A Comparison of Discrete Event Simulation and Syst

AComparisonofDiscreteEventSimulationandSystemDynamicsforModellingHealthcareSystemsSallyBrailsfordandNicolaHiltonSchoolofManagementUniversityofSouthampton,UKAbstractInthispaperwediscusstwodifferentapproachestosimulation,discreteeventsimulationandsystemdynamics.Bothhavebeenusedwidelyinthehealthcaredomain,althoughtherearefewerapplicationsofsystemdynamics.Theaimofthispaperisnottogiveacomprehensivesurveyoftheliterature,butrathertodiscusswhetherthechoiceofmethodologyispurelythepersonalpreferenceofthemodeller,orwhetherthereareidentifiablefeaturesofcertainsystemsthatmakeonemethodologysuperiortotheother.Weillustratetheuseofthesetechniquesbyconsideringtwocasestudies,asimplediscreteeventsimulationmodelofHIV/AIDSandasystemdynamicsmodeloftheUKcardiacsurgerysystem.Weattempttodrawupsomeguidelinestoassistthemodellerinmakingthechoiceoftechnique.1.IntroductionSimulationisarguablythemostcommonlyusedOperationalResearchtechniqueandithasbeenwidelyusedinthehealthcaredomain,chieflybecauseoftheadvantagesithasoverothertechniquesinitsflexibility,abilitytodealwithvariabilityanduncertainty,anditsuseofgraphicalinterfacestofacilitatecommunicationwith,andcomprehensionby,healthcareprofessionals.Thesefeatureshaveoftenmadesimulationthetechniqueofchoiceinmodellinghealthcaresystems,whichmayinvolvecomplexbiological,organisationalandhumanbehaviouralprocesses,andmultidisciplinaryteamsofmodellers(e.g.epidemiologists,clinicians,managers,nurses,GPs,orhealtheconomists).Discreteeventsimulationandsystemdynamicsaretwoquitedifferentapproachestosimulationmodelling.Discreteeventsimulationmodelssystemsasnetworksofqueuesandactivities,wherestatechangesinthesystemoccuratdiscretepointsoftime.Theobjectsinthesystemaredistinctindividuals,eachpossessingcharacteristicsthatdeterminewhathappenstothatindividual,andtheactivitydurationsaresampledforeachindividualfromprobabilitydistributions.Ontheotherhandsystemdynamicsmodelsasystemasaseriesofstocksandflows,inwhichthestatechangesarecontinuous.Asystemdynamicsmodelviews“entities”asacontinuousquantity,ratherlikeafluid,flowingthroughasystemofreservoirsortanksconnectedbypipes.Theratesofflowarecontrolledbyvalves,andsothetimespentineachreservoirismodelledbyfixingtheratesofinflowandoutflow.Althoughthestatechangesareregardedascontinuous,theunderlyingequationsusedtosolvethemodelaredifferenceequations(usuallysolvedbynumericalintegration)whichdiscretisetimeusingatime-slicingapproach.1Systemdynamicsisessentiallydeterministicwhereasdiscreteeventsimulationisstochastic.Systemdynamicscanbeusedqualitativelyandhasstronglinkswiththeproblemstructuringapproachofcausallinkorinfluencediagrams,andsothereisatendencytousesystemdynamicsatahigher,morestrategiclevelinordertogaininsightintotheinterrelationsbetweenthedifferentpartsofacomplexsystem.Discreteeventsimulation,ontheotherhand,hastraditionallybeenusedatamoreoperationalortacticalleveltoanswerspecificquestions;forexample,inthehealthcaredomain,tosolveresourceallocationproblemsortocompareandevaluatemedicalinterventions.2.ThebasicelementsofsystemdynamicsSystemdynamics(SD)isananalyticalmodellingmethodologythatcanbeattributedtoJayForrester[1,2],whoseworkon“industrialdynamics”attheMassachusettsInstituteofTechnologyledtothedevelopmentoftheprocess.Itcombinestwodistinctaspects;onequalitativeandonequantitative,withtheaimofenhancingtheunderstandingofanidentifiedproblemandimprovingcomprehensionofthestructureoftheproblemandtherelationshipspresentbetweenrelevantvariables.Becauseoftheflexibilityoftheprocess,alongwithitsabilitytocombinebothqualitativeandquantitativeinformation,SDhasbeenappliedinmanydifferentfieldsofstudyincludingprojectmanagement,defenceanalysisand,mostrelevantlytothefollowingexamplesillustratedhere,healthcare.ThequalitativeaspectofSDwasnotinitiallyconsideredtobeaveryimportantpartoftheapproach.Howeverinrecentyearsthebenefitsoffocussingonthisaspecthavebeenincreasinglyappreciated[3].Theinitialdiscussionoftheproblembeingmodelledworkstoidentifytheelementsconsideredfundamentaltothesystemandthosethatarelikelytogenerateaninfluenceintheproblemsituation.Theidentifiedelementsarepresentedintheformofaninfluencediagram,anexampleofwhichisshowninFigure1.Foodinstomachhungereating++--vedigestion-Figure1.Influencediagramtodemonstratenotation2Theidentifiedelementsareconnectedbyarrows.The“+”and“−”signsdenotethedirectionoftheinfluence,butdonotshowthemagnitudeoftheinfluence.Forexample,aseatingincreasesfoodinstomachincreases,shownbya“+”;asdigestionincreases,foodinstomachdecreases,shownbya“−”.Inthiswaycomplexandinformativediagramscanbebuiltuptorepresentandclarifytheproblembeinginvestigated,providinginsightsintohowthevariablesinteract.Inmanycasesthequalitativeanalysisofthesediagramsisofconsiderablevalueinitsownright.Theaimofthisanalysisistofindloops,asintheaboveexample,whereelementsareconnectedbyadirectedcycleofarrows.Balancedloopscontainanoddnumberof“−”signs,whereasreinforcingloopsorviciouscirclescontainanevennumberof“−”signs.Theaboveexample,abalancedloop,showshowthesystemregulatesitself.Thehungrierweare,themorewewantt