The first section is a fragment of the user`s manual of the Queuing
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1. Z Cost per time unit this is the cost of maintaining an entity in the queue for one time unit Most QMG blocks have this parameter If different from zero then the cost will be added to the final total operation cost type O if you do not want to calculate the system operation cost Split point First select one of the split rule options By priority you must provide priorities for outputs The entity will look for the output of higher priority If it cannot take this way for example server or assembly that follows is busy etc then the next possible outputis checked according to the priorities By probability you must give N 1 probabilities N being the number of outputs The Nth probability will be calculated so that the sum is equal to one Other rule you can define any other selection rule It maybe any selection algorithm that can be defined as a C function You must provide the corresponding function call Select the Other rule option and type MINQ This is a predefined selection rule that selects the output connected to the shortest queue Servers Distribution this is the function call to a random numbers generator The service time will be generated by the specified generator Type Erlang 2 1 7 for the first server Erlang 2 3 0 for the other Additional delay after leaving the server the entity client can have additional delay before reaching the next block This may be for example a transport delay or2. system equations In the equation d n stands for d xn dt Select Generate code and then Generate and run Now select the simulation mode DIFEQ supports the following simulation modes Varying parameter Preparing files for VARAN Simple run default Consult the DIFEQC help for detail about these run options Select Simple run You also must give the name of the BLUESSS process and the name of the file where the BLUESSS code will be stored Then only confirm defaults or presscontinue or start buttons On the list of include file list will appear the file FUN1 CPP Do not change it this is your FUN1 function You also will see the list of output signals Select all items from the list After this BONDWC generates the system equations fle MYGRAPH EQU and invokes the DIFEQC program It will read the equations generate BLUESSS code invoke the BLUESSS to C translator and finally run the simulation At the run time you must define the parameters Give the following Final time 2 Integration step 0 008 The integration step should be about 5000 time smaller than the simulation final time The initial conditions will appear with the default value zero Do not change them For mor detailed description of the run options consult theDIFEQC The model file equations file BLUESSS code file and the parameters file can have the same name they are given different extensions automatically BND EQU CSM and ICC respectively Now
3. the result of the program run you will see the plots of the output signals for P1 2 to 20 changed in 25 steps exa2 cpg This model is similar to exa cpg but has two input nodes U for the set point and Z for the disturbance Link E Y is a P controller Y X is the controlled process with inertia of the third order P 2 is the controller gain and p 3 is the gain for the disturbance input The parameter P 1 is reserved for the input signal at the node Z While generating the model equation the input at U should be defined as unit step and the input at Z shoud be Other P 1 The signal on P 1 is calculated in a user functions stored in the file parvar cpp This file must be listed on the include file list of FLOWDC The initial conditions and parameters are stored in the file exa2 icc The final simulation time is equal to 15 model time units p 2 3 and P 3 8 After terminating the simulation Bluesss automatically invokes the VARAN program Bond graph examples Mechsys bnd Recall that bond graph is a graphical representation of the dynamics of a physical system used mainly to simulate mechanical systems or electrical circuits This example is described in the sections Getting started and Bond graphs of the manual of the Bond Graph module of Bluesss CP Fig 4 Example of a mechanical system ee sg E E O gt y w px f E Ie px px Fig 5 Bond Graph for the example of fig 4 After entering t
4. 1 OOH 282 00 SERVO 4711 650 SERET ieee 0 00 15800 TERMINAL Count TERM 282 TERMS 158 Total cost 0 00 The queue statistics show the average waiting time maxmal and minimal queue length and average length The LOST columns show the number of entities lost at the corresponding blocks In most cases it should be zero For the servers you can see the total time in service idle time of idle time lost and served entities For the terminal points the corresponding counters show the number of entities that enter the block Note that the two queues have similar length This occurs because the new client selects the shorter queue to wait in However the average waiting time in the second queue is two times greater because the second teller is about two times slower than the first This obviously reflects in the number of clients served by the two tellers Now repeat the simulation starting with Bluesss Queues Declare the use of the VARAN utility Create files for VARAN At the run time declare say 80 repetitions of the simulation run This will create a set of SIM files After running the simulation the VARAN program will be invoked You also can do this executing VARANW EXE Utilities VARAN You will see more statistics as functions of time see VARAN section for more detail Example Group and ungroup a trip This is and example of an application of the group and ungroup blocks Let us simulate a trip by airplane f
5. ONDWC will put the causalities to the model Now save the model use the File Save as menu option Give the file name for example MYGRAPH This example is also available on the original BLUESSS disks stored as MECHSYS BND model Add FUN1 CPP file to the INCLUDE FILE list this will be the file where you will store the FUN1 function You still cannot run the simulation because the model needs the function FUN1 Exit the program and prepare the following C code using any texteditor Float FUNI J4 LP LIME SO 1 return 1007 erse returni r0 Preparing the code it is recommended to use the ifndef 4 endif clause to avoid multiple definitions of the function body The code can be as follows ifndef MYFUN define MYFUN FUNC On definiti n tendif This is a simple excitation the velocity 10 during 0 1time units Note that TIME is the model time Store the function in FUN1 CPP file and return to BONDWC Now Open your model MYGRAPH and select the Generate run Generate and run menu option You will be asked if you wish to calculate the integrals of the flows In the case of a mechanical system these are the positions so respond Y Next BONDWC processes the model You will be shown the list of state variables In this case the variables are as follows x 1 is V x 2 is G The integrals of tlow variables are x 3 integral of V x 4 integral of W x 5 integral of PX You also will see the node parametersand the
6. The first section is a fragment of the user s manual of the Queuing Model Generator module which is a part of the Bluesss simulation package The second section is a summary of some examples of other Bluesss modules For more examples of applications consul the demo available from http Awww raczynski com pn demopn htm SECTION 1 Bluesss Queuing Model Generator module GETTING STARTED To create the first model we will simulate a simple example of a queuing system EXAMPLE A bank employs two tellers Clients enter the bank every 1 minute on average and form separate queues for each teller A new client selects the shortest queue The tellers work with different speed The first one has the average service time equal to 1 7 and the average service time of the other is equal to 3 0 Suppose that the input flow of clients is of type Poisson and that the service time distribution of the two tellers is second order Erlang We want to see the lengths of the two queues and the standard final statistics taken over 480 time units final simulation model time in minutes Enter the QMG program execute it directly or from the Bluesss main program queuing option First select File and New model The Edit menu will appear Select Draw view option A menu with block icons will appear at left Now define the model structure To draw a block select the icon with mouse click Then drag it to the place where you want to put it The blocks which inputan
7. V is the measurement instrument first order inertia The signal ate node E represents the control error the difference U V The transfer functions are as follows link E Y a PID controller with gain P1 integration time T2 and differentiation tiem P2 link Y X the controlled process 1 s s 3s 1 link X V measurement 1 0 1s 1 Such simulation can be useful while looking for optimal setting of the controller Run this model with the simulation final time between 7 and 15 Usin this model you can carry our the varying parameter experiment The signal flow module generates the model equations and invokes the ODE DIFEQC module Select normal run and then Varying parameter simulation mode DIFEQC will generate the Bluesss code and invoke the C Bulder Run the model At the run time you will be asked to give the number of the parameter to be changed automatically This may be any of the PID parameters Type for example 1 to change P1 you tyme the parameter number only and not the parameter name This will change the controller gain Declare the range for the paramater as for example 2 to 20 Note that you must enter the parameter definition screen because the model uses three parameters If you read the initial conditions parameters from the file exa icc then the parameters will be P2 20 P3 0 1 Of course you cannot change the parameter number 1 because it will be changed automatically by the program As
8. d output points coincide are connected automatically To connect blocks that do not follow each other on the screen use LINKS The final model image should be as follows Now go out from the drawing mode use the END DRAW button From the main menu select File and Save as Give the name to the file e g Firstone where you want to save your model The blocks still have no parameters defined To define the parameters selectDefine block parameters from the main menu and then All undefined yet Now QMG will scan the blocks and ask you to give the necessary parameters You must provide the following in the parenthesis there are suggested values Generator Distribution type Negexp 1 0 This defines the Poisson flow of clients with mean 1 between arrivals supposing the time unit to be one minute Initial time the time when the first client arrives type 0 Max entities to generate type O for unlimited Batch size clients may arrive in groups type 1 if they arrive one by one Queues Fifo Lifo Random a character which defines the queue type let it be F the default value Max length if greater than zero the queue will be limited If the limit is reached no more entities can enter it Type O for unlimited queue Zero non zero initial length f it is Z then the queue is initialized as empty one If N then the executable program will ask for the initial length Note that the initial length is given at run time type
9. he BONDWC program directly or from the main BLUESSS program Bond graphs option select File New graph and Edit model structure First you must define the nodes Select Draw a node and Flow source to put the SF node Make a click on the point where you want to put the node Then you are asked to define the node parameters This parameter is the velocity applied to the system as an external excitation To be able to apply the excitation asany function of time define the parameter of this node as FUN1 The FUNx node parameters are interpreted by BONDWC as external functions do not forget to add the parantheses The function code may be created later on In the same way put all other nodes the 0 node 1 node L node R node and C node For each node except those of type 0 and 1 you must provide the corresponding parameters The parameters may be Node L 2 the mass Node C 1 spring constant Node R 0 2 damping The node type will be followed by comma and the corresponding node number Now define the bonds Select Draw a bond to define bonds From the bond menu always select the first one a simple bond without causalities For each bond you must give the corresponding flow and effort These parameters are Bond SF 0 effort F flow V Bond O L effort F flow W Bond 0 1 effort F flow PX Bond 1 C effort G flow PX Bond 1 R effort HX flow PX After defining the model structure select Causality and Generate B
10. l observethat the waiting time in queue 6 is always about two times greater than the waiting time in the queue 2 despite the fact that the average passengers flow per time unit is the same This is due to highly irregular arrivals of passengers ungrouped in the block 5 when an airplane arrives The following animation was done using a satellite map of the United States as the scenario background The corresponding entity routes have been defined queues and flight route and two icons assigned one being a persm the other the airplane icon PSM 2D nnimntor File d icsimulirip_ pm LEM o a alsar N Pam My GTS AY y i Phe at rF we to Y Ludo ge _ p ea 4 n cee To see animation first run your simulation After terminating the simulation run you will see a simple simulation directly over the model scheme To see the animation over the animation scenario invoke the Animator from the main Bluesss menu Enjoy the icon movements on the scenario screen and see how the queues change Before using the animator and editing the scenario consult the Animator Manual SECTION 2 Other Bluesss examples These are only summaries of the examples which are included in the Bluesss package To run the models you must be a Bluesss user Bluesss code Use the Translation run option of the main Bluesss menu to open and simulate the examples trigger csm This code is a complete Bluesss program The declaration in
11. m oscillates and the oscillations are not sinoidal Consult DIFEQC manual Getting started section Rigid2 equ This is a stiff system described by the following equations dx dt 1000x IE Xa dX dt 1001x 2X5 The eigenvalues of the coefficient matrix on the right side are very different one of them being thousand times greater that the other Running the simulation you can observe that the process has a slow and a fast component However the integration routine works well The initial conditions for this example are stored in file rigid2 icc The final simulation time is equal to 0 5 and the integration step is 0 0001 The initial conditions forx 1 and x 2 stored in rigid2 icc are equal to 0 5 and 0 1 respectively On the plots you can observe the slow component in which the transition process is in its starting stage and the fast one that terminates approximately at t 0 005 To see the initial part fast transition process with greater resolution use small integration step for example 0 00005 Signal Flow Examples exa cpg This file containes an example of a control system with a PID controller It can be opened using Continuous gt Signal flow option of the main Bluesss menu This is a simple system of automatic control The node U is the set point the link E gt Y is a PID controller link Y gt X is the controlled process in this case an inertial object of the second order The link X gt
12. other delay between blocks type 0 Cost per time unit like for the queues you can declare the cost per time unit for theserver Cost per operation this cost is independent on the time Each time the service ends this cost is added to the total cost type O for the two costs Resources the servers may need additional resources like a tool or an operator The use of additional resources is somewhat complicated see the QNUGRESOURCES section for details leave this field empty Resource logic do not care may be AND or OR Terminal point Termination number if it is N gt O then the simulation will terminate after N entities have entered the block However you must give the simulation final time anyway It is like parameter in the GPSS SIMULATE instruction It is not recommended to use this parameter if not necessary Type 0 After defining the above parameters save the model again Now select Generate code and then Generate and run Next the following menu appears Prepare files for VARAN Use semaphores Use animator Generate SVOP template The files for VARAN are files with extension SIM where a series of model trajectories is stored These files will be used bythe VARAN program to make the dynamic variance analysis Select this option to see more statistics The Use semaphores should be selected only if you use QMG semaphores to control the inputs of the blocks this is not the case in this model You also can selec
13. r Hierarchical non linear bond graphs a unified methodology for modeling complex physical systems SIMULATION April 1992 Run this example with the final simulation time between 10 and 30 Queuing models QMG module The following models are stored in the Bluesss directory assem blw a simple manufacturing cell with buffers and an assembly operation assem0 blw a simple manufacturing cell with buffers and an assembly operation The assembled parts are routed to different outputs according to the generator block where they are generated The source information number of generating block is stored as an additional attribute X of the part Associated files assemof cpp assem0sv cpp andek blw a queuing system with additional resources The AND logic is used for the resource request Associated file andekr cpp orek blw a queuing system with additional resources The OR logic is used for the resource request Associated file orekr cpp conv6 blw amanufacturing cell with conveyor Can be used to carry out the animation Associated file conv5s cpp If you select Use animator option while generating the code then the executable program will generat the animation file an2 which can be used by the animator Consult the manual of the QMG module for a more detailed description of these models
14. r will generate several warnings Ignore the warnings If the compilation fails there is something wrong in the model Probably a C compilation error occurred Return to the QMG program and check block parameters You can make it using the View parameters and All blocks option Check the distributions and other data for possible C syntax errors After correcting eventual errors generate code again If no compilation errors occur then the simulation program is invoked Now you only give the model final time type 480 the scale parameter default 50 and the number of repetitions of the simulation run type 1 The scale of 50 means that the queue which contains 50 entities clients will fit to the whole screen Then the simulation runs You can see the two queues as the moving red bars The numbers of clients who reach the terminal points are shown as green bars and the status of the servers BUSY or FREE is indicated After simulating 480 time units you will see the plots forthe two queues length as function of time and the final statistics The statistics are shown and stored in the ASCII file named FINSTA TXT which can be imported to Word or other applications The final statistics are as follows Final Statistics Final time 480 00 QUEUES Av waiting time Lmax Lmin Av length Lost OQUBRUES lt 3 12 369 16 0 Tolg 0 00 OQUEURA 3 2 We VA 5 0 Pee 0 00 SERVERS Service trme Idle time Idle Lost Served SERVOS AP POS 2 949 O6
15. rom California to Florida We simulate the checkin queue boarding queue the flight and the luggage claim in Florida with the corresponding queue The following QMG scheme can be used The passengers ae generated in the block 1 and form a queue 2 to check in Then they pass to a boarding room and form other queue group block 3 It is a small air line with no fixed schedule If there are 30 persons waiting the queue then they form a group and depat Then they board an airplane and fly to Florida It is supposed that the airplane isalways available and waits until there are 30 persons in the boarding room The flight is simulated using the conveyor block number 1 On the animation screen the passenger group is displayed using an airplane icon Once the group airplane reaches the target airport in Florida the passengers reappear as separate entities ungroup block number 5 Then they for a queue number 6 to claim the luggage and after obtaining it server 7 they go out of the airport terminal point 8 The model parameters are as follows Generator 1 inter arrival distribution Negexp 4 5 All the queues FIFO unlimited Server 3 Service time Erlang order 2 main 4 Group block 4 Group size 30 Conveyor the flight route length 1500 speed 6 km and km minute Server 7 distribution Erlang order 2 main 4 Once you have created the model run it in Using animator mode and final time of several thousand units minutes You wil
16. s from A CAT but she can have several little cats in certain time intervals In the main program only one object is generated of type SHE After some time SHE has lillte cats they start with their own activities and the population grows Note that even with several thousands of cats some tens of thousands of events in the event queue the program slow down is not significative The program speed is limited ratherby the text display procedure ODE Examples Examp1 equ The equations of EXAMP 1 are 3 dx dt p l x pox This is a simple dynamic system of second order oscillator with damping Note that the damper is non linear and the parameter p2 controls the damping On the edit screen of the ODE module DIFEQC the equations appear as follows G7 ade pil Lx IIS PON 2 oo ib2 Output expressions This part of the model specification must be defined to transform the state vector into the model output vector In EXAMP1 the outputs are Y4 x 1 x 2 Y gt x 1 x 2 Y x 1 Y x 2 You must select at least one of the outputs The selected variables will be shown on the simulation result screens Run the model with simulation final time 20 The model uses two parameters Try it with p 1 3 and p 2 20 These values are stored in the initial conditions parameters fiel examp1 icc so you can read them from that file As the result you will see the time plots for the selected output signals Note that the syste
17. t Use animator option This is not recommended for first model runs This mode will not animate the model It only creates the ANI file to be used by the Bluesss animator See the Animator section for more detail Generate SVOP template option can be used to create an empty procedure SVOP and store it in a file Remember that SVOP is used only if you want to handle semaphores or to perform user defined operations over the attributes d the entity that enters a block If so then you must prepare the procedure before or after the QMG session The SVOP template can help you because it has the complete procedure header with the formal parameters properly declared Be careful and not overwrite the file if you have already prepared and stored it Next you are asked to select queues which will be displayed as functions of time Select the two queues The last question QMG asks you is the list of include files The first file is by default RFirstone remember that Firstone is name you gave the model while saving it The Rfirstone is a C code that contains an auxiliary C part of the target code Other files if any can contain user defined random number generators or selection rules Now QMG generates the model Bluesss code and invokes other Bluesss modules In what follows you only should accept the default settings so you will need to make some mouse clicks First the Bluesss program is translated to C Then C compilation fdlows C compile
18. the first line introduces two reference variables a and b that will be used as pointers to two objects created the main program section Then a process declaration follows The process type isPerson and the two objects of this type can be generated to run concurrently There is only one event namedone declared inside the process With the outine instruction each object reports itself on the screen as active one Note that the attribute name is used to identify the object that issues the message The instructionschedule b gt one to TIME 7 schedules the event one of the object B to be executed at actual time plus one Observe that the f e se instruction means If am a then let b become active within one time unit otherwise let a activate within one time unit This means that the two objects a and b activate each other and the program triggers between the dojects a and b cats csm an example of Bluesss inheritance mechanism This is an example of inheritance and multiple object model It can be used to check the virtual memory management on your computer and the speed of the Bluesss event queue mechanism Three processes are defined in the model A CAT HE and SHE A CAT includes the following events to hunt to eat to sleep and to die HE is a male cat he inherits all the properties of A CAT but can also fight with other cats As the result of thisevent one of them may die The process SHE is a female cat she inherits all the propertie
19. the simulation runs You will see the plots of the signals at the selected nodes A non linear circuit The file RRC BND contains the bond graph for the following simple circuit The resistance R2 is assumed to be nonlinear The non linearity is given by then function FUN2 inserted into the resulting Pascal or BLUESSS code by the user after analyzing the graph and generating the program The file RRCFUN PAS contains an example of a possible code for FUN2 Try to execute the program with the following data to see the influence of the non linearity time unit is Supposed to be 1 second v1 100V R1 100o0hm c 0 000001 F 0 01 microfarads final model time 0 01 initial conditions zero float FUN2 float v 1f v lt 70 return 2000 else return 400 This function makes the resistance r2 variable depending on the voltage on r2 If the voltage is less than 70 then r2 2000 otherwise r2 400 In the bond graph model the parameter of the node r2 is FUN2 x 1 Note that x 1 is equal to vc the voltage on the capacitor The variable vc in not visible from inside of FUN2 The following figure is the bond graph of the model y C YC C6 1 2 w 03 A S 1 j C y yil ir2 YC F 4 R5 r1 fun2 Associated files RRCFUN CPP RRC ICC Other example fig11 bnd The Bluesss screen shown below corresponds to cerain mechanical which will not be discussed here in detail It is one of the models given in the article of Francoise Cellie
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