Online traffic simulation with cellular automata.

OnlineTrafficSimulationwithCellularAutomataR.Barlovic¹,J.Esser²,K.Froese³,W.Knospe¹,L.Neubert¹,M.Schreckenberg¹,andJ.Wahle¹¹PhysikvonTransportundVerkehr,Gerhard-Mercator-Universität,Lotharstr.1,47048Duisburg,Germany²LosAlamosNationalLaboratory,MSM997,LosAlamos,NM87545,USA³debisSystemhausGEI,Ulm,GermanyThedevelopmentofdynamictrafficinformationsystemsisoneofthemostimportantchallengesinthefieldofIntelligentTransportationSystemsITS.Apromisingwayistocouplesimulationsoftheactualtrafficstatetogetherwithonlinecountingdatastemmingfromdetectiondevices,e.g.inductionloops.Theaimistogenerateaone-to-oneimageoftheindividualon-roadcarmotioninthecomputerandtoderivetherelevantinformationfromthesimulationresults.Inaddition,thesimulationservesasan“interpolation”forregionswhicharenotadequatelycoveredbymeasurements.Inthiscontributionthemethodofonlinesimulationsisdiscussedandsomeresultsarereported.1IntroductionExtensiveareasoftheroadnetwork,especiallyinpopulationcentres,operateattheircapacitylimitsorareexpectedtoreachtheminthenearfuture.Sincetheincreasingdemandformobilitypresumablywillnotbecompensatedbyexpandingtheexistinginfrastructure,butithastobeusedinamuchmoreefficientway.Therefore,alotofworkhasbeeninvestedtodevelopAdvancedTravellerInformationSystemATISlikeDynamicRouteGuidanceSystemswhichofferpossibletravelroutes(foranoverviewsee[1-3]).Tomakesuchproposalsthesesystemsneedvaluationcriteriaandadetailedknowledgebaseofthepresenttrafficstate.Typically,trafficdataarecollectedbylocallyfixeddetectors,mostlyinductiveloops.Inurbanregionstheyarepreferablyinstallednearbyintersectionsinordertocontrolandoptimisetrafficsignals.Soitiscomprehensiblethatonlyacertainportionoftheintersectionsareequippedwithsuchdevices,butthisisusuallynotenoughtogetanoverallviewoftheactualtrafficsituation.Apossiblewaytoderivereliableinforma-tionaboutregionswhicharehardlyornotcoveredbymeasurementsistogeneratetrafficstatesbysimulationsonthebasisofmeasuredtrafficcounts.Thisisthebasicideaofonlinesimulations:Localtrafficcountsserveasinputfortrafficflowsimula-tionstoprovidenetwork-wideinformation.ThisapproachisadvantageousbecausetheOnlineTrafficSimulationwithCellularAutomata118factthatallstaticentitiesofthenetworklikeitsstructureorthetrafficlightmanage-mentareincorporateddirectlyintothedynamics.Theoutlineofthispaperisasfollows:Firstly,thecellularautomatonapproachisintroduced.Relevantquantitiesofthemeasurementsarepresented.Additionally,anoverviewofmodificationsoftheoriginalmodelisgivenwhichareneededtorepro-duceavarietyofeffectsknownfromrealtrafficunderseveralconditions.Wewillalsopresentanalyticaltreatmentsvalidatleastincertainlimitsorapproximations.Theunderlyingroadnetworkanddatabasearedescribedinthethirdsection.Somemeas-urementsofthenetworkandthereproductionoftrafficstatesarediscussedinsectionfour.2MicroscopicTrafficSimulationsFromtheviewpointofcomputationalefficiency,trafficflowmodelsshoulddescriberelevantaspectsoftheflowdynamicsassimpleaspossible(see[4,5]andreferencestherein).Severaldifferentapproachesareathandtoday,whichcanbediscriminatedeitherbytheirspatialandtemporalresolutionorbytheirdepthofthedescriptionofcarmotion.Especially,forfastsimulationsoflargenetworkscomprisingofnumerousdifferentkindofroadsandintersectionsacompromisebetweensimulationspeedandcomputationaleffortofthemodelhastobemade.Inthisspiritcellularautomatonmodelswereintroducedandthoroughlyinvestigated.2.1FundamentalsoftheNagel-SchreckenbergModelAmongthenumerouscellularautomata(CA),conceivablefromapurelymathemati-calpointofview,theoriginalNagel-SchreckenbergCAmodel[6]issuitabletomeetFigure1:Timevs.distanceplotsofdensitywaves.Eachtrajectoryrepresentsavehi-cle.Leftpanel:ThepicturewasgeneratedbyusingvideosequencestakenfromanAmericanhighway[7].Itshowsthespontaneousemergenceofajam.Middlepanel:SimilarstructurescanbeobtainedfromsimulationswiththeNagel-SchreckenbergCAmodel.Rightpanel:MetastabilityintheVDRmodel(section2.3)isexpressedthroughthefact,thataninitiallyhomogeneouspatterncanbedestroyedbysmallfluctuations.Thereisnowaytoreconstructtheinitialstateexcepttonoticeablyreducethedensity.ThedifferentslopesofthejammedregionsareduetothechosensetofparameterswhicharesubjectsofathoroughcalibrationofthemodelOnlineTrafficSimulationwithCellularAutomata119theaboverequirements,besidesitisperhapsthesimplestone.Itiscapableofrepro-ducingcharacteristicpropertiesofrealtraffic,likecertainaspectsoftheflow-densityrelationandthespatio-temporalevolutionofjams(Fig.1)[7].Furthermore,CAarebydesignidealforlarge-scalecomputersimulationsandcanthereforebeusedincomplexpracticalapplicationsinaveryefficientway.Forthesakeofcompleteness,werecallthedefinitionoftheNagel-SchreckenbergCAmodelforsingle-lanetraffic.Inthemodelthestreetisthoughttobesubdividedintocells,each7.5mlong,whichcorrespondstothemeanfrontbumper-frontbumberdistancebetweentwoconsecutivecarscapturedinajam(Fig.2).Acelliseitheremptyoroccupiedbyonlyonevehiclewithadiscretevelocityvi˛{0;vmax},withvmaxthemaximumvelocity.Allspeedsaremeasuredincellspertimestep.Themotionofthevehiclesisdeterm