3 introduction into pace - IBE Simulation Engineering GmbH
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1. gt edit gt simulate gt deselect gt fixed To do something more or less meaningful with the module use of module counter we could connect the four instances of Counter To do this several changes and extensions have to be done with the graphical PACE editor These consist in Exchange of the places input and output of the instances of Counter on the right side IBE PACE More Complex PACE Constructs Insertion of transitions beween the output and input places of the 4 instances of Counter Insertion and Attributation of the connectors i Tuse of module counter IDE x count count output u output d Counter input 5 L4 amp E LI count count nod count count E smit output xd input output Counter Counter count gt edit gt simulate Pdeselect gt fixed In real applications the names of the input and output places should also be changed so that they are named unambiguously what we do without here To run a simulation we need tokens attributed with a number We insert three tokens in the upper left place using the following input IBE PACE More Complex PACE Constructs window which opens after the selection of the menu item initial tokens in the selection menu of this place iT Initial Tokens for input tokens attributes code ee i Ze f J Al We assign to the three tokens the initial valu2. Pedt simulate gt deselect gt fixed IBE PACE Simple PACE Constructs The next net shows the unpacking of objects that is the generation of the tokens representing the original objects at another point of the net EinAuspacken Auspacken Transportstrecke u j count count nt n count count count count gt 0 count count 1 gt edit gt simulate gt deselect P fixed Exercise Extend the modules Packing and Unpacking for contai ner which store a different maximum number of objects and for attri buted tokens IBE PACE Statistics and Distributions 6 STATISTICS AND DISTRIBUTIONS 6 1 Statistics 6 1 1 Bar Diagrams and Line Diagrams PACE offers the possibility to represent data items which results during the simulation in time controlled bar or line diagrams You find the handling of these statistical windows in the PACE user manual section 8 8 Time Dependent Diagrams In all diagrams standard functions are defaulted in the in each case assigned block cf PACE user manual It is however possible to change the default diagram function in order to display the behavior of own objects In this case one has to be aware that the functions always return a Smalltalk point x y In the following example a histogram was assigned to a place IBE PACE Statistics and Distributions I NETO17 an Uniform an Uniform v
3. v HistoPlace v Delay v next 200 0 100 0 0 0 0 0 50 0 100 0 150 0 200 0 IBE PACE Statistics and Distributions Line Diagram for a Place Load the image net018 im from the directory tutorial in the PACE installation directory 1 1 NETO18 Loix 0 mo Action m m m 1 m 360 ifTrue m 0 n m 2 3 1415 360 sin 10 rounded 12 Condition n k n Action k k 1 n number of tokens on the statistic place line diagram onthis place 0 Condition n k Action k k 1 gt edit gt deselect gt simulate b fixed The line diagram shows for each time point x axis the number of tokens y axis which lie on the place with legend line diagram on this place which results in a sinus curve IBE PACE Statistics and Distributions Line Diagram for Place line diagram on this place Miel x 15 0 10 0 5 0 0 0 0 0 100 0 200 0 300 0 400 0 500 0 600 0 700 0 IBE PACE Statistics and Distributions Histogram for a Collector You can load this net net019 from the net directory of the tutorial directory in the PACE installation directory The histogram is connec ted to the connector with attribute n a Normal m m m Delay 1 Action n m next n Be 4 81582 fa noc gt edit gt simulate Pdeselect gt fixed Standard Time Histogra
4. Cookbook PACE 2008 IBE Simulation Engineering GmbH 2008 Copyright by IBE GmbH 1994 2008 IBE Simulation Engineering GmbH Postfach 1142 D 85623 Glonn Germany Tel 49 0 8093 5000 Fax 49 0 8093 902687 E mail info ibepace com Home www ibepace com This reference manual is valid for PACE 2008 PACE and the accompanied documentation is furnished under a licence and may not be used copied disclosed and or distributed exept in accordance with the terms of said license No part of this manual may be copied reproduced translated or published in any form without prior written permission from IBE This document is subject to change without notice All features described in this manual represent no obligations of the manufactu rer of this software All brand and product names are trademarks or registered trade marks of the respective companies Contents 1 Introduction 2c2222220 1 1 1 1 The Software Tool PACE 1 1 1 2 Bibliography sees 1 3 2 Attributed PACE Petri Nets 2 1 3 Introduction into PACE 3 1 4 Use of Smalltalk in PACE 4 1 4 1 Working with Objects 4 1 42 Extra Codes Liivoieue ei ya VR rov ep REUS 4 10 5 Simple PACE Constructs 5 1 5 1 Goulllet irinna Lx REDE Zee 5 1 5 2 Random Number Generator 5 1 5 3 Branching oss lov Br ie
5. self placeNamed return gt edit gt simulate Pdeselect gt fixed The right partial network is called by inserting a token into the place Entry The place in which the result is supposed to be delivered is to be indicated in this case as an argument the return places are Return1 and Return2 The respective return place is brought to the return transition as value of the connector variable return With the places Return1 and Return2 in the main net the subpro cess are synchronized with the main process It is guaranteed that the partial network is not executed simultaneously repeatedly If the value nil is indicated instead of the return place the main process does not expect any end message of the subprocess progressing simultaneously If the PartialNet is used independently in several parallel branches of a net it can be guaranteed easily that at one time only one subpro cess progresses see the following figure A token is placed into the 7 22 IBE PACE More Complex PACE Constructs right place this and the entry token are used to start the subprocess Further tokens which are placed into the place Entry can only run if the exit transition fires and inserts a flag into the right place again nen ee Entry O Sequentialization of the calls of PartialNet return return PartialNet return return nil ifFalse self addTokenTo self placeMamed return b edit
6. a Normal distribution 019 cotr with normal b Histogram of a connector distribution IBE PACE Apppendix List of PACE training nets 020 Line diagram of a Line diagram of a connector connector with exponential course 021 Exponential distribution Exponential distribution with connector histo gram 022 Normal distribution with Normal distribution connector histogram 023 Uniform distribution Uniform distribution with connector histogram 024 Counter Incrementing by 1 025 Random generator with Random generator uniform distribution 026 Branching Variant with Branching variant x constant connector attribute 027 Branching Variant with Branching variant fire firing conditions 028 Loop a 4 times loop b then branch off 029 Timeout a Timeout without consequences IBE PACE Apppendix List of PACE training nets 030 Clock with 24 time timetable units 032 Processing in predefi a Semaphores for controlling ned time Only one b Duration ofthe process task at a time c Variation mit capacity 033 Variation of net032 a Semaphores for controlling Processing in predefi py Duration of the process ned time Only one c Variation mit capacity task at a time 034 Variation von net032 Overflow Processing in predefi ned time With overflow 8 Array 035 Creation of an Array b Output of
7. gt simulate gt deselect gt fixed IBE PACE More Complex PACE Constructs 7 5 Improvement and Optimization One can distinguish basically between two kinds of model improvement 1 Procedural Improvement This kind of improvements are carried out by a suitable design of a net and or with improvements of the inscription code These improvements depend usually very strongly on the problem and are therefore part of the modeling 2 Parameter Optimization Models normally can be supplied with different parameter sets and then show a different behavior for each set Frequently the optimal parameter set is searched with respect to specific defaul ted criteria e g as few as possible resources for the processing of a specific work load in a specific time PACE offers support for both kinds of improvements The graphics editor allows to change a net very rapidly to implement and investi gate changes of a net and different solutions To optimize parameter sets PACE offers supporting methods and exact mathematical procedures It allows the program controlled repetition of simulation runs with different code to be assigned to each repetition This can for instance be used to change the values of the model s parameters during the restart of the model mostly in the initialization code In the PACE optimization manual the graphical and mathematical optimization procedures and methods available in PACE are descri bed To the exten
8. which is merely the sum of sinus and cosinus TestExample Testmodule SEE 3 Entry param result param sin param cos result edit gt deselect bfixed IBE PACE More Complex PACE Constructs In more complicated possibly multi dimensional cases in which a pre developed module whose behaviour is not so easy to predict e g a production line has to be incorporated in a model similar algorithmic procedures have to be applied to evaluate the optimal parametrization IBE PACE More Complex PACE Constructs 7 6 Connecting a DLL written in C to PACE We look at the example represented in the following figure in which a circulating token increments a counter up to a certain value and then resets it 1 Cexample1 ICE XL n gt 10 ifTrue n 0 gt edit gt simulate gt deselect fixed To show the interface between PACE and C we replace in the following the Smalltalk inscriptions by messages which call C procedures of the dynamic link library userdll dll to be developed After making these changes our net looks e g as follows IBE PACE More Complex PACE Constructs iT Cexample2 il Es n Call procedure1 n n CallC procedureD n gt edit gt simulate gt deselect gt fixed In the left transition we call with the message procedure0 a C procedure incrementValue which increments the parameter n and returns the incremented value back to
9. 1 Condition z gt 5 Overflow Workmodul Number of tokens in the Workmodul finished Work gt edit gt simulate gt deselect gt fixed IBE PACE Simple PACE Constructs 17 NET034 Workmodul CIE XI Condition z 5 Action z 2 z 1 Working Delay 10 Number of tokens in the Workmodul Action z 2 z 1 u finished Wort Pedt gt simulate gt deselect gt fixed IBE PACE Simple PACE Constructs 5 10 Queues A typical queue problem could read approximately as follows In a production enterprise the material edition is serviced by only one employee which is according to his opinion overloaded The other employees complain about too high delays Judge the situation Dates e 12 employee hour arrive in the average e The middle serving time is 3 33 minute employee e Arrival times and serving times are distributed exponential Pure solution e middle utilization 66 96 e Middle Number employee in the queue can be determined in theory Task Make a histogram for the following queue example for the distribution of the delays onto different waiting room reservati ons see also PACE manual section 10 3 2 IBE PACE Simple PACE Constructs ix Exponential mean 5 delay e next entrance e e waiting queue call up 1 service desk delay e next Exponential mean 3 33 A ud s
10. 5 2 DA LOOP 5 tous es aS Susa AO e esu 5 5 5 5 TIMGOUL zusagen 5 6 5 6 Firing of tokens at a special time 5 7 5 7 Rotating Table 5 8 5 8 Processing 42 2240 1a irn 5 13 5 9 Overflow ose tree 5 16 5 10 QUEUES 2 4 u ov CREE M Aeg b tut 5 18 5 11 Packing and Unpacking of Objects 5 20 6 Statistics and Distributions 6 1 6 1 Statistics us oiv a rar anche 6 1 6 1 1 Bar Diagrams and Line Diagrams 6 1 6 1 2 Resetting Diagrams sees 6 6 6 2 Distributions lessen 6 7 8 2 4 EXxpbnehlllal sooo Bit ee 6 7 6 2 2 Normal eee 6 2 3 Uniform sevo ze eve 7 More complex PACE Constructs 7 1 Use of a Standard Module 7 2 SWIIEN 3044 00 ee 7 3PACE Modules 7 3 1 Implementation of a simple language element 7 3 2 Use of language elements during the development of anet 7 4 Netfunctions 7 5 Improvement and Optimization 7 6 Connecting a DLL written in C to PACE Appendix List of the PACE Training Nets IBE PACE Introduction 1 INTRODUCTION While the PACE manual is describing all features of PACE comple tely with only a few examples the present cookbook introduces into the basics of PACE in more application oriented manner Basically this cookbook contains the topics that are treated during an intro duction usually in P
11. C Action Code This code is executed when firing a transi tion and contains the actuall instructions for the object processing The following example shows Condition Code by which branching is realized The Smalltalk expression m gt 5 resp m lt 5 respond dependent of the actual values of the variables either true or false IBE PACE Use of Smalltalk in PACE How does the net progess in case of n gt 5 17 NETO11 Biel E3 Action n 2 n 1 4 iti n m n Condition n 5 Condition m 5 n m edit gt simulate gt deselect P fixed IBE PACE Use of Smalltalk in PACE During programming unwanted side effects can appear The follo wing net shows an example 17 NETO11 L GE X Action n 2 n 1 m Condition n s 5 Condition m 5 n m gt edit simulate gt deselect P fixed In case of transitions that manipulate objects of the classes Array Association Dictionary OrderedCollection and Set Smalltalk does after an assigment to a variable not work with a copy of these objects but directly with the original instance Therefore sometimes unwanted effects arise that can be avoided through suitable programming normally copying of the object IBE PACE Use of Smalltalk in PACE By the Delay code the firing of the transition is delayed by the assig ned time units Examine this with the following net You can find time window under the menu
12. Methods from x to y Generates a uniform distribution with the lower limit x and the upper limit y next returns the next value of the distribution printOn x Writes an ASCII representation of the receiver in the stream x If the argument also represents a uniform distri bution for the same intervall then true is returned otherwise false IBE PACE Statistics and Distributions If the receiver and the argument represent the same instance of the distribution true is returned otherwise false i NETO25 L OLX Uniform from 1 to 8 z z v Action v z next gt edit simulate gt deselect b fixed IBE PACE More Complex PACE Constructs 7 MORE COMPLEX PACE CONSTRUCTS 7 1 Use of a Standard Module The present example shows the use of a standard module Modules are stored in the subdirectory modules of the PACE directory The i gt newNet Jol x Exponential mean 20 Exponential mean 30 Q t t t t tnext tnext QO ME tnext Exponential mean 13 gt edit gt simulate gt deselect fixed IBE PACE More Complex PACE Constructs example models a production with two kinds of objects which arrive exponentially distributed with a mean value of 20 and 30 minutes For the processing of the objects a mean time of 13 minutes is requi red The processing of the more seldom arriving objects shall be preferred At first th
13. branching with variable connectors 009 4 initial tokens with 2 Activation if two input tokens equal constants 2 are identical diffenrent numbers 2 equal variable input connectors and 1 output connector 010 transition code Incrementing and decrementing 011 Controlled branching a Sorting with token generation b Firing conditions true false c Generation of tokens with incremented attribut 012 Counter with delay a Delay b Comment c Incrementation IBE PACE Apppendix List of PACE training nets 013 2independent counters a Concept of time with different delays b Firing list 014 3 nets with array and a Transition code is executed increments during firing not when activating b 2 possibilities for transition code C Clean separation e Smalltalk code read from and write to an array 015 Inhibitor with constant Number as connector attribute connector 016 Generator and inverter a Module module b Alternating values of a token in 2 places c Delay not relevant for the working of the example 017 2 connected delays a Uniform distribution with histogram at the b Delays place c Connected Delays d Histogramm at a place 018 Sinus curve with a Trigonometrical functions positive offset line b Statistics window diagram c Show the refinement of the curve d Counting up and down e Line diagram at a place Histogram of a conne
14. different elements of the array 036 Variation of net035 8 Array Creation of an Array b Output of different elements of the array 037 Creation of an a Association Association b Output of different elements of the association 038 Variation with a Association Association b Output of different elements of the association and incrementation 039 Dictionary a Dictionary b Output of different elements of the dictionary A 5 IBE PACE Apppendix List of PACE training nets 040 Dictionary a Dictionary b Manipulation of the dictionary 041 Ordered Collection a Ordered Collection b Output of different elements 042 Ordered Collection a Ordered Collection b Manipulation 043 Set a Set b Output of different elements 044 Set a Set b Generation of prime numbers 045 Copying of number and Shallow copy dictionary 046 Copying of dictionary a Deep copy of dictionaries and OrderedCollection b Copy to another token with an OrderedCollection 047 Dictionary Variations of the generation 048 File a Creating of a file which contains an OrderedCollection b Writes only the last of two collections 049 FIFO first in first out IBE PACE Apppendix List of PACE training nets 050 LIFO last in first out with sort for an OrderedCollection 051 Sort out by priorities Output with respect to prioriti
15. employed after their preparation in the entire net or in other nets With this procedure amongst other things also Workflow description languages can be implemented in a simple manner The procedure to be adopted when implementing language elements of such languages is demonstrated in the following with at a simple example 7 3 1 Implementation ofa simple language element To make the procedure transparent a very simple language element will be implemented in the following We choose a simple counter Counter which merely increments numbers Starting point is the following simple Petri net MES Counter i OF Xx input QO Counter gt edit gt simulate gt deselect gt fixed IBE PACE More Complex PACE Constructs It consists of three simple net elements the places input and output which contain the tokens before the entry and after the exit of the module Counter The module Counter is very simpleand shown in the following figure PT Counter Counter i IE x input o count Increment count count count 1 p output gt edit gt simulate gt deselect gt fixed It shows the places input and output drawn more weakly as the interface to the environment and consists only of one transition which increments incomming numbers by 1 To bring the module Counter in a reusable form we have to store it using the function store module in the f
16. exceeded e 0 0 Q gt edit gt simulate gt deselect fixed IBE PACE Introduction into PACE Considering these rules the following statements hold for the illustra tions net002a and net002b The transition in net002a can fire exactly once In this case the net represented in net002b is produced As described above the entry tokens are consumed and a new token is generated 7 NETOO2b Pi x O 0 Q gt edit gt simulate gt deselect gt fixed Example In a production two parts are put together and represent a new third part The transition in figure net003 cannot fire because the capacity of the output place shown in square brackets would be exceeded IBE PACE Introduction into PACE 0G 0 g 0 gt edit gt simulate gt deselect b fixed The conditions for the firing of transitions input conditions are expanded by adding of connector attributes to the entry connectors Taylor 1 E Smith gt edit simulate gt deselect fixed Tokens and connectors can be provided for this purpose with 3 3 IBE PACE Introduction into PACE attributes which are to be seen during the network view as legends of the corresponding network elements The transition can only fire if a token that contains the same constant factor as the connector is on the place The entry tokens are consumed and output tokens are generated in accordance with the attribu
17. point view in the Pace main board The Visual Petri Net Developer i NETO12 l XI Delay 1 n ar n n Action n n 1 gt edit gt simulate gt deselect P fixed If several transitions can fire at the same time the order of firing is not defined resp accidential By this unwanted effects can occur For instance the parallel incoming workpieces in a material flow system are sorted timeless A waiting at the sorting place has to be forced e g with very small delays IBE PACE Use of Smalltalk in PACE Investigate the following net i NETO13 Bl E Q Delay 1 gt edit gt simulate gt deselect b fixed A token in the left net runs five rounds until the first transition in the right net fires What happens in the left and in the right net of the following figure O amp 2 oe x x x Delay x 1 x x er x gt edit gt simulate gt deselect b fixed IBE PACE Use of Smalltalk in PACE In the left case all 3 tokens are planed be the scheduler together that means for execution at the same time they are processed in parallel In the right case the three events are scheduled and execu ted one after the other This is the reason why in the left case 3 time units are necessary until all three tokens have been processed In the right case 6 time unit are necessary to process the tokens To this difference in working modes one
18. the capacity of places Time modelling Modelling of random behaviour with mathematical and empirical probability distributions Inhibitors Global variables and net variables Fuzzy Logic IBE PACE Introduction Call of external procedures e g drivers I O Handler and von programming systems during the simulation resp the execution of a net Net functions Procedures to optimize net functions etc The many extensions of Petri nets and of the Smalltalk library are incorporated in IBE s modelling and simulation language MSL which is described completely in the PACE user manual 1 2 Bibliography Bibliographical references to Petri nets Fuzzy technics and Smalltalk are found at the end of the PACE User Manual Referen ces for Smalltalk are also found at the end of the Smalltalk Primer IBE PACE PAGE Petri Nets 2 ATTRIBUTED PACE PETRI NETS OO U OU UHU Petri nets in their initial form are built up from four element types The static elements are the places transitions and connectors which determine the topology of the net The dynamic elements are the tokens that can move in the net according to certain rules In the attributed Petri nets of PACE there are also modules and channels for the hierarchical construction of nets 1 Graphical Elements of MSL i E x place C9 modul 0 connector channel transition modul gt edit gt simulate gt deselect gt fixed Places are passive elem
19. 7 Rotating Table Let s examine the simple transport problem shown in the following figure It consists of two operating robots and a turntable with three positions If the container in Position1 is empty then Roboti can put a part in it If the container in Positions is full Robot2 can remove the part from it The turntable requires a time unit for turning the contai ners from one position to the next The numbering of the containers represented by tokens where the first attribute is the number of the container and the second attribute is its filling level are not relevant during the simulation They only have to show that the containers are allways stored in the same order on the rotating table The following net modified insignificantly can als be used for the simulation of a conveyor belt Simple transport problem vvith a rotating table PartsSource HandlingRobot1 amp e Position ps fr 1 empty 1 Parts Arrival turntable 1 RequestParts PartsTreatment Positions 3 empty HandlingRobot2 DeliverParts gt edit gt simulate gt deselect fixed IBE PACE Simple PACE Constructs To conserve space we won t discuss the source of the parts to be moved module PartsSource and their further processing module PartsTreatment here We ll simply assume that the parts will arrive and will be processed statistically The two next figures show the two modules PartsSource and PartsTreatment He
20. ACE courses It therefore contains a great number of typical examples which can be used as templates during modeling The handling of PACE is dealt with here only sporadically One finds information about that in the manual or in the online manual The PACE starter that is added to every PACE delivery provides a good entrance into the handling of PACE and into the feed in of inscripti ons into a PACE model For the preparation of inscriptions for the direct carrying out of Smalltalk code in a so called Workspace and for the loading and executing of the examples basic knowledge is necessary about Smalltalk This is provided by the Smalltalk Primer added to the delivery by PACE which contains also numerous examples and practices 1 1 The Software Tool PACE PACE is a SoftwareTool for the modeling and simulation of event oriented systems It employs attributed hierarchical stochastic Petri nets with time and Fuzzy modeling and is therefore particularly well suited for the description of real systems with parallel activities The theory underlying Petri nets was developed by C A Petri in the year 1962 within the framework of his dissertation Communication with Automats at the TH Darmstadt in Germany The target of the work consisted in creating a tool which can be used for the 1 1 IBE PACE Introduction description and the simulation of parallel processes The tool propo sed by Petri achieved particularly due to the graphical a
21. E Simple PACE Constructs module variable that indicates how many objects in the container can be stored and a module variable that indicates the current filling level of the actual container EinAuspacken LE EE x von irgendwo her 1 Em Einpacken Transportstrecke Auspacken ucc nach irgendwo hin gt edit gt simulate gt deselect fixed The window shown in the preceeding figure for the definition and initialization of module variables can be opended in the net editor menu of the Visual Petri Net Developer menu item local variables The module variable NumberOfObjects defines the maximum 5 21 IBE PACE Simple PACE Constructs number of objects in a container the module variable Count indica tes the actual filling level Count is initialized with 0 NumberOfOb jects can be set by the user In the following net the packaging of objects is shown We eliminate all tokens except for the last one and attribute this one with count The value of count agrees when leaving the module with the predefined maximum number in a container 4 NumberOfObjects EinAuspacken Einpacken nr self at NumberOfObjects value count self at Counter value count count 1 self at Counter value count count nr ifTrue x 0 x count 0 count ifFalse x 1 1 1 count self at Counter value 0 count Transportstrecke
22. List of PACE training nets Appendix List ofthe PACE Training Nets File Description Use 000 Token with String Transfer to a connector variable 001 3 initial tokens with 1 To show the element types of constant 1 Token mit 2 an extended Petri net constants Constant input and output connectors 002 3 initial tokens with Conditions for firing with input conditions setting 003 4 initial tokens with Condition for firing with condition and capacity capacity 004 2 initial tokens with Condition for firing with constants constants 005 2 initial tokens with Conditon for firing with constant number and coinstants and taking over of constant input and input attributes output connector 006 2 initial tokens with Condition for firing with constant number and constant token attribute and IBE PACE Apppendix List of PACE training nets variable input and taking over of input and output output connector attributes in variables 3 initial tokens with ER 007 constants A token with a Firing conditions with 2 constants Constant constant token attribute and input and output handling over the constants of connectors the output connector b Problem with the number of arguments for tokens resp connectors 008 Generating transitions a Infinite token generation with 4 numbers b Mode of branching random connector and follo deterministic wing
23. a 1 PartsArrival Position 1 empty gt edit gt simulate gt deselect fixed 1 RequestParts s full s empty s Position 3 p 3 Xempty DeliverParts Module HandlingRobot2 gt edit gt sim Xakzefect gt fixed The model of the turntable shown in the next figure is only a little more complicated Here we see a bit more subtly the input output interfaces Position1 and Position3 from the next higher level with its initial values and the container Position2 which is not accessible to either handling robot The partial net shown here rotates the current attributes regarding the three stated positions IBE PACE Simple PACE Constructs Position Module turntable 1 empty si I tr3 si iri Position2 2 amp empty si Gi tr4 Position3 3 empty gt edit gt simulate gt deselect fixed Since the turntable switches the positions according to a time unit the transition tr4 fires once in each time unit and places a token in each of the places pl1 to pl4 The token inserted in pl1 plans firing up to the next time unit Until that point transitions tr1 through tr3 fire since there is a token in each of the input places of all these transitions and they transport the tokens lying in the three positions on to the next position in each case IBE PACE Simple PACE Constructs 5 8 Processing If a token has to stay in a certain module d
24. ad off the position of the maximum The curve window shows that the maximum value occurs for the input value 0 795 IBE PACE More Complex PACE Constructs e ModuleCurve 20 SI SIR CEPS EE IET 00051015 20 25 30 3 5 40 45 x 0 785455 y 1 41304 To evaluate the demanded input value with one of the optimizers implemented in PACE the TestModule is incorporated into a netfunction Func IBE PACE More Complex PACE Constructs 1 TestExample vec val vec at 1 val HillClimbingOptimizer findMetMaximum Func resultLabel Result scale 0 01 initial ector vector with 0 Entry Testmodule Exit res self netResult res Transcript cr show Ergebnis res printString gt simulate Pdeselect gt fixed i Transcript Ergebnis 0 79 IBE PACE More Complex PACE Constructs For the input values from the optimizer are delivered in form of a vector but the TestModule expects the input value directly the value is calculated at the begin of the netfunction with the assignment val vec at 1 The result is delivered to the optimizer with the statement self netResult res The two small nets to the left serve for the call of the optimizer and for the output of the result into a Transcript window One receives as in the case of the graphical evaluation the result 0 79 To make it possible to duplicate the example we finally announce the module TestExample
25. anching There are essentially two methods to model branching The first method consists in labelling the connectors with constants in order to let flow through only specific objects This possibility only works however for simple objects like Boolean integers strings symbols IBE PACE Simple PACE Constructs erar nf xi an Uniform v Action v e p Dictionary new v next 0 5 ifTrue p at amp uftrag put a p ifFalse p at amp Auftrag put 6 Condition p at Auftrag a Condition p at Auftrag b p p gt edit gt simulate gt deselect b fixed IBE PACE Simple PACE Constructs The second possibility uses Condition Codes 7 NETO26 LE EE x Uniform from Oto 1 Action v next 0 5 ifTrue p a ifFalse p 3th b gt edit simulate gt deselect bfixed Branching which starts from a place is a fundamental conflict in Petri nets This is the reason why one should allways force the direction when modelling branching if possible If nothing is specified the strategy implemented in PACE that is either deterministic or accidental is used The respectively desired strategy can be changed with the following message in a Workspace UserPreferences randomScheduling aBoolean where aBoolean is either true accidential or false deterministic IBE PACE Simple PACE Constructs 5 4 Loop The foll
26. attribute is a constant the corresponding token atttribute must be equal The maximum capacity of the output places may no be reached If an attribute of an input connector is a variable then the value of the corresponding token attribute is assigned to it The transition fires 1 2 The input tokens are destroyed The output tokens are generated in accordance with the markings of the output connectors to token variables are assig ned the values of the transition local variables In case of constant connector attributes the constants are assiged to the token attributes IBE PACE Use of Smalltalk in PACE 4 USE OF SMALLTALK IN PACE 4 1 Working with Objects The processing of objects occurs in the transitions of a net The code necessary for that is formulated with the object oriented programming language Smalltalk 80 In every transition during firing Smalltalk code for the processing of objects is executed In every transition three types of code can be established a Condition Code This code must deliver one of the boolean values true oder false and is executed at first during the activation of a transition Default is true If false is returned the transition is not activated and cannot fire b Delay Code This code must deliver a positive number which defines the delay betrween the activation and the firing of the transition The firing is delayed by so many simulator time units as this number indicates
27. e generation of the two product streams and its processing is modelled A new model is opened for this and the entries shown in the foregoing illustration are carried out in the edit window The next step is to insert and connect the module priority sub of the module library this is the directory modules in the PACE directory i newNet Me E Exponential mean 20 Exponential mean 30 t t t t t next t next Entry O Next Token O Priority Exit a M D tnext Exponential mean 13 gt edit gt simulate gt deselect P fixed IBE PACE More Complex PACE Constructs newNet L OL x Exponential mean 20 Exponential mean 30 t t t E t t next t next prio n prio n Next Token O Priority Exit prio n v Exponential mean 13 edit gt simulate gt deselect fixed The attributes of the connectors prio n have also been inserted As identification of an object the object number n the used which as shown in the next illustration is assigned after an object arrived The priority of the object type arriving more frequently is lower than the priority of the object which arrives more seldom This means that the priority number of the object type arriving more frequently is higher than the priority number of the other object type To start the processing of an object an initial token must be inserted in the place Next token To sta
28. e scale of the curve and press the right mouse button After adjusting the values they are overtaken in the curve window by pressing the return button of the keyboard After this the parameter menu is deleted by selecting with the left mouse button the cross in the right upper corner In the place at top an initial token with value O is inserted which starts the evaluation of the curve We investigate the result curve in the interval between O and 4 If no description of the module is available this interval has to be determined experimentally For instance one can first investigate a larger interval In this case one has to switch on the parameter option automatic scaling in the window of the output curve ModuleCurve To start the simulation switch at least in one of the net windows into simulation mode execute with the right mouse button cursor in a net window in simulation mode first the menu function initialize and the one of the menu functions run or background run The result of the execution is shown in the next figure Using the scaling of the window one can roughly read the input value with the greatest result value If one wants to know this value more precisely itis recommended to switch on the option cursor position display in the parameter menu of the curve Then under the curve in the curve window the position of the mouse cursor is shown If one positions the mouse cursor on the maximum one can re
29. ect b fixed prio 1 ObjectNumber 1 prio 0 ObjectNumber 3 prio 1 ObjectNumber 2 prio 1 ObjectNumber 4 prio 1 ObjectNumber 5 prio 1 ObjectNumber 6 prio 1 ObjectNumber 7 prio 0 ObjectNumber 8 prio 0 ObjectNumber 9 an Exponential gt edit simulate prio 0 ObjectNumber 11 prio 1 ObjectNumber 10 prio 0 ObjectNumber 1 2 prio 0 ObjectNumber 13 prio 1 ObjectNumber 14 prio 0 ObjectNumber 15 prio 0 ObjectNumber 16 prio 0 IBE PACE More Complex PACE Constructs One recognizes the change in the processing order of objects in accordance with the object priorities e g object 3 is processed before object 2 IBE PACE More Complex PACE Constructs 7 2 Switch When modelling working processes very often the case occurs that the working process has to be switched off and on by the operator from case to case In the following figure Switch a module represen ting the switch is contained 2101 1 Switch on Bu gt edit gt simulate gt deselect gt fixed The actual switch is contained in the module switch switch The variable SwitchAdjustment used therein has to be initialized when initializing the module Initializationcode according to 7 7 IBE PACE More Complex PACE Constructs SwitchAdjustment ein SwitchAdjustment is a module variable but could also be delared as a global variable ETeutchsutch M linis ScheduledControll
30. een hardware modules Channels can be compared with tupes in which bundles of cable connections are put together to connect modules The active elements of a Petri net are called T elements whereas the passive elements are called S elements To simplify the understanding of specialized literatur and the present text the usual keywords in use with Petri nets are listed in the follo wing table IBE PACE PACE Petri Nets Process Model System Process German Englisch Stelle Platz place Situation storage Buffer Bedingung condition Transition transiton Transition Ereignis event Process step Konnektor connector Connection Situation Kante Bogen arc crossing point Marke Kern token Information Material Modul module Module partial net Kanal channel Combination of passive net elements IBE PACE Introduction into PACE 3 INTRODUCTION INTO PACE The state of a Petri net is determined by the token contents of its places Modifications of the network status are induced by the firing switching of transitions Under firing one understands the consumption of the entry tokens and or the generation of output tokens The firing od a transition consists of 2 steps namely the activation of the transition and the following token alternation A transition can fire if atleast one token is available in every input place the capacity of every output place is not
31. enTo addTokenTo with addTokenTo with with addTokenTo with with with addTokenTo attributes which are also used when reacting on external events see PACE User Manual chapter 3 IBE PACE More Complex PACE Constructs To support netfunctions independent partial networks must be provi ded by the main net first of all A partial network must have entry places and exit transitions We restrict in the following to one entry place and one exit transition since this case most frequently occurs and since it can be generalized easily A netfunction is started when a token is placed into the entry place by execution of one of the above listed addToken methods As a last step of the netfunction one of the above methods returns a token into the initial net This token can be used for example in order to synchronize the continuation of the calling net with the end of the netfunction and to deliver results to the calling environment An end signal of the netfunction is always necessary either in form of data and or as a token in order to prevent that the non reentrant netfunc tions are called simultaneously repeatedly In order to keep an eye on a concrete example we consider the net netA shown in the following illustration which consists of 3 uses of the module PartialNet which were combined with each other by two transitions We choose this net in order to demonstrate how the task of the modules PartialNet can be transfered
32. ents transitions active elements of a Petri net A token always wanders from one place to the next place passing a transition Transitions always vary in the net with places Connectors connect places with transitions and transitions with places The place in front of the transition is designated also as an IBE PACE PAGE Petri Nets entry or input place that after the transition as an outgoing or output place The current state of a net is defined by the tokens on the places State changes of the net are defined by the movement of the tokens from place to place The token alternation in the net is induced by so called firing of transitions A transition in this case takes over tokens from its input places and stores new tokens in its output places For the hierarchical structuring of nets PACE offers two further net elements namely modules and channels Modules are also active elements and are employed for the reusable organization of partial networks During their construction all network elements may be used On the other hand channels are passive network elements which consist only of places and further channels While the meaning of modules during the development of nets is obvious the meaning of channels which are useful during the development of complex nets is not as easy to understand By means of a simple analogy the channel concept can be clarified however Places can be compared with single cable connections bew
33. erProcs UPaddPrimitive 11001 incrementValue 1 UPaddPrimitive 11011 checkValue 1 void incrementValue upHandle receiver upHandle n value UPSTtoCint n 1 UPreturnHandle UPCtoSTint value void checkValue upHandle receiver upHandle n if UPSTtoCint n gt 10 value 0 UPreturnHandle UPCtoSTint value Then we have to translate userdllvm c e g with Visual C C Version 6 0 In the directory 7 34 IBE PACE More Complex PACE Constructs pace directory Makedil Example we have prepared all files for this purpose After loading the workspace the above C module is displayed and userdllvm dll can be generated automatically In the example directory we move the file name pace2008 imm which contains the example Cexample2 with pressed left mouse button over the file name pacevm exe If we release the mouse button PACE is started from the example directory and our newly generated file userdllvm dll is loaded If we would have started PACE by double clicking on the image pacevm imm our new userdllvm dll would not have been used Instead the default or dummy file userdlvm dll in the Windows system directory would have been invoked Recommendation If a project team uses an extended interface it is recommended to replace the default file userdllvm dll of the team with the new userdllvm dll which implements the extended interface IBE PACE Apppendix
34. ers activeController sensor shiftDown ifTrue SwitchPosition on ifTrue ret al Dialog View confirm Do you want to switch off L u initial amp nswver true Md ee retal true 1 u 1 ifTrue SwitchPosition off ifFalse ret Val Dialog View confirm Do you want to switch on u initial amp nswver true retal true ifTrue SwitchPosition on 1 u SwitchPosition When pressing the shift key until a query window appears the switch position can be changed gt edit gt simulate gt deselect fixed IBE PACE More Complex PACE Constructs If during the execution of the model the shift key is pressed a query window opens and asks if the actual position of the switch has to be changed The delay code 2 for the right transition in the module Switch is necessary to guaranty that all tokens have left the Switch and there fore for the next generated token the new switch position is already effective The proposed method is only usefull if the switch is often passed by tokens If this is not the case and if one wants not to press the shift key until the next token passes the switch one should implement the query as a separat partial net with enough token traffic IBE PACE More Complex PACE Constructs 7 3 PACE Modules In PACE hierarchical Petri nets can be built up in a modular way The network components constructed with the PACE module technique can be
35. ervice e e leaving Simple waiting queue model with one server exit gt edit gt simulate gt deselect gt fixed IBE PACE Simple PACE Constructs 5 11 Packing and Unpacking of Objects During modelling the case occurs frequently that objects tokens have to be gathered and to be distributed later again For example one can think on products which are brought to their workmanship place in baskets or parcels Such cases can be modelled simply when the attributes of the tokens are buffered as the elements of an OrderedCollection repre senting the entire container content and the tokens are destroyed after that packing The OrderedCollection then flows as the attri bute of a token representing the whole container through the net to the point at which the packed tokens have to be processed There one can if this is requested generate the tokens again and attribute tem correspondingly with the elements of the OrderedCollection unpacking We consider here only the simplest case in which the tokens have no attributes and in which the number of packed objects alone is sufficient to describe the container i Net ariables gt initial value gt current value Since we want to formulate the packing and unpacking in each case as modules we first have to introduce two module variables a For simplicity we assume that all container store the same maximum number of objects 5 20 IBE PAC
36. es 052 Output Message to an output window 053 Input of a BarGauge use of a global variable 054 Module variables a Modul globale Variable b Modulvariable 055 Input Yes No with Dialog true false 056 Input string mit Dialog string 057 Changing icons 057 Changing icons of a module 060 Queue a Behaviour of queues b Testing of statistics 061 Working off an order a Simultaneous scheduling of events b Sequential scheduling 100 Handling over of 4 Order of transfers arguments to a connector Further nets IBE PACE Apppendix List of PACE training nets The directory nets contains besides examples which are part of each PACE distribution the following example nets the netxxx net training Unpacking of objects FOERDMOD conveyor belt a Rotating table turntable b Part processing c Roboter1 d Roboter2 e Parts source Switch Switch on off by a switch wite choice of partial nets b Manual intervention PackUnpack Packing and a Packing b Unpacking
37. es 1 100 and 1000 Our window use of module counter now looks as follows IBE PACE More Complex PACE Constructs Tuse of module counter iof x beginn count input 1 100 1000 output LILITTILTIWII Counter gt edit gt simulate Pdeselect gt fixed Up to now we have worked in the edit Mode For we have finshed the development of our simple net we now press the simulate but ton on the left lower corner of the window and start the simulation The next figure shows a snapshot of the net window during the simulation Two tokens lie on the upper left and right place the third tokens with the attribute 832 just moves from the upper right to the upper left place IBE PACE More Complex PACE Constructs Tuse of module counter iof x beginn count count 832 r 7 i A bi E LR pi R a o amp amp N om c a 8 3 K S rate Counter Pedt simulate gt deselect gt fixed This examples also shows that the implementation of standardized semigraphical language elements leads to the same disadvantages as they also occur with the implementation of high level program ming languages Here as there the standardization of language elements makes a certain overhead that would be presumably in part recoverable by an optimizing net editor however because of the increasing computer technology faster and faster process
38. has to pay attention when modelling the working of workpieces with machines which are repre sented by transitions An inhibitor is the negation of a connector through which never a token can flow He is used like a normal input connector with the following difference If a token fullfils the condition the transition cannot fire If no token fullfils the condition the transition can fire The transition in the following net can fire until the token with the number 2 has been transfered to the right place i NETO15 L EE x 9 3 gt edit gt simulate gt deselect P fixed IBE PACE Use of Smalltalk in PACE i NETO15 oix gt edit gt simulate gt deselect fixed The next example shows how the state in the right place can be changed without consuming an input token net016 Ox Generator Inverter bedt P simulate gt deselect gt fixed IBE PACE Use of Smalltalk in PACE net016 Generator Bile Es delay 5 delay 5 gt edit gt simulate gt deselect b fixed net016 lnverter OF x1 gt edit gt simulate gt deselect fixed IBE PACE Use of Smalltalk in PACE Summary Conditions for firing activation 1 2 3 All input places store at least one token The number of attributes of the connector and the tokens have to be equal All places which are connected with the inverted input of a transi tion mu
39. ile menu of the PACE main board After that Counter can be used as a language element during the further development of the net The use of modules resp language elements can be improved by the use of meaningful icons which give an intuitive impression of the semantics behind the language elements In the present example the icon of an abacus is used By this we get the following represen tation of the module Counter IBE PACE More Complex PACE Constructs MES Counter i OF x input Q Counter output gt edit gt simulate gt deselect gt fixed The development of more complex modules can be done in a similar manner Amongst others the following PACE properties can be used advantageously Modules can be developed hierarchically Moudles can have module variables which are instantiated with every use of the module During the development of a module all language elements of Smalltalk 80 and the full Smalltalk library can be used 7 3 2 Use of language elements during the development of a net With the preceeding steps the new language element Counter is available generally We now show how predefined language elements are put together to net programs IBE PACE More Complex PACE Constructs In the next figure the module Counter has been inserted 4 times with the function restore module of the No Selection Menu of the window in edit mode i 1 use of module counter OF XI
40. l distribution the normal distribution and the uniform distribution 6 2 1 Exponential Description The class Exponential is an implementation of the exponential function Methods mean x generates a new exponential distribution with mean value x next delivers the next value of the distribution z is the argument an exponential distribution with the same mean value then true is returned other wise false s are receiver and argument the same instance of an exponential distribution then true is returned otherwise false IBE PACE Statistics and Distributions i NETO21 L OL x Exponential mean 20 e edit simulate gt deselect P fixed 6 2 2 Normal Description The class Normal implements a normal or Gaussian distribution Methods mean x deviation y Generates a normal distribution with mean value x and standartd deviation y next returns the next value of the distribution Attention With a normal distribution also negative values can appear For only positive values of the are meaning ful one has to pay attention that the values of a nomal distribution are not directly assigned to a delay IBE PACE Statistics and Distributions iS NETO22 M E Normal mean 25 deviation amp e gt edit gt simulate gt deselect P fixed 6 2 3 Uniform Description The class Uniform implements the distribution where the probability for all arguments is the same
41. m for Connector n fel Eg 037 0 25 Ha 0 15 DAL 0 05 0 077 0 0 5 0 10 0 a Ba a Ba Ba a Ba IT aa ra Une a Erz or L IBE PACE Statistics and Distributions 6 1 2 Resetting Diagrams For special applications which evaluate an optimum in several simulation runs the opened diagrams must be cleared before the next run in part or in total For this purpose there are the following methods The function resetPlaceStatistics which takes as an argument the name of a place which is connected to the transition that contains the function call resets the graphics of all statistics windows of the indicated place Example self resetPlaceStatistics place1 With the function resetAllStatistics all opened statistics windows of a net can be reset Example self resetAllStatistics IBE PACE Statistics and Distributions 6 2 Distributions In PACE the most important continuous mathematical distributions are available The distributions can be displayed for user defined parameters with the menu items probability densities and probabi lity distributions in the evaluator menu of the PACE main board Visual Petri Net Developer The distributions are completely descri bed in chapters 10 of the PACE user manual There also an example is shown how one can make empirical distributions and use them in simulation models Here we show examples with three important standard distributions namely the exponentia
42. ors more and more storage this doesn t make any difference 7 17 IBE PACE More Complex PACE Constructs 7 4 Netfunctions The multiple insertion of a module shown in the previous example would easily lead in case of bigger modules to inflated nets in which big parts of the net would be identical This would only be questio nable with respect to today s computers if the nets are very large The multiple insertion of a module has however a further disadvantage If changes or corrections of a module are made the changes have to be made at all places where the Modul was inserted Because the net in this case must be edited at different places this can be an extensive and error prone job There was the same problem during the programming in higher programming languages which led to the introduction of blocks Smalltalk of subprograms Fortran or of procedures Algol pascal C The repeatedly needed code is integrated in this case only once into a program and can be called from different program places In PACE there is also the possibility to call blocks from different inscriptions see section 3 4 of the PACE Smalltalk Primer In addition it is also possible to call netfunctions which are executed as subprocesses in parallel to each other and to the main process The process with which the simulation model starts is designated as the main process in this case For the starting of a netfunction there are five methods addTok
43. ossibi lities provided by PACE parameter sets which lead to a good or even optimal flowing of the model If however the number of parameters and the variation area is too extensive the calculati ons frequently cannot be carried out in sensible time With evaluation models the value ranges of parameters and if necessary also the algorithms to change them can be changed by trying out by the user during the models execution By that the following optimization runs then can be carried out in adequate time IBE PACE Simple PACE Constructs 5 SIMPLE PACE CONSTRUCTS 5 1 Counter The following figure shows a counter If a transition fires the contents of the input token is incremented resp decremented by 1 and then inserted in the output token 2 NETO10 GE x Action a 2 a 1 Action 2 1 Pedt gt simulate gt deselect gt fixed 5 2 Random Number Generator A random number generator is made if a flag is attributed with a distribution for example Exponential Normal Weibull The message next is sent to this distribution by the connected transition By this one receives the next random value from the distribution 5 1 IBE PACE Simple PACE Constructs which for example can be assigned to a variable z for the further use or can be used directly in the delay code of a transition an Exponential e e z z gt edit gt simulate gt deselect gt fixed 5 3 Br
44. owing net shows a loop The token with the constant array flows into the loop Each number in the array is then incremented by 1 If all numbers have been incremented the token leaves the loop This is done with a branch where one of the methods described in section 5 3 is used 9 0234 a Action b a size Action b 2 b 1 a Condition b 0 not Action c aat b aat b put c 1 Pedt gt simulate gt deselect gt fixed IBE PACE Simple PACE Constructs 5 5 Timeout The following example shows how a timeout is modelled in PACE If the transition Interrupting Timeout does not fire inbetween 30 time i NETO29 GE x a Normal v v Delay v next Interrupting Timeout visiing Starting Timeout Delay 30 Timeout interrupted Q Timeout gt edit simulate units the transition with the delay fires gt deselect fixed IBE PACE Simple PACE Constructs 5 6 Firing of tokens at a special time In the following example all tokens which have been collected until 3 p m are fired at 3 p m The transition with the delay 9 adds the 9 missing hours until midnight to simulate a 24 hours cycle i NETO30 oix e an Uniform e e Delay e next Waiting for fireing Delay 9 Delay 15 gt edit gt simulate gt deselect gt fixed IBE PACE Simple PACE Constructs 5
45. pproach within short time wide scientific interest but could not achieve because of his initial unwieldiness spread use in the industrial area With the appearance of powerful and cheap computers on the market at the end of the eighties computer supported Petri net simulators which virtually are usable at every workplace became possible One of the best known Petri net simulators with very many advanced features is PACE who has found a broad acceptance within the last years The spectrum of the applications reaches from the processing of abstract mathematical models over the simulation of concrete systems as manufacturing plants or business processes to the programming of complex operations as for example they can be found in the publications of Konrad Zuse The basis of the modern Petri net theory was developed 1970 by J L Peterson Since then Petri nets with today s common symbols for places and transitions are in use In order to cover more and more new fields with Petri nets the initial concept was expanded by many people and adapted to the respec tive needs Also PACE implements a modern form of attributed Petri nets with numerous enlargements Some of the essential enlarge ments are Possibility to build hierarchical nets Net attributation und data processing with the object ori ented programming language Smalltalk Use of individual and problem related icons instead of the standard icons of the net elements Restriction of
46. re we clearly assume a random distribution of the points in time when a part is delivered or used Delivery of parts is as follows module PartsSource the token located at a given place is delayed by the random value of the time delay Then the transition fires and delivers a token to each of the places connected to it One is used to plan the next part delivery The token which runs to the place PartsArrival represents the part delivered from outside the system Module PartsSource an Uniform u u amp te 1 PartsArrival gt edit gt simulatdedelect gt fixed IBE PACE Simple PACE Constructs Module PartsTreatment Uniform from 1 to 5 delay u next DeliverParts gt edit gt simulate gt deselect gt fixed The following two figures model the work of the processing robots Here again we re looking only at the delivery of parts In the contai ner at Position1 there is a token whose attributes indicate which of the three containers on the turntable is in position and that this container is empty The transition HandlingRobot1 can fire only if along with this token there is also a token a part in the place PartsArrival If the transition fires it collects both tokens and places a token with the attribute value full a part in the container at Position IBE PACE Simple PACE Constructs Module HandlingRobot1 s amp empty s full oO tee
47. rt the processing of the next object the lower transition must be connected with the place Next token IBE PACE More Complex PACE Constructs By this one gets the following net which is represented in edit and in simulation mode immediately of initialization i newNet ME Exponential mean 20 Exponential mean 30 t t tnext tnext l 4 prio n prio n Mg ee ur n ObjectNumber E scc ObjectNumber 1 prio 1 Next Token prio 0 Q O Priority Exit L newNet of x O an Exponential an Exponential Exponential mean 1 e b edit simulate t t t next t next j prio n prio n DR n ObjectNumber RENNER x ds ObjectNumber 1 prio 1 Next Token prio 0 0 Li Priority Exit prio n an Exponential gt edit b simulate t tnext Pdeselect Pfixed IBE PACE More Complex PACE Constructs If one finally connects a consumer to the lower transition who documents the order of the tokens in a Transcript window done in the three point code then the net and a Transcript window looks as follows i PriorityExample of x an Exponential an Exponential t t t Entry t t next tnext prio n prio n n ObjectNumber n ObjectNumber ObjectNumber 1 ObjectNumber 1 prio 1 prio 0 Next Token Priority Exit 044 prio n t t tnext Prion m gt desel
48. s are assigned in turn to the variables as these are defined with the attri butation of the connectors Investigate the behaviour of the following net IBE PACE Introduction into PACE i NET100 L EE x 4321 1234 abcd dcba gt edit gt simulate gt deselect P fixed A transition with input connectors with the same variable names can only fire if the values which are assigned to the variables are equal matching A connector variable is known only in the environment of the transi tion to which the connector is coupled Connector variables are local variables One can recognize them by their beginning letter which is a small alphabetic character unlike the global variables which are known to net as a whole and must begin with a capital letter Smalltalk conventions The attributes of tokens on places are independent of the assign ment to the variables of connectors IBE PACE Introduction into PACE What happens in the following net i NETOOS loJx Symbol Symbol OCA a9 a a gt edit gt simulate gt deselect fixed IBE PACE Introduction into PACE Summary Conditions for firing activation 1 2 At least one token must be on all input places The number of attributes of the connector and the token must be equal The contents of the token attributes must be the same if several input connector attributes are the same If a connector
49. sive examples in this chapter there are correspon ding models in the samples directory of the PACE installation directory IBE PACE More Complex PACE Constructs As a tutorial we here demonstrate the most important procedures with a simple transparent example We investigate an unknown test module which we have to provide with a number as input value and which delivers a number as the corresponding result We want to know for which input value the module delivers the maximal output value TestExample SEE Testmodule fixed The search for the optimum is carried out in the following as well graphically as algorithmicly To paint the dependence between the input value and the output value the net in the foregoing figure is extended as follows IBE PACE More Complex PACE Constructs 1 TestExample val gt 4 ifTrue self terminate val val 0 01 Testmodule ModuleCurve increasing amp t val put res gt edit gt simulate gt deselect gt fixed IBE PACE More Complex PACE Constructs The global variable ModuleCurve is defined in the initialization code with the statement ModuleCurve Curve named ModuleCurve clear The Curve ModuleCurve has to be installed from the PACE Views menu For repeated execution of the model the curve is cleared before each simulation run The scaling of the curve the parameter menu of the curve is used To open it postition the cursor on th
50. st not have tokens with the same connecotr legends If several connectors have the same connector legends the contents of the tokens must be equal If the connector attribute is a constant the token attribute must be the same constant The maximal capacity of the output places must not be exceeded The condition code true is requested If the input connector attribute is a variable the value of the corresponding token attribute is assigned to the Itransition ocal variable The transition is activated 9 After activation the firing is delayed be the time units which result from the execution of the delay code The transition fires 10 The action code is executed 11 The input tokens are destroyed 12 The output tokens are generated according to the attributes of the output connectors Variables are assigned the value of the transition local variable in case of constants the constants are used IBE PACE Use of Smalltalk in PACE 4 2 Extra Codes Extra Codes are necessary for the organizational embedding of PACE nets Each model can have four extra codes which can be defined in the Net Editor Menu of the Visual Petri Net Developer menu function extra codes They are used for the following tasks Initialization Code It serves as the name says for the initialization of the net before its execution This includes the initialization of global variables and data fields the opening of files etc Break Code It is e
51. tes of the output connectors that are connector variables or connector constants i NETOOS Loix Number 6 6 gt edit gt simulate gt deselect bfixed gt it simulate Pdeseect Pfiwed If now instead of a constant a variable name is the attribute of a an input connector the value of the token attribute is assigned to the variable during the activation of the transition These variabels are known in the vicinity of a transition that is up to the bordering places and are called transition local variables IBE PACE Introduction into PACE i NETOOO lel x connector connector Place e Ye a Cnr ad Place Token Transition Pedt gt simulate gt deselect gt fixed Connector attributes at the output connectors are employed for the generation of output tokens these are made always while firing During the generation of the output tokens at the output connectors with variable attributes the value of the transition local variables are taken over In case of variables the values of the transition local variabels are assigned to the token attributes for constant connector attributes tokens with constant attributes are produced In general to tokens and connectors as many attributes as desired can be assigned About a connector with connector attribute n only flags with flag attribute n can flow The variable assignment is independent of the tokens on the place The token attribute
52. the net The right transition calls with the message procedure1 the C procedure checkValue which resets the value of n in case that the value 11 is reached To implement the interface between Smalltalk and C we have to extend the C module userdllvm c see the directory makedll in the PACE installation directory to implement the mentioned two proce dures The link list UserProcs has to be extended for this and the two mentioned procedures have to be added PACE 2008 Development of uderdllvm dll File userdllvm c Procedures to be connected by the user For different numbers of parameters there a designated in each case 6 procedures These are connected to Smalltalk using the primitive numbers 110xy The first digit x x 0 5 defines the number of the procedure 7 33 IBE PACE More Complex PACE Constructs The second digit y y 0 4 defines the number of parameters If the number of designated procedures with a special number of parameters is to small in an application the user has to define instead only one procedure and has to branch from this procedure to the other procedures f there are more than 4 parameters the user has to store these in a collection and has to transfer the collection to C include userprim h include userdll h static uplnt value extern void UserProcs void incrementValue void checkValue extern void Us
53. to a subprocess IBE PACE More Complex PACE Constructs EE ie Q PartialNet PartialNet PartialNet gt edit gt simulate gt deselect gt fixed In the present case of course one could avoid the multiple use of PartialNet also by the modeling a loop In more general cases when the modules to be inserted are used on different hierarchical levels of a net there is however no simple alternative to a netfunctio ns apart from inserting the module repeatedly IBE PACE More Complex PACE Constructs The net equivalent to net netA in which the module PartialNet was put only once is shown in the following figure netB ESCHE nu m a E x self addTokenTo self placeNamed Entry with Return1 Return PartialNet self addTokenTo self placeNamed Entry with Return2 Return2 self addTokenTo self placeNamed Entry return with nil Oo O Exit return nil ifFalse self addTokenTo self placeNamed return gt edit gt simulate gt deselect fixed As an alternative to it the net represented in the next illustration can also be used IBE PACE More Complex PACE Constructs m self addTokenTo self placeNamed Entry Entry with Return1 C Q Return PartialNet self addTokenTo self placeNamed Entry with Return2 eo self addTokenTo self placeNamed Entry return with nil Exit return nil ifFalse self addTokenTo
54. uring the execution this can be realized as follows Delay 1 L waiting to be treated YorkingModul Work finished gt deselect P fixed gt edit gt simulate The token stays as long in the module till the working time is over IBE PACE Simple PACE Constructs i NETO32 WorkingModul 4 Order waiting to be treated Waiting for work Order in work Q Delay 3 Work finished gt edit gt simulate gt deselect P fixed By the number of the tokens with which the place Waiting for work is initialized the maximal number of the simultaneous working processes in the module can be set for example maximal number of batch processes If the Modul is supposed to carry out only one task at a time also the following WorkingModul with an inhibitor can be used IBE PACE Simple PACE Constructs T NET033 WorkingModul CIE XI Delay 3 In work E Order in work _ Order waiting to be treated Work finished Pedt gt simulate gt deselect gt fixed IBE PACE Simple PACE Constructs 5 9 Overflow Usually tokens would accumulate before a module if it can not include any more tokens In following example the tokens which would accumulate in case of a busy module are drawed off into the place designated with overflow If one would leave out the overflow place so the superfluous tokens would be destroyed i NETO34 Loix Delay
55. xecuted when a simulation run is interrupted by the user or with a break message In the break code there could be e g intermediate evaluations and reports which inform the user about the progress of the simulation Continuation Code If a simulation run is interrupted the user can change parameter adjustments according to the actual situation of the simulation to influence the further execution of the simulation model With the continuation code these adjustments can be read in and are available for the further execution of the model Termination Code The termination code is used for finishing tasks like evaluation output and if necessary graphical representation of the simula tion results the closing of files etc Initialization code and termination code is actually used in each larger model see the examples in the directory samples Break code and especially continuation code is necessary for inter active simulation models in which the user has to influence the IBE PACE Use of Smalltalk in PACE execution of the model Examples of interactive simulation models are Training Models With interactive simulation models schedulers freight traffic running control etc can economically be prepared for their later Work Evaluation Models It often isn t clear from the start of complex system models how the model behaves under different initial parameters Although it is possible to determine with the optimization p
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