A multi-lane traffic simulation model via continuo

arXiv:1302.0488v1[cs.MA]3Feb2013Amulti-lanetrafficsimulationmodelviacontinuouscellularautomataEmanueleRodaroCentrodeMatem´atica,FaculdadedeCiˆencias,UniversidadedoPorto,R.CampoAlegre687,4169-007Porto,Portugale-mail:[e-mail]¨OznurYeldanDipartimentodiMatematica,PolitecnicodiMilano,PiazzaLeonardodaVinci32,20133Milano,Italye-mail:[e-mail]5,2013AbstractTrafficmodelsbasedoncellularautomatahavehighcomputationalefficiencybecauseoftheirsimplicityindescribingunrealisticvehicularbehaviorandtheversatilityofcellularautomatatobeimplementedonparallelprocessing.Ontheotherhand,theothermicroscopictrafficmodelssuchascar-followingmodelsarecomputationallymoreexpen-sive,buttheyhavemorerealisticdriverbehaviorsanddetailedvehiclecharacteristics.Weproposeanewclassbetweenthesetwocategories,definingatrafficmodelbasedoncontinuouscellularautomatawherewecombinetheefficiencyofcellularautomatamodelswiththeaccu-racyoftheothermicroscopicmodels.Moreprecisely,weintroduceastochasticcellularautomatatrafficmodelinwhichthespaceisnotcoarse-grainbutcontinuous.Thecontinuityalsoallowsustoembedamulti-agentfuzzysystemproposedtohandleuncertaintiesindecisionmakingonroadtraffic.Therefore,wesimulatedifferentdriverbehav-iorsandstudytheeffectofvariouscompositionsofvehicleswithinthetrafficstreamfromthemacroscopicpointofview.Theexperimentalresultsshowthatourmodelisabletoreproducethetypicaltrafficflowphenomenashowingavarietyofeffectsduetotheheterogeneityoftraffic.11IntroductionTrafficmodelsarefundamentalresourcesinthemanagementofroadnet-work.Arealprogressinthestudyoftraffichasobtainedwiththeintroduc-tionofthemodelsbasedoncellularautomata(CA)1.Acellularautomatonisacollectionofcells(sites)onagridofspecifiedshape(lattice)thatevolvesthroughanumberofdiscretetimestepsaccordingtoasetoflocalrulesbasedonthestatesofneighboringcells,formoredetailssee[9].CAmodels(CAMs)havetheabilityofbeingeasilyimplementedforparallelcomputingbecauseoftheirintrinsicsynchronousbehavior.Asetofsimplerulescanbeusedtosimulateacomplexbehavior,thusthesemodelsareconceptu-allysimple(forthetheoryandapplicationsofCAasmodelsforcomplexsystemsinseveralscientificfields,see[2,3,5]).ThetrafficmodelsbasedonCAarecapableofcapturingmicro-leveldynamicsandrelatingthesetomacro-leveltrafficflowbehavior.However,theyarenotasaccurateastheusualmicroscopictrafficmodels2suchasthetime-continuouscar-followingones[1].Abasicone-dimensionalCAMforhighwaytrafficflowwasfirstintroducedbyWolfram,wherehegaveanextensiveclassificationofCAMsasmathematicalmodelsforself-organizingdynamicsystems[23,24].NagelandSchreckenbergproposedthefirstnontrivialtrafficmodel(theNaSchmodel)basedonCAforsingle-lanehighwayin1992[17].Thisisatime-andspace-discretemodelwherethetrafficroadisdividedintocellsof7.5manditisdefinedonaone-dimensionalarrayofafixednumberofsiteswithclosed(periodic)boundaryconditions.Thevelocityisexpressedasthenumberofcellsthatavehicleadvancesinonetimestep.Themaximumvelocity(vmax)isassumedtobe5cells/sec(135km/h)andeveryvehiclehasthesametargetvelocityvmax.Eachupdateofthemovementsoftheve-hiclesisdeterminedbyfourconsecutiverulesthatareperformedinparalleltoeachvehicleateachsecond.Inliterature,theCAtrafficmodelsareup-datedsimilarlywheretheyonlydifferontherandomizationstepintroducedtoaddsomerandomness,forasurveysee[15].NotethatinallofthemthecellsrepresentthespaceasitisintheNaSchmodel,sointhesequelwecallthemas“NaSch-type”models[12,18,20,21].Inthispaper,weproposeanewtrafficmodelviacontinuouscellularautomata(CCA)whichgetsclosertothecar-followingmodelsbyintroduc-1Throughoutthispaper,abbreviationCAreferstobothcellularautomata(plural)andcellularautomaton(singular).2Weusetheterm“usualmicroscopictrafficmodels”torefertothemicroscopictrafficmodelsotherthanCA,whichareingeneraldefinedbymeansofasystemofdifferentialequations.2ingsomecontinuitywithoutlosingthecomputationaladvantagestypicalofCAMs.Continuouscellularautomata(orcoupledmaplattices)arecellularautomatawherethestatesofthecellsarerealvaluesin[0,1],andthelocaltransitionruleisarealfunction.TheyhavehavebeenintroducedbyKanekoassimplemodelswiththefeaturesofspatiotemporalchaos,andhaveappli-cationsinmanydifferentareaslikefluiddynamics,biology,chemistry,etc.(formoredetailsoncouplemaplattices,see[8,10]).Inthisworkwedroptherestrictionthatthesetofstatesis[0,1],andweusethenameCCAtoconsiderCAwherethesetofstateisingeneralaninfinitesetofthesamecardinalityofthecontinuum.Therefore,weconsiderahybridbetweentheusualmicroscopictrafficmodelswhichareveryaccurateinpredictinggen-eraltrafficbehaviorbutcomputationallyexpensive,andtheCAMswhichareveryefficientduetotheirsimplicityandintrinsicparallelismmakingthemnaturaltobeimplementedforparallelcomputing.Thisprocessofpassingfromthetypicalcoarse-granularityofCAMstothecontinuityinspaceisdonewithachangeofvisionwhereweabandonthecell-spacecor-respondenceandassumethatcellsrepresentvehicles.Thusweconsideramodelwithopenboundaryconditionswherethenumberofcellsisequaltothenumberofvehicles.Inthisway,weobtaintheimmediateadvantageofhavinglesscellstocompute(justthenumberofvehicles).Thecontinuityalsogivesusthepossibilitytorefinethemi