Simulation-with-Arena-教案

SimulationwithArena,3rded.Chapter11–Continuous&CombinedDiscrete/ContinuousModelsSlide1of11ContinuousandCombinedDiscrete/ContinuousModelsChapter11LastrevisionJuly21,2003SimulationwithArena,3rded.Chapter11–Continuous&CombinedDiscrete/ContinuousModelsSlide2of11WhatWe’llDo...•Whatisacontinuoussystem?•Simplelinearcontinuoussystems•Combineddiscrete/continuoussystems•Non-linearandcomplexsystemsSimulationwithArena,3rded.Chapter11–Continuous&CombinedDiscrete/ContinuousModelsSlide3of11ContinuousSystems•Discretesystems–Statechangesoccuratisolatedpointsintimecalledevents•Continuoussystems–StatechangesmayoccurcontinuouslyovertimeFlowoffluidsandfluid-likematerialsTemperaturechangesChemicaloperationsBiologicalprocessesSimulationwithArena,3rded.Chapter11–Continuous&CombinedDiscrete/ContinuousModelsSlide4of11ContinuousSystems•Simplesystems(linear)RateofchangeisconstantbetweeneventsFuturevaluecanbecalculatedfromstartingvalueandrateCanstepdirectlytocalculatedevent•Complexsystems(non-linear)RateofchangemaydependonothercontinuousprocessesSpecializedapproachesusedtocapturechangeApproximatescontinuouschangebymakingaseriesofsmallstepsbetweentheusualdiscreteeventsSimulationwithArena,3rded.Chapter11–Continuous&CombinedDiscrete/ContinuousModelsSlide5of11ContinuousSystems•ExampleofsimplecontinuoussystemfillingatanksmoothlyovertimeSimulationwithArena,3rded.Chapter11–Continuous&CombinedDiscrete/ContinuousModelsSlide6of11ContinuousSystems•Basicconstructs:Levels&RatesfromElementsPanel•ALevelisthevaluethatischangingovertime•ARatedeterminestherateofchangeofthelevel•BotharesimilartoVariablesinthattheycanbeassignedanewvalueatanytime.•LevelsmayalsochangeastimeadvancesifthevalueoftheassociatedRateisnon-zero.•ALevelandaRateshouldbeusedasapair(e.g.Ifyouhave4Levelsyoushouldhave4Rates)SimulationwithArena,3rded.Chapter11–Continuous&CombinedDiscrete/ContinuousModelsSlide7of11SimpleContinuousSystems•ContinuousElementspecifiesintegrationparameters:NumberofDifEquations–Insimplesystems,leaveatdefaultofnumberofRate/Levelpairs.NumberofStateEquations–Ignoreinsimplesystems.Minimumstepsize–Theminimumtimeadvancebetweenintegrationsteps.Use0.0insimplesystems.Maximumstepsize–Themaximumtimeadvancebetweenintegrationsteps.Useahighvalue(100)insimplesystems.SavePointInterval–Themaximumtimebetweensavepointsforrecordingcontinuousstatistics(CSTATS).Method–UseEulerlinearalgorithmforsimplesystems.SimulationwithArena,3rded.Chapter11–Continuous&CombinedDiscrete/ContinuousModelsSlide8of11SimpleContinuousSystems•DiscretecontrollooptoemptyandrefillatankSimulationwithArena,3rded.Chapter11–Continuous&CombinedDiscrete/ContinuousModelsSlide9of11CombinedDiscrete/Continuous•DetectModulefromBlockspanel“watches”forandhelpspredictevents.•Watchesforvalueofavariabletocrossathresholdvalue(e.g.atanklevelreachingitsmaximumvalue)•SimilartoCreateModuleinthatanentityiscreatedwhencrossingoccurs.SimulationwithArena,3rded.Chapter11–Continuous&CombinedDiscrete/ContinuousModelsSlide10of11CombinedDiscrete/Continuous•FillandemptylogicusingDetectmodulesSimulationwithArena,3rded.Chapter11–Continuous&CombinedDiscrete/ContinuousModelsSlide11of11ComplexSystems•Non-linearsystemsrequirespecialalgorithmslikeRunge-Kutta-Fehlberg(RKF).•Stepsizesmustbesetcarefully.•SmallerstepsizewillgeneratemoreaccurateresultsbecauseArenawillcalculatecontinuous-changevariablesmoreoften.•Largerstepsizewillrunfaster,butyourerrortoleranceswillneedtobesethigher.•Manysituations(likeagravityfedtank)areactuallynon-linear,butcanbeaccuratelyapproximatedwithfaster,linearmethods.