model If the user wants to introduce the data with a text file it must contain two columns separated by a tabulator key The first column must contain the timing and the second column the data to analyse Information about various replications must be added without any kind of extra information just repeating the timing column Software CASA User s manual Page Computer Aided Simulation Analysis Select Source i fe Text File Use a text file Choose file ye Current File Use current model There is a model opened BRANCH 1 With 50 100 8 Yes Else 9 Yes ASSIGN Decide 1 NumberOut True Decide 1 NumberOut True 1 NEXT 1 ASSIGN Decide 1 NumberOut False Decide 1 NumberOut False 1 NEXT 3 Model statements for module Process 1 1 ASSIGN Process 1 Numberin Process 1 Numberin 1 Process 1 VIP Process 1 VVIP 1 11 DELAY Triangulari 5 1 1 5 VA 58 ASSIGN Process 1 NumberOut Process 1 NumberOut 1 Process 1 VVIP Process 1 VVIP 1 NEXT 2 Model statements for module Dispose 1 ASSIGN Dispose 1 NumberOut Dispose 1 NumberOut 1 DISPOSE Yes Model statements for module Dispose 2 i Number of Hours to calculate production for each of these number of hours 2 Proceed Fig A 9 Autocorrelation panel Data selection If the model is used the data to study must be the number of entities that pass through a determined poi
11. 4 137585187809497 Iteration 2 Current R 14 T Student 0 025 13 2 160368723 2097077 Optimal R gt 13 89924113038106 Iteration End Current R gt Optimal R R 14 Cl wide epsilon 0 04 Calculate Fig A 18 Result screen of the calculation of number of replica Software CASA User s manual Page 13 Finally we must consider that when we introduce the datum as a text file it should have a specific layout In fact it should be introduced as the form of a column the medium value that the variable has taken in each of the replica simulated A 8 Validate the model with the real system The aim of the validation of a model panel consists in the verification of the kindness of the results of the simulation through the comparison with the mean of the real system Three results are found acceptance or not of the model as valid risk of accepting a non valid model number of necessary replica to respect a certain limit risk The panel s graphic structure is in the beginning similar to the former point Thus the user can choose between using a text file or an opened model of which he should select a variable to be studied The information in the text file must be presented in column form in order to have a correct datum interpretation In the second screen the user has got four fields to fill in before carrying out the calculations Fig A 19 In the upper part it is necessary to determine the value of the
12. O NumberOut Create PO NumberOut 1 NEXT 3 BRANCH 1 With 0 8 45 Yes With 0 2 5 Yes DELAY 0 NEXT 6 QUEUE Seize T1 Queue SEIZE 2 Other Resource P3 1 NEXT 8 DELAY EXPO 1 1 NEXT 9 DELAY 0 NEXT 10 DELAY EXPO 0 5 NEXT 11 RELEASE Resource P3 1 NEXT 10 10 DELAY EXPO 2 NEXT 12 12 DUPLICATE 1 3 ASSIGN Dispose T4 NumberOut Dispose T4 NumberOut 1 DISPOSE Yes Table 2 SIMAN EXP File PROJECT Unnamed Project Siman Code Generation No Yes Yes Yes No No No No No FAILURES Failure 0 Count GAMMA 7 15 GAMMA 2 3 RESOURCES Resource P3 Capacity 1 FAILURE Failure 0 Ignore REPLICATE 10 HoursToBaseTime 160 Yes Yes 24 Hours No No Yes VARIABLES Create PO NumberOut CLEAR Statistics CATEGORY Exclude Dispose T4 NumberOut CLEAR Statistics CATEGORY Exclude ENTITIES Entity PO QUEUES Seize T1 Queue FIFO AUTOSTATS Yes DSTATS Create PO NumberOut aCreate PO NumberOut Dispose T4 NumberOut aDispose T4 NumberOut CASA COMPUTER AIDED SIMULATION ANALYSIS Specification The CASA software has as objective the aid in the performance analysis of discrete event simulations The program has different features like model validation or factorial design The results of the simulations are obtained by executing the SIMAN models or in some cases they can be provided by data text files The ARENA simulation software www
13. UNIVERSITAT POLIT CNICA DE CATALUNYA A performance analysis tool of discrete event systems Albert Penarroya Francesc Casado Jan Rosell IOC Divisi de Robotica IOC DT P 2007 1 Gener 2007 Institut d Organitzaci i Control de Sistemes Industrials A PERFORMANCE ANALYSIS TOOL OF DISCRETE EVENT SYSTEMS Albert Pe arroya Francesc Casado and Jan Rosell Institute of Industrial and Control Engineering Technical University of Catalonia Barcelona Spain E mail jan rosell upc edu A PERFORMANCE ANALYSIS TOOL OF DISCRETE EVENT SYSTEMS Albert Pe arroya Francesc Casado and Jan Rosell Institute of Industrial and Control Engineering Technical University of Catalonia Barcelona Spain E mail jan rosell upc edu KEYWORDS Petri nets SIMAN Discrete event simulation Computer aided tools ABSTRACT The analysis of the logic correctness of the system and its performance evaluation are usually carried out using respectively the Petri nets formalism and the discrete event simulation Several tools exist for both The Platform Independent Petri Net Editor PIPE is a free software tool developed in Java for the modeling simulation and qualitative analysis of Petri nets It has been designed with an open philosophy so that extensions can be easily incorporated SIMAN is one of the first discrete event simulation languages developed It has extensively proven its power This paper first presents a module for the PIPE software that all
14. a if i wl m w y WwW C 7 1 gt Ves s i l Si i o if il 2i I 4 Computing the number of replications required This option computes the number of replications needed in order to obtain confidence intervals with a specified precision If the desired half width of the confidence interval is then the following iterative procedure is programmed to compute the required number of replications 1 Starting with Ro replications estimate o by S 2 a 0 R I R 1 R gt 2 E 2 Estimate a first value of R by substituting t by z in expression 2 RI A 2 2 3 Increment R until 2 is satisfied using t RI 2 The program shows a text window with the final result and all the intermediate results of each iterative step performed Model Validation This option is an aid for the validation of the model The real system data used for the validation 1s the average of one of the performance measures selected by the user uo The statistical t test is performed First it determines Vou lo 3 Sin Then if tol lt t the model is accepted with a probability a of having rejected a valid model n 1 2 Then the probability of having accepted a non valid model is computed as Ferris et al 1946 l Nos ea pae go fesa r 0 r Lee 0 2 n 1 t where is the allowed difference between the model and system means n is the number of replications and I p q x is the
15. arameters Humber of Replications 10 Warm Up Time Replication Length HoursTobaselimerl 60 Hours per Day 24 Terminating Condition Save Replication Parameters Store Changes Fig A EXP file parameters modification window A 4 Compilation and execution This panel s function is to simplify the compilation and simulation of the models This process is divided in four steps compilation of the model file compilation of the experiment file gir Page 6 linkage of both files and simulation That is why this window has four buttons Fig A 8 one per each step Under the buttons there is a window where the results of each step are shown for the user to know if there is any problem Result Space Utilization Category quantity Numeric Character Elements 8 0 1 0 15 Blocks 10 D DE D 0 Entities 100 0 18 Attributes O per 0 0 entity TOTAL 0 33 D 25 Maximum SIZE 1200000 1500000 Extra data space for elements OK bytes Total data space required 6389K bytes Link completed with O error s and OD marning s Fig A 8 Compilation and Simulation panel A 5 Autocorrelation analysis This panel is used to study the independence and randomness of the numeric values obtained with the simulation of the model The method consists in drawing the autocorrelation graph and dispersion diagram When the user accesses this panel Fig A 9 two sections can be observed There is the option of using a text file at the
16. between two points Fig A 12 If that is the case two lines of the code must be selected Software CASA User s manual Page 9 Humber of Entities select only a line La Humber of Entities select only a line Average of Entities select two different lines Fig A 12 Two options in the warm up period panel To work with the number of entities through a point one line must be selected to add a counter in the model before the chosen line In case of studying the average number of entities the software calculates the average of entities from a mark before the first line to a mark after the second one If the user wants to work with a text file tt must follow the same rules as in the previous case However the following window when clicking over Proceed is different There are two options on the top of the panel for the user to define Fig A 13 First of all the wide of the window used to filter the data must be specified Window Sire Data Division 20 4 Mean wide Fig A 13 Warm up Period Panel options The second parameter is optional and can be used to divide the graphic in blocks in order to see the median of each block and determine the warm up period in an easier way When the button Generate is pressed the plot is generated using the Welch method and the divisions if they have been selected Fig A 14 Page 10 F Computer Aided Simulation Analysis Window Size Data Division METS Mean wide 10
17. e translation to SIMAN allows a better simulation of manufacturing systems since the new incorporated module permits among other features the introduction of different time distributions or the definition of failures Moreover the obtained SIMAN code facilitates the use of the second tool for the performance analysis of the system The second tool introduced in this paper is the software CASA Computer Aided Simulation Analysis It has been developed as an aid in the performance analysis of manufacturing systems modeled using SIMAN It has several features not encountered in other simulation packages like the capability of performing factorial designs or model validation Both tools are currently being used in undergraduate courses at the Industrial Engineering School of Barcelona Technical University of Catalonia They are available at lafarga cpl upc edu REFERENCES Banks J Carson J and B Nelson 1996 Discrete Event System Simulation Prentice Hall Upper Saddle River NJ USA Desel J 2000 Teaching System Modelling Simulation and Validation in Proceedings of the 2000 Winter Simulation Conference pp 1669 1675 Ferris C L Grubbs F E and C L Weaver 1946 Operating Characteristics for the Common Statistical Tests of Significance Annals of Mathematical Statistics June 1946 The Institute of Mathematicals Statistics Guru A P Savory and R Williams 2000 A web based interface for storing and Execu
18. efresh D places WELL DEFINED OK No Free Transition OE No multiple arcs per path DE ONE 21 WT arc into trans OF ONE 21 WT arc From trans OK Edit Places Figure 2 SIMAN Code Generation Module SIMAN code generation module In order to include this new module the following changes have been introduced to the basic PIPE functionality First the capacity to distinguish between different types of places type A places to represent activities type B places to represent finite resources like machines or robots type C places for control places and type D places to represent the system input or variable resources like pallets or fixtures Second the capacity to introduce code into the net places in order to specify some parameters and values needed when translating to SIMAN In order to generate SIMAN code from a Petri net first it is necessary to specify the type of places and the initial marking Then the code associated to each place must be introduced For type A places it is necessary to specify the delay time of the activity for type B places the time between failures and the downtimes for type C places the group to which they pertain since type C places are grouped in sets for type D places the time between arrivals whenever they represent the system input Moreover if there is a conflict in type A or type D places it is necessary to specify how it 1s to be solved 1 e by chance or by the type of entity which is
19. en introduced the software carries out all the combinatory of effects and levels automatically does the pertinent simulations and goes to the following Page 18 screen In this new screen the user must specify the confidence desired for the confidence interval and with which variable to study Fig A 26 Cl th xi S S D 1 alpha 95 90 Variables to Study Sa ntity 1 TotalTime Bi Entity 1 WaitTime Entity 1 NumberOut Entity 1 VYA Time El i Fig A 26 Parameters for the calculation of the factorial design effects Afterwards when clicking the Select Variable button the main effects of the several factors are calculated as well as their confidence interval and they are presented in a graphic and intuitive way in order to compare all the effects Fig A 27 Finally the user can go back and select another variable with the Go Back button CI 1 alphaj g5 g0 94 100 Results Effect Results Effect 1 CI 2 505 0 648 Effect 2 Cl 1 577 0 91 Effect 3 CI 6 498 1 767 Fig A 27 Result screen of the factorial analyisis A 11 Informative Panel This last panel offers extra information in relation with this software Precisely it offers information about the software version about the authors and about the Colt package which is the free statistical package that has been used to carry out some calculations The Fig A 28 shows
20. exactly which is this information Software CASA User s manual Page 19 Software CASA Computer Aided Simulation Analysis Freeware amp Opensource version 1 0 NN Authors Es This softuare has been developed as a part of the Master Thesis done by Francesc Casado i Pastor and Albert Pe arroya Isanta both students at the Industrial Engineering School of Barcelona ETSEIB Technical University of Catalonia UPC re under the supervision of Prof Jan Rosell Gratac s member of the Institute of Industrial and Control Engeneering IOC Technical University of Catalonia UPC Extra Information This software makes use of the Colt 1 2 0 Packages available through the Internet i pac EI Colt License Agreement Packages cern colt cern jet cern clhep Copyright c 1999 CERN European Organization for Nuclear Research Permission to use copy modify distribute and sell this software and its documentation for any purpose is hereby granted without fee provided that the above copyright notice appear in all copies and that both that copyright notice and this permission notice appear in supporting documentation CERN makes no representations about the suitability of this software for any purpose It is provided as is without expressed or implied warranty Packages hep aida Written by Pavel Binko Dino Ferrero Merlino Wolfgang Hoschek Tony Johnson Andreas Pfeiffer and others
21. he one that was opened before In the central and inferior part there are two Software CASA User s manual Page 15 lists With these two lists the user can select which variable will be used in the comparation Fig A 21 Clicking on the Proceed button the next screen is shown Open Model 2 Select the second model Select Model variable Enot Entity 1 TotalTime Entity 1 VVaitTime Entity 1 NumberOut Entity 1 VATime eeri Select Model2 variable Entity 1 VaitTime Entity 1 NumberOut Entity 1 VATime Process 1 Queue WaitingTime Process 1 Queue NumberinQueue Resource 1 Utilization Fig A 21 Screen for the comparison between two models If there is any problem a warning message appears on the screen and if not a new screen is shown In this screen the user must select the two parameters shown in Fig A 22 the confidence percentage for the interval to calculate and the queue area value for the Fisher Snedecor test Cl i F Snedecor Variance Analysis al Queue area J 0 25 1 alpha g5 g0 94 100 Fig A 22 Parameters to determine for the two models comparison Page 16 When clicking the Calculate button the software realizes all the required calculations and draws on the screen Fig A 23 the found interval as well as other datum of interest related to the calculations Cl F Snedecor Variance Analysis 1 alpha Queue area Calculate 90 Results Model A Entity 1 TotalTi
22. ig A 3 Arena Path CArchivos de programaiRockwell Softwarearena T O Fig A 3 Arena folder selected In order to work with a SIMAN coded model it must be in use This action must be done using the button Open and selecting the model mod file in the drive The experiment file must be stored in the same folder and must have the same file name for the software to find it Once a model is opened it is shown as in Fig A 4 Open i Close i Save as Open new model Close current model Save Current model as There is a model opened Fig A 4 Open close and save file buttons A model is in use If the user closes the model the software returns to its previous state and the changes done to the model are lost If it is necessary to store the changes the third button Save must be used A 3 Edit Modify models This panel allows the user to edit or modify the model in use Modifications can be done manually or assisted by the computer just by clicking on the chosen button shown in the monitor Fig A 5 Page 4 Manual Change Edit mod File Edit exp File Modify Experiment Parameters Fig A 5 Model Edition options In order to manually modify any of the two files mod o exp it is necessary to click on the chosen Edit button in Manual Change In both cases a window such as the one in Fig A 6 is shown where the code lines can be modified freely Once the changes are done Store Changes button must be pressed to save them
23. me Model B Entity 1 TotalTime Data Info Model Current Cl 6 11 2 23 Variance e A Replic 8 34 3 88 fo Model 4 mean is lower than model B mean tw i a toll Mean B 6 59886 Variance A 0 0021247222933333345 Variance BJ 9 976945353777776 alpha 0 05 F Snedecor Queue Area 0 25 Second model Variance is higher F Sb Sa 4695 646760558819 F Sned 0 25 9 9 1 590910000001955 The assumption of equal variances is false Standard Error va Yb 0 9989529556526228 Freedom degrees 10 T Student 0 025 10 2 22813885 20055887 6 108586 2 2258058918154244 8 334391891815425 3 8827801081845754 Model A mean is lower than model B mean Fig A 23 Result screen of comparison between two models A 10 Factorial Analysis In most of simulation studies it is necessary to compare configuration alternatives or different scenarios in order to be able to choose the one with the best results while taking the disposable resources into account The factorial design is used to study this type of comparison This software permits to carry out a factorial study at two levels through two and six factors In the upper part of the factorial analysis screen there is a slider bar Fig A 24 used to select the number of effects Software CASA User s manual Page 1 Humber of parameters ap Please select the number of parameters to change 2 3 4 5 Gi Fig A 24 Selectio
24. n of the number of effects Then clicking the Continue button the effects can be specified To specify them it is necessary to change the lines of the model or experiment files in a space in the screen s inferior part The original line corresponds to the level whereas the modified one corresponds to the level Fig A 25 Thus a same line can not be twice modified since the program interprets the change like a single line To choose among the mod and exp files there are two radio buttons that generate a new list of the former type ASSIGN Decide 1 NumberOut True Decide 1 NumberOut True 1 NEXT 1 ASSIGN Decide 1 NumberOut False Decide 1 NumberOut False 1 NEXT 3 Model statements for module Process 1 1 ASSIGN Process 1 Numberin Process 1 Numberln 1 Process 1 WVIP Process 1 VWIP 1 11 DELAY Triangulari 5 1 1 5 VA 58 ASSIGN Process 1 NumberOut Process 1 NumberOut 1 Process 1 VVIP Process 1 VVIP 1 NEXT 2 AGT ModFile ExpFile f Model statements for module Dispose 1 ASSIGN Dispose 1 NumberOut Dispose 1 NumberOut 1 DISPOSE Yes Model statements for module Dispose 2 ASSIGN Dispose 2 NumberOut Dispose 2 NumberOut 1 DISPOSE Yes Insert here the changes you desire to make in the selected line 119 DELAY __ Triangular 5 1 5 1 76 VA Continue Fig A 25 Specification of levels for the factorial design When all effects have already be
25. nt in the model This point is selected by the user by clicking on one line of the code the program will count the number of entities that pass just before the point selected The time interval between measures must be defined with the camp available at the bottom The time interval cannot be higher than the total time of simulation When clicking on the button Proceed the software reads the text file or compiles and simulates the model depending on the option chosen In the next panel lag must be defined in order to calculate the dispersion diagram Fig A 10 After that when clicking on the button Graficate the results appear on the screen Fig A 11 Lag Fig A 10 Autocorrelation options Page 8 Ea TEE fe Correlation Plots Autocorrelation Lag 1 159 fee sty EA i ALA aN AAMA ARA i TAL VUIT UN Dispersion LAG 1 R 1 0 099 Fig A 11 Autocorrelation graph and dispersion diagram vvith chosen lag A 6 Warm up Period Analysis When a model is created and simulated it is interesting to obtain information in a stationary mode so that the warm up period does not interfere in the results That is why it is interesting to determine the moment in time where the warm up period can be considered to be ended This panel works as the one before with the little difference that apart of working with the number of entities that pass through a point it does also accept the average of entities stored
26. ontents of the MOD and EXP SIMAN files which are respectively the model and the experiment components that correspond to the logic and data in the model These files can then be stored to disk An Example The following simple example illustrates some of the features of the SIMAN code generation module The Petri net is shown in Figure 3 It is a cyclic net where type D place PO represents the availability of three parts to be processed Type A places Pl P2 and P4 represent three different activities Parts are processed either by P1 and P4 or by P2 and P4 Activity P2 requires the use of the resource represented by type B place P3 The following code is introduced into the net places Place P0 Code indicating that the conflict is solved by chance 20 of parts go to place P1 80 to place P2 decide probability T0 0 8 T1 0 2 i Place P1 Code indicating the delay time delay EXPO 1 1 i Places P2 and P4 Code indicating the delay time EXPO 0 5 and EXPO 2 respectively in a similar way as place P1 Place P3 Code indication the time between failures and the downtime H failures timeON GAMMA 7 15 timeOFF GAMMA 2 3 H The SIMAN code obtained is shown in Table 1 and Table 2 The MOD file includes the program flow while the EXP file includes the definitions of the variables and resources Table 1 SIMAN MOD File CREATE 3 HoursToBaseTime 0 0 Entity PO HoursToBaseTime 1 1 NEXT 2 ASSIGN Create P
27. ows the automatic generation of SIMAN code from a Petri net Then a tool is proposed to aid the performance analysis of manufacturing systems from its SIMAN model These tools are designed as a support for students in the understanding of the simulation methodology INTRODUCTION The two main objectives when analyzing a manufacturing system are the evaluation of the logical correctness i e the qualitative analysis and the evaluation of its performance 1 e quantitative analysis Petri nets formalism and discrete event simulation are used to carry out these objectives and therefore both must be included in the engineering students curricula Desel 2000 Taking into account this the objective of this paper is to introduce an aid to help students in the understanding of the use of simulation techniques as a methodology for the analysis of manufacturing systems Petri nets are a formalism that allows the modelling of systems involving concurrency resource sharing synchronization and conflict and allows the validation of the correctness of the system by analyzing the qualitative properties of the net modelling the system Murata 1989 There are several software tools see the Petri Nets World web www intormatik uni hamburg de TGI PetriNets tools that allow the modeling simulation and analysis of Petri nets The Platform Independent Petri Net Editor PIPE http pipe2 sourceforge net is a Java based open source graphical tool for
28. plica Afterwards when the Proceed button is clicked a new screen is shown where the user must fill in two fields which are the confidence desired for the statistic and the wide of the confidence interval Fig A 17 Page 12 CI 1 alpha 90 95 s 100 Cl wide epsilon 2 be Fig A 1 Parameters needed to calculate the number of replica Then when clicking the Calculate button the software reads the datum and carries out the iterative calculations needed to determine the number of replica The current and the desired intervals as well as the number of replica that are necessary or sufficient to achieve this interval are shown Besides the final results the software shows on the screen all the iterative calculation so that the user can have the information of the process in detail Fig A 18 Cl 1 alpha 95 90 95 100 Results From a text File Data Info Mean 0 8 Standard Error 0 03 Number of Replications 4 Current Cl 0 8 0 11 Desired CI 0 8 0 04 In order to obtain the desired results 14 replications should be done Aproximation using Normal Distribution Normal 0 025 1 959963984540054 Optimal R gt 11 440144474399451 gt Starting R Now we can approximate using T Student Current R 12 T Student 0 025 11 2 200985160097668 Optimal R gt 14 426784872870767 Iteration 1 Current R 13 T Student 0 025 12 2 1788129801929554 Optimal R gt 1
29. qual standard error of the difference is computed as follows 2 se 9 7 9 and the degrees of freedom are 2 R R v 10 b 5 R R a OOO ae R 7 1 R 7 1 As in other program options all the computations are shown to the user in a text window Factorial design The last option of the program allows the performance of a factorial design using up to six factors Each factor is assigned two values The user selects the number of factors to consider and introduces two values to be considered for each of them The program automatically computes all the possible combinations design points and executes the corresponding replicates of each one This option graphically outputs the confidence intervals of each of the principal effects of the chosen factors Figure 6 When the confidence interval does not include zero then the factor is considered significant CONCLUSIONS The availability of software tools for the understanding of the simulation methodology in the analysis of manufacturing systems is a key aspect for engineering studies This paper has proposed two tools that cover both Petri nets and discrete event simulation First a module that automatically generates SIMAN code from Petri nets has been incorporated to the Platform Independent Petri Net Editor PIPE an open source graphical tool for drawing and analyzing Petri nets Although PIPE allows the simulation of Petri nets th
30. statistic for the calculation of the interval C section and which is the mean of the real system Real system mean Moreover it is necessary to fill in the field of the B desired value maximum risk of accepting a non valid model which is allowed and the A value maximum normalized difference between the model mean and that of the real system CI Real system mean E Mean A3 1 alpha g5 g0 95 100 Calculat Desired Risk Lambda Lambda 0 6 beta ds T 25 40 5 100 Fig A 19 Parameters to be established for the model validation Then when clicking on the Calculate button the calculations with those values are realized and the final results as well as the calculation process are shown on screen Fig A 20 Furthermore general information of the datum with the mean the variance and the number of replica is shown in order to help the user to adjust the real parameters Page 14 m o oo all FR 1 alpha a 90 Mean 4 75 CI Real system mean Desired Risk i ambda Calculate Lambda 0 8 beta 20 K 0 25 50 5 100 Results From a text File Data Info Mean 4 77 Model is accepted as VALID Variance 2 73 Risk of accepting a non valid model 64 0 Number of Replications 6 jj k 0 25 50 75 100 In order to have the Desired Risk 20 15 replications would be needed Replication number 6 Model Mean 4 7683333333333335 Variance
31. ting Simulation Models in Proceedings of the 2000 Winter Simulation Conference pp 1810 1814 Murata T 1989 Petri Nets Properties Analysis and Applications Proc IEEE vol 77 No 4 Apr pages 541 580 Pedgen C D 1986 Introduction to SIMAN in Proceedings of the 1986 Winter Simulation Conference pp 95 103 APPENDIX CASA USER S MANUAL Software CASA User s manual Page 1 A CASA Manual A 1 General Procedure This software has been created in order to help the user to make a quantitative analysis of the numeric results obtained after a discreet event simulation Among the options it offers we could talk about warm up period or auto correlation two model comparison factorial analysis or determination of the number of replications needed Thats why studying this parameters can be automated and simplified However not all the variables can be analyzed because of the characteristics of the simulation code The Graphic Interface is divided into panels which can be selected clicking on the respective tab on the left as can be seen in Fig A 1 Each panel is independent and can carry out the chosen functionality except panels one and two which are meant to open and modify the code files Computer Aided Simulation Analysis occ P Arena Fath File nottound Open i Close i Save as Open a ei E H 00000000009 Fig A 1 Tab Based Structure Page 2 The ten tabs with its
32. ured around two main sections describing respectively the PIPE module and the software tool for the simulation analysis PLATFORM INDEPENDENT PETRI NET EDITOR Description The Platform Independent Petri Net Editor PIPE is a graphical tool for the modelling and analysis of ordinary Petri nets It allows invariant analysis state space analysis and comparison and classification PIPE also offers simulation capability that illustrates the token game through the evolution of the net markings PIPE2 Platform Independent Petri Net Editor 2 Producer amp Consumer xml File view Draw Animate Help Cee t A 0 8 I i sda T H A OD IR SR EH O4 gt 4 6 Analysis Module Manager New Petri net 1 xml FMS xml FMS2 xml i Producer amp Consumer xml 5 0 Available Modules SIMAN Code Generation Simulation State Space Analysis Find Module Figure 1 PIPE GUI Its modular architecture and open source philosophy allows the development of new features In this paper we propose a module to automatically generate SIMAN code from Petri nets This module requires some kind of coloring to the ordinary Petri nets managed by PIPE as explained in the next subsection FI P3 ds SIMAN Code Generation xi Sourcenet ets A RAMNFLAPATEINATS xml Browse aC Net validation 4 places WELL DEFINED OK B places WELL DEFINED FALSE C places WELL DEFINED OK R
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