十字路口红绿灯的控制效应(英文)

1THEEFFECTOFTRAFFICLIGHTCONTROLONASINGLEINTERSECTION(collegeofPhysicsandelectronicsengineeringofGuangxiNormaluniversity,Guilin541004,Guangxi,China)Acellularautomatamodelforasingleintersectionwithopenboundaryconditionsispresented.Inthismodel,thevehiclesareallowedtoturntheirdirectionswithaprobability.Weanalyzethetrafficflowcharacteristicsofthemodelandtheoptimizationofgreenratio.Thesimulationsunderdifferenttrafficconditionsaregiven.Itcanbefoundthattheoptimizationofgreenratiodependsontheboundaryconditionsbutindependentsontheperiodoftrafficlight.Thereisaoptimumrangeofgreenratioforfixedboundarycondition.Theinfluenceofturningprobabilityontrafficflowisalsodiscussed.Turningpermissionleadstothedisappearofcongestiononstreet.Keywords:cellularautomatamodel;optimumgreenratio,openboundary;singleintersection1.IntroductionInrecentyears,trafficjamshavebecomethemostdifficultproblemincity.Andwecanfindthattrafficjamsalwaysappearneartheintersections.Atthecontrolledintersections,trafficlightshaveimportantinfluenceuponthetrafficflow.Ifthetrafficsignalsettingisunsuitable,itwillnotonlyhasdestructiveeffectsontraffic.butalsoendangerthepedestrians.So,howtooptimumthetrafficsettingisthemainconcernforthetrafficengineersandresearchers.Anumberoftrafficsignalcontrolmodelshavebeendevelopedinthepast.Thesemodelsareusuallyformulatedusingthelanguafeofcellularautomata(CA).ThefirstmodelofcitytrafficwasintroducedbyBiham,MiddletonandLevine(BML).Thismodelcanpredictasortofphasetransitionfromfree-flowtoajammedstate,butthemodelassumptionsaretoosimpletobetakenseriouslyforpracticalpurpose.LateramoreseriousmodelofcitynetworkwasintroducedbyChowdhuryandSchadschneider(ChSch).ThismodelcombinestheBMLmodelandNagel-Schreckenberg(NaSch)modelofhighwaytraffic.Itcandemonstrateaphasetransitionfromthe“free-flowing”phasetothecompletely“jamming”phaseatavehicledensity.Anditalsogivesthetimedependenceoftheaveragespeedsofthecars.Inaveryrecentyears,theChSchmodelwasextendedbyE.Brockfeldtoaccountfordifferenttypesofglobalsignalization.Basedonthesemodels,someextendedworkwasproposed.Intheaboveapproaches,themainconcernhasbeenfocusesontheglobalstrategiesofthetrafficnetworkandfrequentlytheroleofisolatedintersectionhasbeensuppressed.Fouladvandetal.believedthatinordertohaveabetterinsighttotheproblemofcitynetwork,onemusthaveaclearpictureatsinglecrossroads.Theyproposedamodelfortheintersectionoftwourbanstreetsand2optimizedthetrafficflowatthecrossroadsbyminimizingthetotalwaitingtimeorthetotaldelay.Inallthementionedmodels,therearenoturningforvehiclesatintersectionsandtheperiodicboundaryconditionsarechosen.Inthispaper,wepresentacellularautomatamodelforasingleintersectionoftwourbanstreetswithopenboundaryconditions,andthevehiclesareallowedtoturntheirdirectionswithaprobability.Weaimtoanalyzethetrafficflowcharacteristicsofasinglecrossroadsandtrytogettheoptimumsignal-settingstrategytoimprovethetrafficcapacityofroads.Theorganizationofthispaperisasfollows:InSec.2,weintroducethemodel;InSec.3,weproposethesimulationsofourmodelunderdifferenttrafficconditions.Thetrafficflowcharacteristicsofthemodelisdiscussed.Thentheoptimizationofgreen-timesdependedontheboundaryconditionsandtheperiodoftrafficlightareanalyzed.Theinfluenceofturningprobabilityontrafficflowisalsogiven.Finally,asummaryisgiveninSec.4.2.DefinitionofthemodelOurmodelhasthesimpleststructure:one-waytoone-wayintersection(seeFig.1.1).Onestreetiseast-bound(referredasthestreetX)andtheotherisnorth-bound(referredasthestreetY).Theyintersectatthemiddlecenter.ThetrafficlightswitchatregulartimeintervalsT.Itremainsgreenfortheeast-boundvehiclesanditisredforthenorth-boundvehicles.WedenotetheperiodofgreenphasebyTg.AndtheratioofTg/Tisdefinedasgreenratio,denotedbyGs(Gs=Tg/T).Asincellularautomatamodel,eachstreetconsistsofLsites.AndEachsiteiseitheremptyorisoccupiedbyonevehicle.ThespeedVofeachvehicletakesoneoftheVmax+1integervaluesV=0,1,2,...,Vmax.SupposeXnisthepositionofthenthvehicle,andVnisthespeedofthenthvehicleattimet.Snisthedistancebetweenthenthvehicleandthecrossinginfrontofit.Ifthereisnosignalahead,Snisassumedtobe∞.Whenadriverdecideshisnextmovement,hewillconsidernotonlythedistanceofthecarahead(denotesasdn)butalsoitsmovingdistance(denotesasΔX).So,thestateofthenthvehicleattimet+1maybeobtainedbyapplyingthefollowingrules:Step1:Acceleration:Vn→min(Vn+1;Vmax)Step2:Brakingduetoothervehiclesortrafficlightstate.Case1:ThetrafficlightisredinfrontofthenthvehicleorisgreenforthelaststepoftheperiodTg:Vn→min(Vn;dn-1+ΔX;Sn-1)3Case2:Thetrafficlightisgreeninfrontofthenthvehicle:Vn→min(Vn;dn-1+ΔX)Step3:Randomizationwithprobabilitypn:Vn→max(Vn-1;0)Step4:Movement:Xn→Xn+VnAnd,vehiclesatthecrossingcanturntheirdirectionswithpossibilityPt.Insimulationweadopttheopenboundaryconditionforbothroads.BoundaryconditionsaredefinedasinRef.[?]:Ati=0,whichmeansoutofthesystemavehiclewiththeprobabilityα1(α2)andwiththevelocityVmaxiscreated.Thiscarimmediatelymovesaccordingtotheaboverules.Iftheinjectedcarcannotmove,itisdeleted.Attheendoftheroad,thecarssimplymoveoutofthesystemwithprobabilityβ1(β2).Here,α