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Chapter4SolversThischapterdescribesthevariousanalyticandsimulationsolversthatareavailable.ThesolversareselectedthroughtheSolvebutton,andmustberunafterthemodelhasbeenfullyspeci edbyapplyingthevariouseditorsundertheitemEdit(seeChapter3).Generalsuggestionsaboutwhichsolverstoapplyforspeci cmodelandmeasuresarepresentedprecedingthedetaileddescriptionofthespeci csolvers.Thischapterusestheclassi cationofmeasuresandmodelsasintroducedinSection1.4ofChapter1.4.1ChoosinganAppropriateSolverApplicabilityofboththeanalyticsolversandsimulatorsdependsonthetypeofper-formabilitymeasureandmodelclassconsidered.Allmeasuresandmodelclassesarede-scribedindetailinChapter1.Givenamodelandmeasure,achoicebetweenanalyticsolutionandsimulationhastobemade.Therearesomebasicruleswhenanalyticsolversandsimulatorscanbeapplied: AnalyticsolversonlycanbeappliedtothetwomodeltypesinSection1.4ofChapter1,i.e.,tomodelswithallexponentialactivitiesorwithatmostoneenableddeterministicactivityatthetime.Simulationcanbeappliedtoallmodelclasses. Modelsmusthavea nitestatespaceforanalyticsolution. Ifactivityvariablesareused,onlysimulationcanbeapplied.Table4.1givesthemeasureandmodelclassesforwhichanalyticsolverscanbeapplied,andTable4.2givesthisinformationforthesimulators.Usethetablesasfollows.First,identifywhichmodelclassamodelbelongstoandwhichmeasuretypeistobederived.Thesolverthatcanbeappliedcanthenbefoundintheright-sidecolumn.So,forinstance,thearssolvergivesthemeanoftransientinterval-of-timemeasuresformodelswhereall4-14-2CHAPTER4.SOLVERSAnalyticSolvers(forrewardvariablesonly)Steady-stateInstant-of-timeMean,ApplicableororVarianceorAnalyticModelClassTransientInterval-of-timeDistributionSolverAllactivitiesSteady-stateInstant-of-timeaMean,VariancedssandissexponentialandDistributionTransientInstant-of-timeMean,VariancetrsandDistributionInterval-of-timeMeanarsDistributionpdfExponentialandSteady-stateInstant-of-timebMean,dissdeterministicVarianceactivitiesandDistributionaifonlyraterewardsareused,thetime-averagedinterval-of-timesteady-statemeasureisidenticaltotheinstant-of-timesteady-statemeasure(ifbothexist).bprovidedtheinstant-of-timesteady-statedistributioniswell-de ned.Otherwise,thetime-averagedinterval-of-timesteady-statevariableiscomputedandonlyresultsforraterewardsshouldbederived.Table4.1:Modelsandmeasuresversustheapplicableanalyticsolver.Simulators(forallmodels)Steady-stateInstant-of-timeMean,ororVarianceorApplicableTransientInterval-of-timeDistributionVariableSimulatorTransientInstant-of-timeMeanRewardvariableTSimandandandITSimInterval-of-timeVarianceActivityVariableTSimSteady-stateInstant-of-timeMeanandRewardVariableSSimVarianceandActivityVariableTable4.2:Measuresobtainablewithdi erentsimulationsolvers.4.1.CHOOSINGANAPPROPRIATESOLVER4-3timedactivitiesareexponentiallydistributed.TheabbreviationsusedinTable4.1fortheanalyticsolvershavethefollowingmeaning(wegivethenamesastheyappearinthemenuitemsofthecontrolpanel): dss:Solve-DirectSteady-StateSolver iss:Solve-IterativeSteady-StateSolver diss:Solve-DeterministicIterativeSteady-StateSolver trs:Solve-TransientSolver ars:Solve-AccumulatedRewardSolver pdf:Solve-ProbabilityDistributionSolverForthesimulatorsinTable4.2weusethefollowingabbreviations: SSim:Solve-Steady-StateSimulator TSim:Solve-TerminatingSimulator ITSim:Solve-ISTerminatingSimulator(ImportanceSampling).Animportantdi erencebetweenhowtheanalyticsolversareappliedandhowthesimulatorsareappliedistheprecisespeci cationoftheperformabilitymeasure.Foranalyticsolutions,thechoiceofthesolverdeterminesthespeci cperformabilitymeasurewhichwillbecomputed.Inotherwords,givenaspeci edrewardstructure,theperformabilitymeasure(includingaspectsasmeanorvariance,transientorsteady-state,etc.)isspeci edbythechoiceofthesolver.Forsimulation,ontheotherhand,theprecisespeci cationoftheperformabilityvariableiscarriedoutseparatelyunderEdit-PerformabilityVariables,byselectingEditStatsinthePerformabilityVariableSpecificationwindow.Onlywhethertransientorsteady-stateresultswillbeobtainedisdeterminedbythechoiceofthesimulator.ItmustbeunderstoodthattheTables4.1and4.2givethepotentialuseofthesolvers;itisnottosaythattheresultswillalwaysbederivedinareasonabletimespanorcanbe tintostandardsizememory.Theseconsiderationsareofprimaryimportanceforthepracticalapplicationofthesolversandarethereforediscussedinsomemoredetail.Advantagesanddisadvantagesoftheuseofthedi erentsolversprovidedbyUltraSANarepresentedinfourlists:advantagesanddisadvantagesofanalyticsolutionsandadvantagesanddisadvantagesofsimulation.Thelistsarenotclaimedtobeexhaustive,buttrytocapturetheproblemsmostlikelytobeencounteredinthepracticalapplicationoftheUltraSANsolvers.4-4CHAPTER4.SOLVERSAdvantagesofanalyticsolution Exactcomputationofasolutioniscarriedout,i.e.,opposedtosimulationtheoutcomedoesnotdependonageneratedstreamofpseudo-randomnumbers. Fortheinstant-of-timeperformabilityvariables,distributionscanbeobtainedwithoutextracostinadditiontotheirmeanandvariance. Accuracyofthesolutioncan,formostsolvers,beincreasedwithoutexcessiveincreaseinth
本文标题:Transient Instant-of-time Mean, Variance trs
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