高速公路交通的元胞自动机模型及仿真

广西师范大学硕士学位论文高速公路交通的元胞自动机模型及仿真姓名：朱留华申请学位级别：硕士专业：系统理论指导教师：孔令江;刘慕仁20070401iiOONoise-First→→NaSchETCMTCETCMTCiiNaSchp0AbstractiiiCellularAutomataModelsandSimulationofHighwayTrafficGraduatestudent:ZhuLiu-HuaAdvisers:Prof.KongLing-Jiang,Prof.LiuMu-RenSpecialty:SystemicTheoryDirection:ComputationalPhysicsGrade:TwothousandandfourAbstractWiththerapiddevelopmentofsocialeconomy,itleadstotheincreasingofmotorvehiclesandtheseverejamsofroads.Trafficproblemshavebecomeanimportantfactortorestrictthedevelopmentofcitiesbecauseofgrievouslackingofroadsandrelativelagoftrafficmanagement.Therefore,howtoimprovetheusingrateofroadsandthesafetypropertyoftransit;toconstructthetrafficmodelswhichareconsistentwiththefact,andtofindtheintrinsicmechanismandrulesoftrafficflowfortheguidanceofanticipation,managementandlayoutoftraffic,whichhavebecomeavitalsubjectinthefieldofscientificinvestigation.Manyexpertsandscholarsindifferentcountrieshaveconcentratedontrafficproblemseriouslyandproposedmanymodelsoftrafficflowinordertodulltrafficjamsandreducetrafficaccidents.ManyscientistswidelyfocusoninvestigationofCellularAutomatatrafficflowmodels.Comparewithothermodels,itnotonlyconservesthenonlinearbehaviorsandotherphysicalcharacteristicsoftrafficflow,butalsoitisoperatedinthecomputereasilyandmodifiedneatlytosimulatevariouseffectsoftherealtrafficconditions,suchasthestochasticslowdownoftheroad-blocks,thetollbooths,thejuncturesofhighways,therandomicitiesofretardarce,thedrivers’inordinatereaction.Inthedissertation,theseveraltrafficproblemsareinvestigated.Aimatthefaultoftheexistingtrafficflowmodels,weproposemodifiedtrafficflowmodelsandperformcorrespondingnumericalsimulationandtheoreticalanalysis.Moreover,thecharactersofcoexistenceofElectronicTollCollectionandManualTollCollectionsystemsareanalyzedanddiscussedThemainpartsofthedissertationareasfollows:Firstly,basedontheNoise-Firsttrafficflowmodel,weproposedanimprovedcellularautomatontrafficflowmodeltorestrictstochasticslowdownprobabilityvialocaldensityandcurrentvelocity.Itwasshownfromnumericalsimulationthatthetransitionoffreeflow→Abstractivsynchronoustrafficflow→widemovingtrafficflowcanberealizedviapropermodificationoftherelevantparameters.Secondly,theeffectsoftollboothsonthetrafficflowareinvestigatedinthechapterthree.BasedontheNagel-SchreckenbergmodeloftrafficflowthetrafficflowmodelsonETCandMTCsystemsareestablishedWeobtainthefundamentaldiagramsoftrafficflowunderdifferentparametersviausingcomputernumericalsimulationMoreover,thecharactersofcoexistenceofETCandMTCsystemsareanalyzedanddiscussedThirdly,basedonthevelocityeffectmodel,weproposethemulti-velocity-effecttrafficflowmodelviaconsideringmulti-neighborinteractionahead.ThefundamentaldiagramsobtainedfromnumericalsimulationapproachtotheempiricaldatabycomparingwithNaSchmodelunderthesamenoise.Itinducesthemetastablestateandhysteresiswithouttrafficnoise.Moreover,withthehelpofmean-fieldtheory,weobtainanalyticalsolutionsofthismodel.Finally,wegivetheconclusionsofourworksandpresenttheprospectoffurtherinvestigationoftrafficflow.KeyWords:cellularautomaton,numericalsimulation,synchronousflow,metastablestate4111.1[1]209014.8%13.7%199620002008[2]20001990102087.520[3]605030GDP13200175.510.654.62[3]209020%1.2[4]31.2.1),(txρ),(txu),(txΘ1.2.1.1LWRLighthillWhitham1955LW[5]Richards1956[6]LWRρq0)(=∂∂+∂∂xutρρ(1-1)——)),((),(txutxueρ=(1-2)(1-1)(1-2)0][=∂∂∂∂++∂∂xuuteeρρρρ(1-3)(1-3)ρρρρ∂∂+=eeuuc)()(0∂∂ρeu)()()(ρρρρρeeeuuuc∂∂+=Daganzo[7]LWRLWR-“”1.2.1.2PayneH.J.Payne19714xTuuTxuutudtdue∂∂−−−=∂∂+∂∂=ρρµρ)]([1(1-4)u)(ρeuTµ)(ρeusT0.7=)(5.0ρµeu′−=[8]H.J.Payne),()(txSxut=∂∂+∂∂ρρ(1-5)),(txS0),(txS0),(txS0),(=txS(1-4)(1-5)PaynePayne1979FREFLOPayne[9-13]1.2.2Boltzmanntvr∆∆∆,,PrigogineHermanBoltzmannBoltzmann[14]Prigogine-HermanHelbing5HelbingfBoltzmann×′′−+∂∂+−∂∂−∂∂−=∂∂),()1()()()(220trPvfDvVfvrvftfρχτ]),()(),()([22∫∫−−−ωωωωωωωωvvvdvdvdvd(1-6)ω,v0VDP′χ′ρ2d])([11VVxPxVVtVe−+∂∂−=∂∂+∂∂ρτρ(1-7)P),(),(),(txtxVtxPθ=),(txθ)(ρeVτHelbing)(ρeV)]()/1()(1)[(2maxmax0veBTAVVδρρρρτθθρααα−+−=(1-8)Helbing“”HelbingMASTER[15]1.2.31.2.3.1L.A.Pipes1953[16]6)(11kkxxTx−=+(1-9)kkxx,1+),,(nnnnuxufx∆∆=(1-10)nnxu,n1.2.3.2CellularAutomaton,CA208090[17,18]CA[19-28]CACACACA1.2.3.2.1S.Wolfram1983184[17]L7310CA1-11-11842)1000,1011(184184184[29]5.0=cρNagelSchreckenberg19921841NaSch[30]L7.5vmax~0V},,2,1,0{maxVv∈maxV)(tdii1),1)(min()3/1(maxVtvtvii+=+2))(),3/1(min()3/2(tdtvtviii+=+3)0,1)3/2(max()1(−+=+tvtviip4)1()()1(++=+tvtxtxiii1)()()(1−−=+txtxtdiii1-2[31]2max=V4/1=p,8t(1)(2)31+t1-2NaSch(2max=V,4/1=p)maxVNaSchFukuiIshibashi1996FI[32]MmaxVM≥,)1(p−maxVp)1(max−VmaxVM,MFINaSchFImaxVmaxVNaSch1FI9NaSchFI[33-39],,maxV)(tS)(tL(1maxV)CANaSchNaSchNaSchChowdhury[31]NaSch[40]GWM[41][42]1Nagatani1841993[43]1998A.AwazuNaSch[44]10CA[31][45]1.2.3.2.2CABihamMiddletonLevine1992BML[46]LL1-3ρcρρcρ1-3(a)1-3(b)1-3(a)BML(25.0=ρ);(b)BML(41.0=ρ).11:3232×.BML[47-49]BMLNagatani[50]Cuesta[51][52]CACA[53][54](overpass)[34-36]1.3122.1NaSchNaSchNaSchNaSchVDR[55]BJH[56]2T[57][58]NaSchVDR=,,)(0ppvp00=vv(2-1)=,,0)(pvpmaxmaxVvVv=(2-2)VDRVDRNoise-F