XPenelope User Guide - Professor Hermann de Meer
Contents
1. 26 A Simple model ss a a AS A GG e ld Bale ee 29 Model editor containing six Markov states and one branching state 30 States and transitions 4 29 2 rr decd Se eh Be qe dea Sede Be 31 ili 28 29 30 31 32 33 34 35 36 The completed model 2 2 Ss ae ae Greed a Sarak a Dark 32 The parameter Set edit r Vta NEE Ba e e ist E 33 The results of th experiment pesa rr a a 40 Model of the Erlang k distribution e 40 Recursive nature of the Erlang k distribution 41 Macro for the Erlang k distribution o e 41 The Connect macro 1 ads ec re AA Sa A 41 Ihe PARACE eo naeh 42 A simple model with an invocation of the Erlang macro 42 iv 1 Introduction PENELOPE is a software tool for the dependability evaluation and the optimization of performability PENELOPE is based on the theory of extended Markov reward models DEME 92 The primary task of PENELOPE is the optimization of performability measures The user may interact with PENELOPE either through a graphical user interface or through a command line interpreter 1 1 Extended Markov Reward Models Let Z Z t t gt 0 denote a continuous time Markov chain with finite state space S To each state s S a real valued reward rate r s r S IR is assigned such that if the Markov chain is in state Z t S at time t then the instantaneous reward rate of the M2. Copy To Makes a copy of the selected parameter set to an arbitrary model Type in the desired parameter set name in response to the prompt Name of copy and then press OK Then the name of the model is prompted for Rename Renames a parameter set Type in the desired parameter set name in response to the prompt New parameter set name and then press OK Delete Deletes the selected parameter set 5 Open jOpens the parameter set editor see Sec 2 6 for the selected parameter set Cancel Leaves the parameter set index All operations marked with require that a parameter set has been previously selected from the list A double clicking of a list item will perform the Open action 2 4 The Experiment Index Avail gamma less E Availability COA compare performance Capacity gamma less Capacity or Avail E Impact_of_Cov _Avail E Impact_of_Cov_Avail stationary sana sana test sim 1000tu ar N1 E sim 1000tu nr N4 create Copy Copy To Renamef Delete Open Cancel Figure 3 Experiment index The experiment index see Fig 3 is a list of all experiments available for the selected model One of the following buttons may be selected Create Creates a new experiment A name of the new experiment is asked for Then the experiment editor is opened see Sec 2 7 Copy Makes a copy of the selected experiment Type in the desired experiment name
3. Copyright and Reference Information This material preprint accepted manuscript or other author distributable version is provided to ensure timely dissemination of scholarly work Copyright and all rights therein are retained by the author s and or other copyright holders All persons copying this work are expected to adhere to the terms and constraints invoked by these copyrights This work is for personal use only and may not be redistributed without the explicit permission of the copyright holder The definite version of this work is published as L Hermann De Meer and Hana Sevcikova XPenelope user guide Technical report University of Hamburg Hamburg Germany Dec 1996 See http www net fim uni passau de papers DeMeer1996a_ for full reference details BibTeX XML XPenelope User Guide for XPenelope Version 3 1 Technical Report Hermann de Meer Hana Sevcikova November 1996 Department of Computer Science University of Hamburg demeer informatik uni hamburg de sevcikovO ro2 informatik uni hamburg de Abstract XPENELOPE provides a user friendly X window environment for PENELOPE It supports the tasks of model creation speci fication and control of series of experiments and visualization of the results PENELOPE provides numerical and simulative methods based on the theory of Markov decision processes that are applicable for the optimization of performability measures The optimization paradigm is based on the conc
4. A state name must start with a letter and may contain any of the characters A Z a Zz 0 9 and Reward Reward rate any arithmetic expression may be en tered in this field see Sec 2 5 4 e A transition has one of the following parameters Rate State transition rate applies only to transitions originating in a Markov state Probability Probability of the transition applies only to tran sitions originating in a branching state Any arithmetic expression may be entered e A macro terminator has the following parameters Name Name of the terminator e A macro invocation has the following parameters see Fig 7 Name Name of the macro invocation Class Class of the invoked macro this is the model name assigned to the macro definition Condition Any arithmetic expression If the expression is zero the macro invocation will be ignored Other wise the macro invocation will be substituted by its definition at experiment execution time This field is initialized with 1 0 Parameters A list of all parameters that appears in the macro definition Each parameter may be substituted by 10 Class Erlang Condition j lambda jambda N IN rew rew ok Cancel Figure 7 Macro parameters dialog an arithmetic expression the substitution is per formed at experiment execution time Initially each parameter is substituted by itself The names o
5. ltana Eltana 10 tu Etana 10 tu 1sw ar E Etana 10 tu 1sw nr a e Cancel E Figure 19 Which Experiment dialog e Dif Exp Parameter JE gamma 5e 05 OK Cancel Figure 20 Dif Exp Parameter dialog The toggle button Difference graph determines whether the resulting graph a difference graph is or not The choices in the Diff after menu Param By clicking at one of the buttons marked with the parameter name the Dif ference Values dialog will appear see Fig 17 Select one value from the 22 list labeled A and one or more values from the list labeled B The toggle buttons A B and B A determine the subtrahend and minuend The result lines are created as the difference between any two lines with the same name Rewards Choose exactly two rewards which the difference line is made from Experiments By clicking at this button the Which Experiment dialog see Fig 19 with a list of all possible experiments for this model appears Choose one of the experiments and then press OK If the selected experiment contains more than one varying parameter the Dif Exp Parameter dialog see Fig 20 pops up By clicking at one of the buttons marked with the parameter name select a fixed value for each parameter The result lines are created as the difference between any two lines with the same name The subtrahend lines belong to the current experiment the minuend lines belong to the experim
6. XPenelope supports the model creation the experiment management and the visualization of the results The macro mechanism of XPenelope makes it possible to split large models into smaller and simpler submodels The user friendly X window interface the operating system independent database permanently executed consistency checks and many other features make XPenelope a versatile working environment for the modeling and optimization of reconfigurable systems Many application examples can be found in DEME 94 40 References KATK 92 MAUS 90 DEME 92 DEME 94 MEMA 92 MEIT 92 MUNK 93 TIM 86 TURN 92 K tker S Entwicklung und Implementation ausgew hlter Algorithmen der stochastischen Optimierung zur Erweiterung von PENELOPE Master thesis University of Erlangen Niirnberg 1992 Mauser H Implementierung eines Optimierungsverfahrens fiir rekonfigurier bare Systeme Diplomarbeit University of Erlangen Niirnberg 1990 de Meer H Transiente Leistungsbewertung und Optimierung rekonfigurier barer fehlertoleranter Rechensysteme Arbeitsberichte des IMMD der Univer sitat Erlangen Niirnberg Vol 25 No 10 October 1992 de Meer H Kishor S Trivedi and Mario Dal Cin Guarded Repair of Dependable Systems Theoretical Computer Science Spe cial Issue on Dependable Parallel Computing Vol 129 July 1994 http www informatik uni hamburg de TKRN ro_homed htm de M
7. abstraction from Markov decision theory EMRMs are a marriage between performability modeling techniques and Markov decision theory and provide a general framework for the dynamic optimization of reconfigurable dependable sys tems 1 2 Features of PENELOPE Reconfiguration edges denote options to reconfigure from one state to another At every instant of time a different decision is possible for each reconfiguration edge A strategy S t comprises the set of all possible decisions at a particular instant of time t 0 lt t lt T Strategies can be time dependent or stationary In the latter case the parameter t can be dropped 5 S t A strategy 5 t is considered optimal if the performance of the system under strategy t is better or equals than the performance of the system under any other strategy S t 1 PENELOPE offers two types of methods for the computation of optimal strategies and per formance functions e Transient Optimization The system is investigated for a finite period of time the so called mission time T Op timal strategies 5 t are computed for every instant of time t 0 lt t lt T The results are depicted as S t which is a function of the remaining time 1 t T t where t denotes the elapsed time In addition the expected accumulated reward E Y t is also computed for all initial states provided the optimal strategies were applied e Stationary Optimization The optimization is perfor
8. command line After a few seconds the model index should appear on the screen Step 2 Press the Create button in order to create a new model 29 Step 3 Step 4 Step 5 Step 6 Select the item Markov State from the Edit menu This activates the Markov state mode in this mode every mouse click in the drawing area produces a new Markov state For every Markov state in figure 25 click the left mouse button at the correspond ing position in the drawing area For every mouse click a circle with a question mark appears on the screen Select the item Branch State from the Edit menu This activates the Branch state mode in this mode every mouse click in the drawing area produces a new branching state Make one mouse click in the drawing area in order to create the state Cov The drawing area should now look like figure 26 2 OP ae 2 Figure 26 Model editor containing six Markov states and one branching state Phase 2 Assign names and rewards to the states Step 7 Step 8 Step 9 Select the item Set Parameters from the Edit menu This activates the Set pa rameters mode in this mode you may click at any object in order to modify its parameters The question marks displayed on top of each state signal that the parameters for the states have not yet been entered Thus click at the state N2 the leftmost state The Parameters dialog appears Enter the node name N2 in the field Name enter
9. in response to the prompt Name of copy and then press OK Then copies of the experiment definition and of the results of this experiment are made Copy To Makes a copy of the selected experiment to an arbitrary model Type in the desired experiment name in response to the prompt Name of copy and then press OK Then a name of the model is asked for Rename jRenames an experiment Type in the desired experiment name in response to the prompt New experiment name and then press OK Delete Deletes the selected experiment Open Opens the experiment editor see Sec 2 7 for the selected experiment Cancel Exits the experiment index All operations marked with require that an experiment has been previously selected from the list A double clicking of a list item will perform the Open action 2 5 The Model Editor Options Branch State Ea Transition Reconfiguration Edge Macro Terminator Macro Set Parameters Delete CT Figure 4 Model editor The model editor see Fig 4 is a canvas on which state transition diagrams can be rendered The following symbolism is used within the model editor Object Representation Branching State Reconfiguration Edge Macro Terminator Macro Missing Parameters Inconsistent Macro The arrows inside the macro symbols are called sockets They point inward outward if the attached transition or reconfiguration edge is en
10. the reward rate 1 in the field Reward Press the OK button Repeat step 8 for each state Phase 3 Create the transitions and reconfiguration edges Step 10 Select the item Transition from the Edit menu This activates the Transition mode in this mode you may click at two states in order to create a transition between these states 30 Step 11 Step 12 Step 13 Step 14 First we will create the transition between state N2 and state Cov click at state N2 then at state Cov A transition with a question mark on top of it appears Repeat step 11 for each transition If you create the transition from R1 to N2 you probably don t want to connect the states by a straight line Therefore you may proceed like this click at state R1 then click somewhere between state R1 and N2 and finally click at state N2 This will produce a transition consisting of two line segments Select the item Reconfiguration Edge from the Edit menu This activates the Reconfiguration edge mode in this mode you may click at two states in order to create a reconfiguration edge between these states The example model contains only the reconfiguration edge between state N1 and R1 Thus first click at state N1 and then at state R1 A reconfiguration edge between the two states appears The drawing area should now look like figure 27 Figure 27 States and transitions Phase 4 Assign transition rates and probabilities to the edges S
11. 24 Step 25 Step 26 Step 27 delta gamma Parameter Cancel Figure 29 The parameter set editor Click at the item alpha and enter the value 0 01 in the field Value Repeat step 23 for the parameters beta c and delta Select the item gamma and press the button N Arbitrary Values Now enter the values le 5 le 4 le 3 le 2 and le 1 in the field Values one value per line Press the Save button A dialog appears prompting you for the Parameter Set Name Enter PSet and press the OK button A message dialog with the text Parameter Set Saved appears press the OK button Phase 7 Create the experiment definition Step 28 Step 29 Step 30 Select the item SimpleExample in the model editor and press the Open button A pop up menu appears select the item Experiment Index The experiment index appears Press the Create button of the experiment index in order to create a new experi ment definition A dialog appears prompting you for the Experiment Name Enter Exp and press the OK button The experiment editor appears 33 Step 31 Step 32 Step 33 Step 34 Press the button Parameter Set which currently has the label The Para meter Sets dialog appears which shows a list of the available parameter sets Currently only the parameter set PSet is available Select this parameter
12. ant Values The values for this parameter are taken from the set zle a ff i 0 N 1 where a is the value from the field Start Value f from the field Factor and N from the field Number of Steps Press the Save button in order to save the parameter set or press Cancel to exit the parameter set editor 2 7 The Experiment Editor The experiment editor see Fig 10 is used to create experiment definitions to run experiments to save experiment definitions and results to display results and to save computed strategies An experiment definition requires the following information 14 Parameter Set Mode Mission Time Strategy Step Width Experiment Editor Availability f Model 4processors Availability Gamma Var Parameter Set f Mode Transient Optimization lt gt Stationary Optimization lt gt Simulation Transient Analysis E Mission Time 1000 Save Strategy Strategy Index f Load Results eaters Stationary Analysis f Step wiath jo 1 Taylor Degree GO 1 G2 93 f Info O Model O Structure Analysis U Trace izg na Save Save As Run Info Show Figure 10 Experiment editor e Parar meter Sets Available Parameter Sets Routing 2Var i Routing Const Parameter Set Routing A OK Cancel Figure 11 Parameter Sets dialog The name of th
13. ard is pressed the new results can be joined with the previous by clicking at the button Join in the Forward Experiment dialog or they can be deleted by clicking at the button Delete To exit the Forward Experiment dialog the button Cancel must be pressed 2 9 2 Change Graph Dialog Change Graph Select strategy e Change Lines n gt 1 r N1 gt 10 0006 780 9 Inz gt 0 0007 574 6 N2 gt 1 0 0008 471 6 0 001 360 9 N3 gt 0 0013 2775 0 002 191 7 0 005 98 0 01 62 2 Strategy N3 gt Rd Figure 24 Change Graph and Change Lines dialog The user has a possibility to change interactively the course of strategy lines in the result graph The Change Graph dialog see Fig 24 is a list of all strategies in the experiment Select a strategy its line should be changed By clicking at the button OK the Change Lines dialog see Fig 24 appears Press the button Cancel to leave the change graph dialog Change Lines Dialog The Change Lines Dialog contains an editable text widget Each curve in the graph is represented by a co ordinate set in the text widget The user may change this co ordinates Each line must be terminated with new line character Between every two co ordinate sets 1s an empty line Press the button OK to change the graph To leave the Change Lines dialog without any change is done click at the button Cancel By clicking at the button Save in the Experim
14. arkov chain at time t is defined as X t rz In the time horizon 0 t the total reward Y t fj X r dr is accumulated Note that X t and Y t depend on Z t and on an initial state The distribution function W y t P Y t lt y is called the performability A Markov chain Z for which a reward function r has been defined is called a Markov reward model For ergodic models the instantaneous reward rate and the time averaged total reward converge in the limit to the same overall reward rate lim E X t lim E Y t E X t For each unit of time in which the system is in a certain state the corresponding number of reward units X is added to the total reward f X r dr Thus it is possible to define a yield measure or a loss measure for the system by using appropriate reward rates Extended Markov reward models EMRMs enrich Markov reward models by the feature of reconfiguration edges Whenever the system is in a state in which a reconfiguration edge origi nates a decision must be made whether or not to switch to the target state of the reconfiguration edge The optimal decision may be time dependent Additionally the Markov reward mo dels are extended by so called branching states These are states in which the system does not spend any time With the help of branching states 1t is possible to assign reward values to state transitions so called pulse rewards EMRMs were derived in order to provide an
15. ations to be performed Termination criterion for Value Iteration Default 107 Available methods for the solution of linear equations Gauss Power Gauss Seidel or SOR Number of iterations for the iterative methods Power Gauss Seidel SOR Termination criterion for iterative methods for the solution of linear equa tions Default 10 Relaxation parameter for SOR method Default 1 2 In the strategy iteration two values a and b are considered as equal if la b lt d where d is the value of the Max difference field Default 107 The toggle button Model determines whether the info file should contain the model description or not The toggle button Structure Analysis determines whether a structure ana lysis of the model should be provided or not If the toggle button Trace is on a trace of the computation is provided for the given time steps Default 20 In the menu What one can specify the tracing states to be traced Meaning of the buttons Save Strategy Strategy Index Load Results Save This button may be pressed if the experiment was run in the former and computed strategies exist A strategy name is asked for Shows Edits the list of all strategies saved for this model see Sec 2 8 If the results of the experiment were previously saved they can be loaded resp reloaded from the experiment database by clicking at this button Saves the experiment definition and the results of this expe
16. create the forward declaration or press Cancel to abort the operation 2 6 The Parameter Set Editor The parameter set editor see Fig 9 is used to assign concrete values to the model parame ters Each parameter may have one or more values For all possible value combinations one experiment will be executed The numbers entered in the parameter set editor consist of digits an optional embedded deci mal point and an optional exponent suffix For example both 3 14 and 0 314e2 are valid numbers Each number is rounded to twenty digits le 21 0 Select a parameter from the parameter index and activate one of the following radio buttons 13 e Parameter Set i alpha beta delta RENTA Parameter gamma i Values 0 01 Value Range Q 1 Value 0 02 i 0 05 Y N Equidistant Values N Arbitrary Values Q N Log Equidistant Values Save Cancel Figure 9 Parameter set editor 1 Value There is exactly one value for this parameter field Value N Equidistant Values The values for this parameter are taken from the set 2le a s i i 0 N 1 where a is the value from the field Start Value s from the field Step Width and N from the field Number of Steps N Arbitrary Values The values are taken from the field Values This field can hold an arbi trary number of values Each number must be in a separate line N Logarithmic Equidist
17. dth and N Number of Steps The Value is the first possible parameter value 0 If value lt O the radio button is made unvisible The value in field Number of Steps is accepted if N gt 1land x gt 0fori N 1 Forwards value The value is the start value for the new interval The value in field Number of Steps is accepted if N gt 1 Logarithmic Equidistant Mode The Forward Experiment dialog appears The informa tions in the first three lines is equal to the Forward Experiment dialog in the equidis tant mode If the Backwards radio button is selected the parameter values are taken from the set z e a ff 0 N 1 where a is the Start Value f is the Factor and N is the Number of Steps The value in field Number of Steps is accepted if N gt 1 Multiple Mode The Forward Experiment dialog appears see Fig 23 There are two text widgets In the upper one there are values which the experiment had already run for This text widget is not editable In the second one new values may be inserted At least two values have to be inserted Each number must be in a separate line Press the button Run to run the experiment for the new values Then the Forward Experiment and Graph Parameters dialog disappears and a Working dialog see Fig 12 is shown After the experiment is performed the new results can be seen in the Graph Parameters dialog 25 see Sec 2 9 Now if the button Forw
18. e associated parameter set Press this button in order to display the Parameter Sets dialog see Fig 11 One of the available pa rameter sets may be selected Press OK to return to the experiment editor One of the modes Transient Optimization Stationary Optimization Si mulation Transient Analysis or Stationary Analysis can be selected A mission time must be specified for the transient optimization transient analysis and for the simulation A fixed strategy may be specified for the transient and stationary analysis and for the simulation It can be loaded in the Strategy Index see Sec 2 8 Load The strategy is considered as a fixed strategy for this experiment no optimization will be performed The step width for the transient optimization and the transient analysis de termining the accuracy can be specified 15 Taylor Degree Start State The values 0 1 2 or 3 are possible The default Taylor degree is 1 The start state of the simulation Number of Runs The number of runs for the simulation Iteration Mode Strategy Iteration or Value Iteration may be selected for the stationary optimization Absorbing States Click at this button if the model contains absorbing states for the appro Iterations Value Iter Eps Method Method Iter Epsilon Omega Max difference Info priate computation method to be performed for the stationary optimization and stationary analysis Number of iter
19. ee LS 35 4 Conclusion References 11 38 39 List of Figures nA A Q N 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Model indek snene n TS Ps y Ete at epee a 4 P rametersetmde 22 a a E a rta 5 Experiment index bis bie ka e Ae aa a a 6 Model editor ot E A Sire oa Oe oe 7 Macros dialog box 4 2 ELE re 9 Parameters dialog gga bs A ae A RR A a 10 Macro parameters dialog SG ets See ede SEE CEE SQ ESS 4 11 Forward Declaration dialog 2 sai cs was un a ee We DS 13 Parameter s t editor 2 5 2 08 28 dee rain 14 Experiment editor ta ee eG areas en ae ee Sey eS 15 Parameter Sets dial g Sa wa BER TE WE FIRE 15 Working UE e 2 2 22a ee ee AA RE A es 17 Info window duela rin eg Dee AA ale BIE Sale aa 17 SE ALC OM NAER et Miet a Go stake a AMR KD WER AR EGER 18 Strategy editoi e ee e A A a a 19 Graph Parameters dialog 22 a a ea 20 Value Difference Values and Which rewards dialogs 20 Parameter Set dialog 2 ek dee ee dh RA 22 Which Experiment dialog 2 2 ew ee a aE eS 22 Dit Exp Parameter dialog amp 20 za sa AAA ee ee ies 22 A plot program displaying a strategy o e 24 Forward Experiment dialog for equidistant mode 24 Forward Experiment dialog for multiple mode 25 Change Graph and Change Lines dialog
20. eer H Mauser H A Modeling Approach for Dynamically Reconfig urable Systems Proceedings of the 2nd Int Workshop on Responsive Com puter Systems Kamifukuaoka Saitama Japan 1992 Meitinger M Entwurf und Implementierung eines Programms zur graphi schen Aufbereitung von Analyseergebnissen unter X Windows Master thesis University of Erlangen Niirnberg 1992 Munkert F Entwicklung und Implementierung einer benutzerfreundlichen X Window Oberfl che fiir das Leistungsbewerte und Optimierungstool PENELOPE Master thesis University of Erlangen N rnberg 1993 Tijms Henk C Stochastic modelling and analysis a computational ap proach Chichester Wiley 1986 Turner P J ACE gr User s Manual Oregon Graduate Institute of Science and Technology Beaverton Oregon 1992 41
21. ent Editor all changes are saved 2 10 Resources Some attributes of XPenelope can be customized by the user In order to do this entries must be made in the file SHOME Xdefaults and subsequently the X server must be restarted or the command 26 xrdb load HOME Xdefaults must be executed Here is a list of the customizable resources their default values and their meaning XPen geometry 100 100 Position of the model index after invocation XPen background Gray90 Background color XPen foreground Black Foreground color XPen printCommand lpr P s Command to print a file s is a placeholder for the file name and must appear in the resource string XPen PrinterName value psrO Default printer name XPen plotDrivers XGraph xgraph driver LB n Text text driver XY Available plot drivers The plotDrivers resource contains an arbitrary number of driver specifications Each spe cification is separated by a newline character A specification has the general format Title Driver Capabilities where Title is the text that appears in the Driver menu of the graph parameters dialog Driver is the name of the program which will be called to display the data Capabilities is a string which contains any of the following characters L The driver is able to display logarithmically scaled axes B The driver is able to display barcharts 27 X The driver is able to display alphanumer
22. ent selected in the Which Experiment dialog The Rewards menu specifies if the reward axis has nominal scale Nominal or normalized Time average The choices in the Which menu all The runs of all reward strategy lines are displayed part Choose rewards strategies from the Which dialog see Fig 17 theirs run should be displayed The choices in the Experiment menu one The results of one experiment i e the current experiment should be displayed more Choose one or more additional experiments from the Experiments dialog the reward or strategy functions of the additional experiments will be displayed together with the reward or strategy functions of the current experiment The toggle button Aggregated Rewards determines whether the rewards selected in the Which menu are aggregated or not Meaning of the buttons OK Displays the graph see Fig 21 Forward Runs the experiment in another interval see Sec 2 9 1 Change The user can change explicitly the result lines of a strategy graph see Sec 2 9 2 Cancel Leaves the graph parameters dialog 23 Exp 1 4Knoten Time i i gamma x 10 3 Figure 21 A plot program displaying a strategy In the graph strategies are labeled as Nodel gt Node2 which means that the reconfiguration edge starting in Node 1 and ending in Node2 is active A node N that appears in a macro named M is designated M N Node names such as M M M N wil
23. ept reconfigurability Transient as well as stationary control strategies and performance functions can be computed Contents 1 3 Introduction 1 1 1 Extended Markov Reward Models o 1 1 2 Peatures Of PENELOPE 445 3 a hee eo a 1 1 37 Platorms 2 on a hae NE eae Rang Seat do De aaa ea 3 XPenelope User Guide 3 2 1 CINDOC AO e oa toes er SS Es aa er O kenn 3 22 Ihe Modelsindex en ee Sec Ss a AS ae 4 2 3 The Parameter Sel Index sa ae Seid ed a 5 2A The Experiment Index is e Se As a Er a ER 6 25 The Model Editor s u amp 2 2 4 2 222 22 2222 23 A ae Ae at 7 29 1 Ihe File Menu s u 2er res Dao oao Oy A Ee BE 8 293 2 Th Ed Menu aca sa er es Beat 8 2 3 3 Lhe Options Menu 4 2 24 2 2 4 24 Ad 11 2 5 4 Arithmetic Expressions 0 000000 0000 11 2 5 5 The Forward Declaration Dialog 13 2 6 The Parameter Set Editor 24 2 2 22 oe OR AA AA 13 2 7 The Experiment Editor tesis Deus e Deg Bey Hee Ba Ss 14 2 8 The Stratesy Index 223 Sa ot et ee te A hg 18 2 8 1 The Strategy Editor 4 2 205 2 0 28 2 Wer A A 19 2 9 The Graph Parameters Dialog none 20 2 9 1 The Forward Experiment Dialog o 24 2 9 2 Change Graph Dialog 2 208 204 2 whee e eR 2 42T 26 2 10 Resources is cca ccna 4h era Sad Bed Bed hed Hes he eS 26 Examples 29 JL VB RaMpl ae sr doe rl as a eel dee ela a ot 29 3 2 Example ta Whe ta Bhan Wiese ie ee ASM SG Se ies De
24. erpreter The computed strategies are returned in a textual format with a clearly defined syntax This enables automated preprocessing and postprocessing of model strategy data e Using the graphical user interface XPenelope MUNK 93 the models are created inter actively In this case the user is working with familiar symbols such as circles for states and arrows for state transitions Additionally the graphical user interface offers a lot of extra functionality e Automated execution of experiment series e Graphical preparation of experiment results e Automated checking of model consistency e Definition and evaluation of hierarchical and iterative models using a special macro mechanism e Definition of model parameters and an arbitrary number of parameter sets per model e Preparation of computed strategies e Operating system independent data management model data base parameter set data base experiment and results data base strategy data base e Printing of models and results for documentation purposes 1 3 Platforms XPENELOPE runs under the following architectures e Sun 4 with SunOS 4 e Sun 4 with SunOS 5 Solaris XPENELOPE requires an existence of the X Window System release 11 version 4 or higher and of the OSF Motif GUI system version 1 1 or higher 2 XPenelope User Guide 2 1 Invocation XPenelope is invoked by executing the command xpenelope from the command line This will bring up the
25. f all states terminators and macro invocations in a model must be unique Delete Activates the delete mode In this mode the select button may be pressed over an object in order to delete it Clear Erases the whole model 2 5 3 The Options Menu The options menu consists of five toggle buttons Show Grid Makes the grid visible invisible Snap to Grid Activates deactivates grid snap mode In this mode all newly created ob jects will be centered with respect to the nearest intersection of the grid Show Node Names Shows Hides the names of states and terminators Show Node Rewards Shows Hides the reward values of states Show Transition Rates Shows Hides the rates of transitions 2 5 4 Arithmetic Expressions An arithmetic expression consists of numbers parameter names operators and function calls The operators obey the usual precedence rules for arithmetic operators 11 Operator highest gt 5 5 lowest test for inequality gt highest IO 2 CS Ze EEE lt gt Slowest Parentheses may be used to override the default precedence rules If the comparison succeeds the comparison operators on precedence level 5 return 1 0 otherwise they return 0 0 The comparison operators are generally only useful in the Condition field of the Macro dialog box The following functions are defined SORTO EXPO LN x natural logarithm In x A number is a sequence of digits wi
26. gle button positive the values of reward rates will be displayed as positive values By selecting the toggle button negative the values of reward rates will be displayed as negative values The three lists X Axis Y Axis and Z Axis contain the possible axis labels lt State gt lt Reward gt and names of the parameters with more than one value In the text widgets under each list the user may change description of the axis If the model has more than one varying parameter then fixed values must be selected for the parameters This is done by clicking at one of the buttons marked with the parameter name and by selecting one or more of the possible values from the Values dialog see Fig 17 Default value is the first value in the list of the possible values If more than one value is selected the parameter gets a variable mode No more than one parameter may have the variable mode In the Driver menu a plot program can be selected By default the following drivers are installed XGraph Driver for the xgraph program a freely distributable plot program Gnuplot Driver for the gnuplot program also freely distributable Text Driver for a textual representation of the results the text is displayed using the UNIX view program ACE GR Driver for the ACE GR program a freely distributable plot program TURN 92 XGadd Driver for the xgadd program which has been developed for the PEPSY tool at the Univer
27. gy name in response to the prompt Name of copy and then press OK Then a name of the model is asked for Rename Renames a selected strategy Type in the desired strategy name in response to the prompt New strategy name and then press OK Delete Deletes the selected strategy Open jOpens the strategy editor for the selected strategy see Sec 2 8 1 Cancel Exits the strategy index All operations marked with j require that a strategy has been previously selected from the list A double clicking of a list item will perform the Open action 18 2 8 1 The Strategy Editor Strategy Editor Availability Strategy Transient Strategy lt gt Stationary Strategy Mission time 000 Parameter Strategy gamma 0 01 INT R2 3 7 N1 0 E gamma 0 001 N2 R3 129 4 N2 0 gamma 0 0013 N3 R4 780 9 N3 0 gamma 0 002 gamma 0 005 gamma 0 0002 gamma 0 0005 gamma 0 0007 gamma 0 0008 gamma 8e 05 gamma 0 0001 Q New Parameter Combination lt gt New Parameter Name ligamma value 0 0006 al y ok Strategy for all combinations i Ok e Cancel E Figure 15 Strategy editor The strategy editor see Fig 15 is used to create modify and display strategies It contains e Toggle buttons Transient Strategy and Stationary Strategy which determine a type of the selected strategy e Mission time The mission time is used only for transie
28. h recursion step The macro invokes itself 1f N lt k 35 Figure 33 Macro for the Erlang k distribution otherwise the macro Connect is called Connect is a macro which simply connects the input with the output The branching state Com is needed to connect the outputs of the two macros with Out because it isn t allowed to connect more than one edge to a macro terminator The following paragraphs show how to create the Erlang macro Phase 1 Create the Connect macro Step 1 Invoke XPenelope and press the Create button of the model index Step 2 Select the item Macro Terminator from the Edit menu This activates the Macro terminator mode in this mode every mouse click in the drawing area produces a new macro terminator Step 3 Click the left mouse button twice in the drawing area in order to produce the terminators In and Out Step 4 Select the item Set Parameters from the Edit menu 36 Step 5 Step 6 Step 7 Step 8 Step 9 Click at the first macro terminator The Set Parameters dialog appears Enter In in the field Name and press the OK button Repeat step 5 for the second macro terminator name Out Select the item Transition from the Edit menu Click at the terminator In and then at the terminator Out A transition between the two terminators will appear see figure 34 Figure 34 The Connect macro Select the item Save from the File menu and save the macro under the name Con
29. ical strings as tick labels on the X axis Y The driver is able to display alphanumerical strings as tick labels on the Y axis Several arguments are passed to the driver program 1 Name of input file 2 Title 3 Name of X axis 4 Name of Y axis Additionally the following options may be passed to the driver xalpha Alphanumerical tick labels on the X axis yalpha Alphanumerical tick labels on the Y axis logx Logarithmically scaled X axis logy _Logarithmically scaled Y axis bar Display bar chart instead of graph The input file contains XY pairs one for each line The X and Y values are separated by one space character The XY pairs are grouped by their Z value a line indicating the Z value 6699 precedes the corresponding XY pairs this line starts with the character Example N1 gt N1 0 1 10 0 2 30 0 4 60 N1 gt N2 0 1 15 0 2 40 0 4 80 This file stands for the XYZ pairs 0 1 10 N1 gt N1 0 2 30 N1 gt N1 0 4 80 N1 gt N2 28 3 Examples This section contains two step by step examples which show how to create and use models and macros with XPenelope 3 1 Example 1 on Figure 25 A simple model from DEME 92 p 52 The first example shows how to create the model depicted in figure 25 The following reward rates shall be assigned to the states Phase 1 Create the states Step 1 Invoke XPenelope by entering the command xpenelope on the
30. igure 5 Macros dialog box Having the Macro menu item selected the Macros dialog box pops up see Fig 5 It contains a list of available macros select one of the list items and then press OK Press Cancel if the operation should be aborted If a recursive macro definition is to be created a macro which has not yet been defined has to be used The Forward button can be selected in order to create a macro forward declaration see Sec 2 5 5 If a macro invocation and a macro definition don t match the macro invocation will be displayed as a crossed out box In this case the in consistent macro invocation must be deleted and a new consistent invo cation has to be created 9 Set Parameters Activates the parameter modification mode In this mode any object may be selected in order to modify its parameters This does not apply to reconfiguration edges which are parameterless If an object has been newly created a question mark is displayed on top of the object this indicates that there are still parameters to be set Cancel Figure 6 Parameters dialog If an object is selected a dialog box will appear allowing to change the object parameters see Fig 6 The OK button must be pressed in order to apply the new parameters to the object No changes are made if the Cancel button is pressed e A Markov state or a branching state has the following parameters Name Name of state
31. l automatically be abbreviated to M 3 N If one of the varying parameters has a variable mode the line labels in the graph contain the value of this parameter in parentheses If the Experiments menu is set to more the line labels in the graph contain a number in parentheses that determines which experiment the lines belong to The labels without such number determine lines from the current experiment 2 9 1 The Forward Experiment Dialog 8 Forward Experiment iii Parameter delta N Equidistant Values Interval lt 0 01 0 05 gt Start Value gt Backwards 0 Forwards 0 06 Step Width 0 01 Number of steps l gin Lite i Cancel Figure 22 Forward Experiment dialog for equidistant mode 24 f 8 Forward Experiment E Values 0 01 0 001 0 0001 gt Figure 23 Forward Experiment dialog for multiple mode There are three different forward experiment dialogs depending on the parameter mode equidistant log equidistant or multiple values of the parameter selected in one of the axis lists Equidistant Mode The Forward Experiment dialog appears see Fig 22 The first three lines give an information about the selected parameter name mode and interval of values where the experiment had already run Active one of the following radio buttons Backwards value The parameter values are taken from the set 2le a s i i 0 N 1 where a is the Start Value s is the Step Wi
32. l description language Structure analysis of the model Output of the trace function on defined states Optimal strategies Accumulated rewards State probabilities e Error messages of PENELOPE All informations marked with j require that the corresponding Info toggle button is set on see bellow The Info is displayed using the UNIX less program 17 Show Shows the results of the experiment The Graph Parameters dialog pops up see Sec 2 9 Cancel Leaves the experiment editor 2 8 The Strategy Index E Avail stationary Avail always reconfigure E Avail never reconfigure Availability E Availability DB Availability DB var par Create E Figure 14 Strategy index The strategy index see Fig 14 is a list of all strategies available for the selected model One of the following buttons may be pressed Create Creates a new strategy A new strategy name is asked for Then the strategy editor 1s opened see Sec 2 8 1 Load tLoads the selected strategy in the experiment definition The name of the loaded strategy appears in the experiment editor If the selected strategy is of a transient type the mission time of this strategy appears in the widget Mission Time in the experiment editor Copy Makes a copy of the selected strategy A name of the copy is asked for Copy To Makes a copy of the selected strategy to an arbitrary model Type in the desired strate
33. med for an infinite time horizon A strategy S is op timal if no other strategy S exists such that the time averaged mean total reward E X limp FE Y t gained under strategy S exceeds the one gained under 5 E X can be dependent or independent of state 7 In the latter case EIX E X for all 2 is called the optimal overall reward rate The optimization itself is performed by the deployment of standard methods from Markov decision theory TIJM 86 The adap tation of these methods to the analysis of EMRMs is out of the scope of this reference manual More details can be found in KATK 92 In addition PENELOPE offers procedures for computations under fixed deliberately eligible strategies e Simulation Under a fixed strategy the behavior of the system is simulated The mean total accumu lated reward for an arbitrary initial state is computed e Transient Analysis The transient analysis is carried out under a fixed strategy that can be deliberately speci fied The strategy can be either of a transient or a stationary type e Stationary Analysis The stationary analysis is carried out under a fixed strategy The strategy can only be of a stationary type PENELOPE offers two possibilities for the user to interact with the system e The extended Markov reward models are defined by using a model description language These models can be analyzed and optimized by invoking appropriate commands from the PENELOPE command line int
34. model index see section 2 2 If xpenelope is called for the first time the model database will be created and some sample models will be copied into the user s database Normally the location for the model database is the directory SHOME xpenelope This may be overridden by setting the environment variable PENELOPEDB to the desired path name 2 2 The Model Index E A A Example Mak A Mak a lt M gt A Mak b lt M gt AA Makro lt M gt AA Test lt M gt Beispiel BetterRouting BigModel Connect lt M gt Drehbank i Create Copy Rename Delete Open Print Quit Figure 1 Model index The model index is a list of all predefined models and macros see Fig 1 Macros are marked with the suffix lt M gt One of the following buttons may be pressed Create Creates a new model The model editor is opened see Sec 2 5 Copy Makes a copy of the selected model Type in the desired model name in response to the prompt Name of copy and press OK Then the whole model together with its parameter sets experiment definitions and results of experiment series and strategies 1s copied Rename jRenames a model Type in the desired model name in response to the prompt New model name and press OK Delete Deletes a model together with its parameter sets experiment definitions and results of experiment series and strategies Open Brings up a pull down me
35. nect Phase 2 Create the nodes of the Erlang macro Step 10 Step 11 Step 12 Step 13 Step 14 Create the terminators n and Out of the Erlang macro as shown in steps 2 to 5 Create the Markov state A and the branching state Com as shown in example 1 Select the item Macro from the Edit menu This activates the Macro mode in this mode every mouse click in the drawing area produces a new macro invoca tion The Macros dialog box appears Select the item Connect from the list and press the OK button Click the left mouse button while the cursor is in the drawing area An invocation of the Connect macro will appear Phase 3 Create a forward declaration for the Erlang macro At this point we have the problem that we need to use the Erlang macro This macro however has not yet been defined Thus we have to create a forward declaration which informs the model editor about the names of the macro sockets and the names of the macro parameters The parameters of the Erlang macro are Number of phases 37 Step 15 Step 16 Step 17 Step 18 Step 19 Step 20 Step 21 Step 22 Step 23 Select the item Macro from the Edit menu The Macros dialog box appears Press the Forward button The Forward Declaration dialog appears Enter Erlang into the Class field Click at the In button and enter In in the Socket name field Then press the Insert button This insert
36. nt strategies e A list of Parameter combinations Each combination is represented by names and values of the varying parameters Both name and value can be modified in the text widget Name and Value By clicking at the up arrow resp down arrow the previous resp next parameter of the selected parameter combination appears The button OK next to the arrows must be pressed in order to apply the parameter modification to the parameter combination list To create a new parameter of the selected combination click at the toggle button New Parameter write a name and a value and then press OK To create a new combination click at the toggle button New Parameter Combination write a name and a value of the first parameter in the new combination and then press OK New combination is created The remaining parameters of this combination can be put in by clicking at New Parameter 19 e Strategy This text widget contains a strategy of the selected parameter combination For the syntax see MAUS 90 Both transient and stationary syntax are valid The strategies can be modified by the user Each line must be terminated with new line character In the text widget Strategy for all combinations write a line that is equal for all para meter combinations By pressing the button OK next to this text widget strategies for all parameter combinations are modified in the line with the same reconfiguration state Meaning of the buttons Save Sa
37. nu which offers the following choices Model Editor Opens the model editor see Sec 2 5 Parameter Index Shows Edits the list of all parameter sets defined for the model see Sec 2 3 4 Experiment Index Shows Edits the list of all experiment definitions see Sec 2 4 Print Prints the model as a PostScript file A dialog with the following choices appears Send to printer Sends the PostScript file to the indicated printer Send to file Stores the PostScript graphics in the specified file Quit Quits the program All operations marked with j require that a model or a macro has been previously selected from the list A double clicking of a list item performs the Open Model Editor action 2 3 The Parameter Set Index E 4 Knoten Gamma Var Avail c gamma var E Availability Gamma Var Availability Gamma less Availability delta 0 001 E Availability delta 0 1 COA compare performance COA gamma less E Capacity oriented Av Konstant Figure 2 Parameter set index The parameter set index see Fig 2 is a list of all parameter sets available for the selected model One of the following buttons may be selected Create Creates a new parameter set The parameter set editor is opened see Sec 2 6 Copy Makes a copy of the selected parameter set Type in the desired parameter set name in response to the prompt Name of copy and then press OK
38. ransition from the Edit menu Create all necessary transitions as shown in figure 33 38 Figure 35 The Erlang macro Step 36 Save the macro under the name Erlang It is important that this name is the same as the name that has been specified in the forward declaration dialog The completed macro definition should look like figure 35 Phase 6 Use the Erlang macro Step 37 Select the item Macro from the Edit menu The Macros dialog appears Step 38 Select the item Erlang from the list and press the OK button Step 39 Click the left mouse button while the cursor is in the drawing area An invocation of the Erlang macro appears Step 40 Select the item Set Parameters from the Edit menu Step 41 Click at the macro invocation The Macro dialog appears Step 42 Enter a node name Step 43 Enter the value 1 in the field N in order to initialize the recursion depth counter Step 44 Modify the parameters mu rew and k to suit your application Step 45 Build your model around this macro invocation An example is shown in fig ure 36 4 Conclusion The combination of the tools Penelope and XPenelope enables a fast and comfortable creation and optimization of extended Markov reward models 39 Figure 36 A simple model with an invocation of the Erlang macro Penelope contains algorithms for the analysis and optimization of statically and dynamically reconfigurable systems
39. riment if there are any 16 e Experiment Status Working L Abort Figure 12 Working dialog Save As Saves the experiment definition and the results of this experiment if there are any under a new name The experiment name is asked for Run Starts the experiment While the experiment is performed a Working dialog appears see Fig 12 The experiment may be aborted with the Abort button of the Working dialog Info Availability ll Number of value combinations 12 PENELOPE Version 1 5 gt load usr tmp daaa02886 done gt gt Mission time 1000 dt 0 1 gt gt gt Strategy Strategy computed in a time horizon 0 999 9 M 3 R2 3 Acc rewards computed in a tine horizon 0 999 9 Covl 640 907 Cov2 666 219 Cov3 680 867 NO 578 935 N 641 59 N2z 666 902 N 681 55 Nd 690 202 R2 641 59 R3 666 902 Rd 681 55 REL 625 324 RB2 660 636 RBS 675 284 ROL 640 963 RC2 666 275 RC3 680 923 beta 1 delta 0 01 n3 1 r3 1 1 1 Figure 13 Info window Info Shows information on the performed experiment see Fig 13 The Info file contains e Parameter combinations Model in PENELOPE s mode
40. s the input socket In into the Socket names list Click at the Out button and enter Out in the Socket name field Then press the Insert button This inserts the output socket Out into the Socket names list Enter k in the Parameter name field and press the Insert button This inserts the parameter k in into the Parameters list Repeat step 20 for the parameters mu N and rew Press the OK button Click the left mouse button while the cursor is in the drawing area An invocation of the Erlang macro will appear Phase 4 Edit the macro parameters Step 24 Step 25 Step 26 Step 27 Step 28 Step 29 Step 30 Step 31 Step 32 Step 33 Select the item Set Parameters from the Edit menu Click at the invocation of the Connect macro The Macro dialog appears Enter the node name C in the Name field Enter the condition N k in the Condition field The meaning of this condition 1s that this macro must not be invoked if k and N are not equal Press the OK button Click at the invocation of the Erlang macro The Macro dialog appears Enter the node name E in the Name field Enter the condition N lt k in the Condition field Change the content of the field N from N to N 1 This means that N is incremented with each recursion step Press the OK button Phase 5 Complete the macro definition Step 34 Step 35 Select the item T
41. set and press the OK button The label of the Parameter Set button has changed to PSet to reflect the currently selected parameter set Enter the value 500 in the field Mission Time Enter the value 0 1 in the field Step Width Make sure that the radio button labeled Transient Optimization is active Phase 8 Start the experiment Step 35 Step 36 Press the Run button The Working dialog appears Wait until this dialog disappears from the screen Then the experiment has finished Press the Save button A message dialog with the text Experiment Saved ap pears press the OK button Phase 9 Show the results Step 37 Step 38 Step 39 Step 40 Step 41 Step 42 Step 43 Step 44 Step 45 Step 46 Press the Show button The Graph Parameters dialog appears Make sure that the program XGraph has been selected in the Driver menu Select the item Log Lin from the Scale menu in order to scale the X axis loga rithmically Press the OK button After a few seconds the graph shown in figure 30 appears Interpret the results The curve labeled N1 gt R1 indicates that above this curve the reconfiguration edge from state N1 to state RI is active E g for gamma 0 001 the reconfiguration edge is active from the start of the mission until 41 8 time units before the end of the mission Remove the graph window by pressing the Close button You may now modify the se
42. sity of Erlangen N rnberg MEIT 92 In the Scale menu can be specified if the X or Y axis should have a linear or a logarithmic scale There are four possibilities Lin Lin X axis linear Y axis linear Lin Log X axis linear Y axis logarithmic Log Lin X axis logarithmic Y axis linear Log Log X axis logarithmic Y axis logarithmic In the Mode menu can be chosen between a graph Graph or a bar chart Histogram The menus Mode and Scale do not apply to the Text driver The toggle button Suppress 0s determines whether strategy changes which always happen at time O should be suppressed or not The default is to suppress these strategy changes 21 e Parameter Set Experiment Availability Model 4processors Mode Transient Optimization Mission Time 1000 Parameter Set gamma Performance Graph Figure 18 Parameter Set dialog The toggle button Show Parameter Set determines whether a window containing graph in formations see Fig 18 is shown by pressing the OK button or not This window is for a documentation purpose This information can be saved in a data file by clicking at the button Save Then a file name is asked for In the text widget Experiment Name the inscription of the resulting graph may be changed f Avail gamma less f Availability f COA compare performance f Capacity gamma less f Capacity or Avail f sana test f sim 1000tu ar N1 E sim 1000tu nr N4
43. tep 15 Step 16 Step 17 Step 18 Select the item Set Parameters from the Edit menu Click at the transition between state N2 and state Cov The Parameters dialog appears Enter the transition rate 2 gamma in the field Rate Press the OK button Repeat step 17 for each transition If you click at a transition originating in a branching state the Parameters dialog will contain a field Probability In this field you have to enter the probability of the transition c or 1 c in our example The drawing area should now look like figure 28 31 Figure 28 The completed model Phase 5 Save the model Step 19 Select the item Save from the File menu A dialog appears which prompts you for a model name Enter SimpleExample and press the OK button Step 20 A message dialog with the text Model saved appears Press the OK button Phase 6 Create a parameter set We will now assign concrete values to the individual model parameters The values we will choose are Model parameter Value s Step 21 Select the item SimpleExample in the model editor and press the Open button A pop up menu appears select the item Parameter Index The parameter index appears Step 22 Press the Create button of the parameter index in order to create a new parameter set The parameter set editor shown in figure 29 appears 32 e Parameter Set Editor Save Step 23 Step
44. teps have to be performed in order to create a transition 1 Click at the start node 2 If no intermediate vertex is needed goto step 3 otherwise click anywhere in the canvas except over other objects in order to cre ate a new vertex Repeat this step until all intermediate vertices have been created 3 Click at the target node Now the transition will be displayed Reconfiguration Edge Activates the reconfiguration edge mode In this mode an equivalent Macro Terminator Macro procedure as in the transition mode is used in order to create a reconfi guration edge Activates the macro terminator mode In this mode a new macro termi nator is created if the select button is pressed Models containing macro terminators are called macros a macro terminator is the connection of the inside world of the macro to the outside world If a macro is invoked by using the Macro item of the Edit menu the macro termi nators will be shown as little arrows sockets within a larger frame The direction of an arrow indicates the direction of the transition which is attached to the corresponding terminator Activates the macro mode In this mode a new macro invocation is created if the select button is pressed Available Macros a Mak a A a Mak b AA Makro AA Test Connect Erlang ErlangMak Kap4 2 Makro Kap4 2 Makro LastCase Macro Name OK Forward Cancel F
45. tering leaving the macro 7 The menu bar of the model editor offers four choices File Loading saving and printing models Edit Creating modifying and deleting objects Options Grid and node name operations Help Currently only the menu item Help on Version is offered It displays the version number of the program The following sections discuss the individual menus 2 5 1 The File Menu New Creates a new model Open Loads a new model that is selected from the model index Save Saves the model If the model has been previously saved the same file name will be used Otherwise a file name is asked for Save As Saves the model under a new file name The file name is asked for Print Prints the model as a Postscript file Options are available to save the file or to send it directly to a printer Exit Leaves the model editor 2 5 2 The Edit Menu The first eight choices of the edit menu determine which action is performed if the left mouse button is pressed the select button within the model editor A indicator to the left of the menu items shows which item currently is enabled Markov State Activates the Markov state mode In this mode a new Markov state is created if the select button is pressed Branch State Activates the branch state mode In this mode a new branching state is created if the select button is pressed Transition Activates the transition mode In this mode the following s
46. th an optional embedded decimal point An exponent suffix may be appended i e the letter e an optional sign and a sequence of digits Examples 3 3 14 0 0314e2 314e 2 A parameter is a sequence of characters starting with a letter the parameter name may contain letters digits and underscores _ The actual value of a parameter is defined in the parameter set editor see Sec 2 6 Examples 1 x 1 x 3 2 a el 2 a EXP 1 x itz SQRT 1 x 1 x 12 2 5 5 The Forward Declaration Dialog Class Example Socket names Parameters Input In alpha Input2 In beta Outputl Out Output Out Socket name Parameter name Qin Out Insert Delete Delete ok Cancel Figure 8 Forward Declaration dialog The purpose of the forward declaration dialog see Fig 8 is to declare a macro which has not yet been defined The following information has to be provided Class The name of the model that will contain the macro definition Socket names The names of the macro terminators Use the button Insert to insert new socket names and the button Delete to delete the selected socket names The radio buttons In and Out determine the direction of the socket Parameters The names of the macro parameters Use the button Insert to insert new parameter names and the button Delete to delete the selected parameter names Press the OK button in order to
47. ttings of the Graph Parameters dialog in order to modify the appearance of the graph For example you might select lt Time gt from the X Axis list and lt Strategy gt from the Y Axis list If you now press the OK button the graph appears with the X and Y axes swapped Click at the radio button Performance Graph in the Graph Parameters dialog You may select one or more performance curves by selecting the part item in the Which menu The Which dialog appears Select one or more items in the list of model states and press OK Press the OK button in the Graph Parameters dialog A performance graph for the selecting states appears 34 Figure 31 Model of the Erlang k distribution The second example shows how to create and use macros In this example a macro which models the Erlang k distribution shall be created Figure 31 shows the model of the Erlang k distribution it consists of a chain of k Markov states with a transition rate of k j Erlang k distributions are generally used to model non exponential distributions with a small variance An Erlang k distribution can be thought of as one Markov state which is connected to an Erlang k 1 distribution see figure 32 This means that a model for the Erlang k distribution can be built using a recursive macro The macro for the Erlang k distribution is depicted in figure 33 The macro contains a parameter N which is incremented by one with eac
48. ves the strategy editor Save As Saves the strategy editor under a new name The strategy name is asked for View Shows the current strategy The Graph Parameters dialog pops up see Sec 2 9 Cancel Leaves the strategy editor 2 9 The Graph Parameters Dialog e Graph Parameters Availability Strategy Graph Experiment Name javana Difference Graph Gif fer ENpeements Performance Graph lt Time gt lt Strategy gt lt Strategy gt Strategy gamma gamma E peale 0 negative lt Time gt gamma Which all c Driver XGraph ara RE Ss Mode Graph kTime gt kStrategy gt Experiment one Scale Lin Lin Slater Sitar pirane 3 de E Suppress 0s E ec U Show Parameter Set X Axis Z Axis Forward Change Cancel Figure 17 Value Difference Values and Which rewards dialogs XPenelope uses 2D plot programs to display the results of the experiments The Z Axis of the graph parameters dialog see Fig 16 represents the capability to plot multiple data sets per graph Select a kind of graph by clicking at one of toggle buttons 20 Strategy Graph The three lists X Axis Y Axis and Z Axis contain the possible axis 39 66 labels lt Time gt lt Strategy gt and names of the parameters with more than one value Performance Graph By selecting the tog
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