版权说明:本文档由用户提供并上传,收益归属内容提供方,若内容存在侵权,请进行举报或认领
文档简介
2014MCMOutstandingWinners贾冬TemContr2014MCMOutstandingWinners贾冬TemControlur谢延ForofficeuseForofficeuseF1 校苑数25142全球首T1 T2 T3 T4 F3 F4 AMathematicalContestinModeling(MCM/ICM)SummaryFreewayTrafficModelBasedonCellularAutomataandMonte-CarloMethodBasedonCellularAutomataandMonte-Carlomethod,webuildamodeltodiscusstheinfluenceofthe“Keeprightexcepttopass”rule.Firstwebreakdowntheprocessofvehiclemovementandestablishcorrespondingsub-models,inflowmodelforcar-generation,vehicle-followingmodelforonevehiclefollowinganother,andovertakingmodelforvehiclepassingThenwedesignrulestosimulatethemovementofvehiclesinsub-models.Wefurtherdiscussrulesforourmodeltoadapttothekeep-rightsituation,theunrestrictedsituation,andthesituationwheretransportationiscontrolledbyintelligentsystem.Wealsodesignaformulatoevaluatethedangerindexoftheroad.Wesimulatethetrafficontwo-lanefreeway(twolanesperdirection,fourlanesintotal),andthree-lanefreeway(threelanesperdirection,sixlanesintotal)viacomputerandanalyzethedata.Werecordtheaveragevelocity,overtakingrate,roaddensityanddangerindexandassesstheperformanceofthekeep-rightrulebycomparisonwithunrestrictedrule.Wevarytheupperspeedlimitationstoanalyzethesensitivityofmodelandseetheimpactsofdifferentupperspeedlimits.Left-handtrafficisalsoBasedonouranalysis,wecomeupwithanewrulecombiningthetwoexisting(thekeep-rightruleandtheunrestrictedrule)foranintelligentsystemtoachievebetter2014MCMOutstandingWinnersTeam#Page2of1Introduction......2014MCMOutstandingWinnersTeam#Page2of1Introduction.................................455Terminology..............................Assumptions..............................2TheModels.................................6678DesignofCellular....................Inflow .............................Vehicle-FollowingModel.......................OvertakingModel...........................OvertakingProbability....................OvertakingCondition....................DangerIndex.........................TwoSetsofRulesforCAModel...................KeepRightExcepttoPassRule...............UnrestrictedRule.......................3SupplementaryAnalysisontheModel.................DesignoftheAccelerationandDecelerationProbabilityDistribu-tions...................................DesigntoAvoidCollision......................4ModelImplementationwithComputer.................5DataAnalysisandModelValidation.................. ...........................2014MCMOutstandingWinnersTeam#Page3of..2014MCMOutstandingWinnersTeam#Page3of...Density.................................OvertakingRate............................Danger .............................6SensitivityEvaluationoftheModelunderDifferentSpeed7DrivingontheLeft.............................8TransportationunderIntelligentSystem................NewRuleforIntelligentSystem...................AdaptionoftheModel........................ResultofIntelligentSystem.....................9Conclusions.................................Strengthsand ........................10.1Strengths................................10.2Weakness................................References....................................Appendices...................................2014MCMOutstanding2014MCMOutstandingWinnersPage4ofTeam# Today,about65%oftheworld’spopulationliveincountrieswithright-handtrafficand35%incountrieswithleft-handtraffic.[worldstandards.eu,2013]Incountrieswithright-handtraffic,likeUSAandChina,regulationsrequestdriv-ingandwalkingkeeptotherightsideoftheroad.Multi-lanefreewaysinthesecountriesoftenemployarulethatrequiresdriverstodriveintheright-mostlaneunlesstheyarepassinganothervehicle,inwhichcasetheymoveonelanetotheleft,pass,andreturntotheirformertravellane.Thisruleondrivingandovertakingisreferredtoasthe”Keeprightexcepttopass”rule,orthekeep-rightruleinourpaper.Theruleincountrieswithleft-handtrafficisexactlymirrorsymmetricaltothekeep-rightrule(”Keepleftexcepttopass”).So,what’sthepurposeofapplyingsucharule?Doesthekeep-rightruleamelioratethefreewaytrafficcondition?Transportationfreeoftherestrictionofthekeep-rightrule(Vehiclescanchooseeithersideforovertaking.)isreferredtoasobeyingtheunrestrictedrule.Howdoesthekeep-rightruleperformcomparingwiththeunrestrictedrule?BasedontheCellularAutomatamodelandtheMonteCarloalgorithm,weestablishamodeltosimulatefreewaytrafficunderdifferentconditions(underthekeep-rightruleortheunrestrictedrule,inlighttrafficorinheavytraffic,2-laneor3-laneperdirection).Ourmodelisdividedinto3sub-modelsthein-flowmodel,thevehicle-followingmodelandtheovertakingmodel.TheinflowmodelemploysthePoissonprobabilitydistributionforthesimulationofthevehicle-generationprocess.Thevehicle-followingmodelintroducesaspecialprobabilitydistributionmodelwhichmakesthesimulationoftheprocessofacarfollowinganothermorerealistic.Theovertakingmodelsimulatestheover-takingbehavioranddefinesthedangerindextoevaluatethesafetyriskofacertainfreeway.Wealsobuildanextendedmodelfortransportationunderthecontrolofanintelligentsystem.WeimplementthemodelinMATLAB,andobtainsufficientdata.Wetesttheaveragevelocity,thedensity,theovertakingrateandthedangerindex,analyzetheirpropertiesandassesstheperformanceofthekeep-rightrulebycomparisonwiththeunrestrictedrule.Inaddition,weanalyzethesensitivityofourmodelunderdifferentspeedlimits.Itturnsoutthatourmodelisrobust.Thenwecometoourconclusionswhichconsistwithcommonsense.Wealsoputforwardanewrulefortransportationunderthecontrolofanintelligent2014MCMOutstandingWinnersPage5ofTeam#2014MCMOutstandingWinnersPage5ofTeam# Table1: VcurrentvelocityofthevehiclemaximumvelocityofthevehicletheupperspeedlimitofthefreewaythevelocitybeforeovertakingthevelocityintheovertakingthedistancebetweenavehicleandthevehicleaheadofittheminimumgaprequiredforsafetyconsiderationtheminimumgapafterthevehiclestopsPIEVtime(humanreactiontime)theovertakingprobabilitytheaccelerationprobabilitythedecelerationthefrictionalforcewhenbrakingdangerindexinoneovertakingeventdangerindexoftheroadsystemtheaccelerationduringthecomponentparalleltothelaneofaccelerationduringovertakingtheavailabledecelerationTwo-laneroad:Twolanesonright-halfoftheroad,fourlanesinThree-laneroad:Threelanesonright-halfoftheroad,sixlanesinDangerindex:Anindexdesignedinourpapertoevaluatethedangeroftheroadsystem.Minimumsafetygap:Thedistancebetweentwovehiclesthatdeemedsafeenoughinourmodel.Keep-rightrule:KeeprightexcepttopassUnrestrictedrule:Vehiclesarenotrestrictedandcanovertakeothersfromeitherside.Free-drivingstyle:Whenthereisnovehiclesnearby,driverswillnotaccel-erateordeceleratedeliberately,butthespeedwillstillfluctuateslightly.•••••••Theroadisstraightandthereisno•2014MCMOutstandingWinnersTeam#2014MCMOutstandingWinnersTeam#Page6ofThewidthofonelaneisonlyenoughforonevehicle.Allvehicleshavethesamevolume.Thereareonlytwokindsofvehiclesontheroad(fastoneandslowone).Theenvironmentandclimatearegoodfordriving.DrivingontherightisthePedestriansare•••••• TheDesignofCellularLargequantitiesofformertrafficsimulations[WagnerPetal.2005]basedonCellularAutomata(CA)indicatethatCAmodelisafeasibleandeffectivemethodtoemulatetrafficflow.Space,timeandstatusarealldiscreteinCellu-larAutomata.Forexample,themodeldividestheroadintosmallrectangularcells,andtimeisdividedintosmallunits.Thisfeaturepredigeststhesimulationprocesssignificantly.Besides,thestatusofacelliscontrolledbyitsneighboringcellsfollowingasetofrules,whichismuchsimilartoreal-lifetrafficwhereacar’smovementlargelydependsonitsneighboringcars’movement.Therefore,itisrationalforustoapplyCellularAutomatainsolvingourproblem.Inoursimulation,wedivideeachlaneinto1000cells.Eachcellis4meterslonginlengthandwidthandhastwoproperties,thecurrentvelocityVandthemaximumvelocityVm.AcellisemptywhenVis0,becauseacarwon’tstopinourcrash-freesimulation.Weconsideronlyonedirectionofthefreewayforsimplicity.Thus,afreewayofnlanesisconvertedintoann*1000matrix.Inoursimulation,weemploytwokindsofvehicles,fasteronestosimulatethecarsandsloweronestosimulatethetrucks.Foreachlane,thefirst6cellsareusedascar-generationarea,trafficflowisobservedinthelast10cellsandtrafficdensityiscalculatedonthebasisofthelast500cells.Ourmodelupdatesoncepersecond,whiletheperiodT=1sistheaveragereactiontimeofadriver.WediscussthebasicprocessesfortheCAInflowProcess:Accordingtotheinflowmodelthatwewilldiscussassignvehiclesinthevehicle-generation2014MCMOutstandingWinners上海交通大学贾冬雨,史昭阳Pof2014MCMOutstandingWinners上海交通大学贾冬雨,史昭阳PofTeam#<ac••speedisV0=V+∆VDecelerationProcess:Ifthedistancebetweenavehicleandthevehicleaheadofit(Frontbumpertofrontbumperdistance,wecallitthegap,andthegapisdenotedbyGanditsunitiscell.Whenthereisnovehicleahead,Gissetto+∞.)isnomorethanV,thevehicledeceleratesV0=(G−1)/T•MovingProcess:VehiclesmoveforwardbyV∗TcellsonlywhenG0G(V).(G(V)istheminimumgaprequiredforsafety0ssandistobedefinedSpecificruleswillbesetintheinflowmodel,thefollowingmodelandtheovertakingmodeltosimulatetrafficundertheKeep-Right-Except-To-Passruleandtrafficundernosuchrestriction.InflowTheinflowmodel,orthevehicle-generationmodel,simulatesthestochasticarrivalsofvehiclesattheentranceofthefreeway.Foreachlane,thefirstsixcellsinthecellularautomataaresetasvehicle-generationarea.Weassumethatthearrivalofeachvehicleobeysthebinomialprobabilitydistribution.LettsdenotethesamplingtimeintervalandNdenotethetotalofvehiclearrivalsduringts.ThenNcanbeapproximatedtoobeythePoissonprobabilitydistribution.LetPts(N)betheprobabilityofNandwehaveλNe−λN>Pts(N)NWithtsbeingonesecondinourimplementation,wecanassigntheexpecta-tionofNtoarangeofvaluesfrom0to3.6.Nbeingthetotalofvehiclearrivalsineachsecond,theexpectationofN,caneffectivelyreflectthetrafficcondition.Thesmallertheλis,thelighterthetrafficis;thegreater,theheavier.Thusweareabletosimulatedifferenttrafficconditions,lightorheavy,byassigningcor-respondingvaluestoλ.Afterthevalueofλisset,wegetthestochasticnumberofvehiclesenteringthefreewayforeverysecondinsimulation.Whichlanetoenteristhenrandomlyassigned.Ourmodelsupportstwokindsofvehiclesofdifferentvelocityranges,theinitialspeedofallvehiclesaresetto20m/s.Suchpracticebringssimplificationanddoesn’tweakentheresult.2014MCMOutstandingWinnersTeam#Page8of2014MCMOutstandingWinnersTeam#Page8ofThatisbecausethespeedofallvehiclestendstoconvergetowardavaluecontrolledbythetrafficdensityandbythedistributionofaccelerationproba-bilitywhichistobeintroducedlater.Whentrafficdensityislow,vehiclescanalwaysacceleratefreelytothemaximumspeedwithoutworryingaboutcolli-sions,sotheconvergencespeedisnearthehighestspeedallowed.Whentrafficdensityishigh,allthelaneswillbefilledwithvehicles,andthespeedofthetrafficflowisdecidedbythespeedoftheslowestvehicleonthelane,sothecon-vergencespeedisnearthelowerspeedlimit.Thepreliminaryanalysisontheconvergencespeedwillbejustifiedbylaterimplementationofthemodel.elclosetorealityandpractical.Becauseoftheconvergencetendency,thesameinitialspeedpolicycanyieldsimplificationwithoutharmtothesimulation.Vehicle-FollowingTheFederalHighwayAdministrationoftheUnitedStatesDepartmentofdriver’sreactiontimeasPIEVtime.PIEVtimeconsistsoffourparts:••••Perceptionprocess:AdriverperceivesthechangeindrivingIntellectionprocess:ThedriveranalyzestheinformationabouttheEvaluationprocess:ThedriverdeterminesdrivingbehaviorbasedonVolitionprocess:ThedriverexecutesthedrivingWeapplythePIEVprocessinourvehicle-followingmodelandovertakingmodel.Ineverytimecycle,wefirstobtainthevelocityandpositionofeachvehicle,calculatethegap,andthendeterminethedrivingbehavior(whethertocontinuefollowingortochangelaneforovertaking).Accordingtodrivingbehavior,computetheaccelerationandupdatethespeedandposition.Decisionondrivingbehaviorbasedprimarilyonthecurrentgap.IftheGissafeenough,accelerationisfeasible;otherwise,thevehicleshoulddown.Here,wedefinetheminimumsafegapGtobeT∗V.(TstandsforsrrPIEVtime,andVisthecurrentWeassumethatdecisionsondrivingbehaviorfollowcertain2014MCMOutstandingWinnersTeam#Page9ofWhenG>Gs,2014MCMOutstandingWinnersTeam#Page9ofWhenG>Gs,thevehicletendstoaccelerate(Laterwewillintroduceprobabilitymodeltosimulatethetendency.),untilachievingthespeedlimitoritsmaximumpossibleWhenG<Gs,whethertoovertakeortofollowisdeterminedbythetakingprobabilityPoandtheovertakingconditions(PoandconditionsaretobediscussedintheovertakingWhenfollowing,avehiclecanaccelerate,decelerateorkeeptheoriginalspeed.Weintroducetwoparameters[SUNyue2005],theaccelerationproba-bilityPaanddecelerationprobabilityPb.Thehigherthespeed,thesmallerthePaandthegreaterthePb.Vlrepresentsthehigherspeedlimitofthefreeway,andVmaxisthemaximumspeedthevehiclecanreach.Thisprobabilitymodeltakesintoaccountthefactthatspeedingcan’tbeignored.WhenV>Vl,PagetsevensmallerandPbgetsevenbigger,whichmakesitpossibleforspeedingbutthepossibilityissmall.WeuseastochasticvariableRforimplementation:•••IfR<Pb,thevehicleIfR>1−Pa,thevehicleOtherwise,thevehiclemaintainsthecurrentBasedontheprobabilitymodel,wecreateseveralrulesfortheCellulartomata:(Themaximumpossiblespeedofvehiclei,thecurrentgapG,theminimumsafegapisGsanditsvelocityisdenotedasV,PaandPbarefunctionsofvelocityV,andPa+Pb≤1.)Freedrivingrule:IfG≥min(Vmax,V+ V0probabilityPb;,V−•Safedecelerationrule:IfG<Gsbutwon’tcrashifmovingV0=max(Vmin,V−Vminisunder-postedthelowerspeed•Crash-freerule:Ifmovingforwardcausescrash,stopbehindtheThevaluesofPaandPbarelistedintable2forfastcars,table3forslowOutstandinPaef4Team#:OutstandinPaef4Team#:foF 6数 34V/cell·−1100Table3:AccelerationandDecelerationProbabilityforSlow 56V/cell· 0 OvertakingThedriverwilldecidewethertoovertakeanothercarwiththeprobabilityPo.ProbabilityPodependsonthevehicleAandthevehicleBahead.LetVmax1bethevelocityofvehicleA,andVmax2bethevelocityofvehicleB.TheprobabilityPosatisfies:Vmax2<,,1−0.9·Po Vmax2≥max maxItisrationaltoassumethatthelargerthedifferenceinvelocity,themorelike-lythevehicleistoaccelerate.TheprobabilitydistributionreflectsthetendencyAdrivercan’tovertakeashepleases.Overtakingcanbesometimesdanger-ous,andavehicleshouldtobeabletoovertakesuccessfully,i.e.abletoreturntotheformerlane,undertheKeeprightexcepttopassrule.Thus,restrictionsaremadeonovertaking.ConditionofthegapG0onthetargetlaneislargerthanGs,thevelocityofthevehicleislargerthanthatofthevehicle2014MCMOutstandingWinnersTeam#2014MCMOutstandingWinnersTeam#Page11ofDangerHereweredefinetheminimumsafegapGsusingadifferentmethodtocal-culatethedangerindex.ThetheoreticalrelationshipbetweenGsandthecurrentvelocityVis:12mV2=f(Gs−fisthefrictionalforcewhenbraking;G0istheminimumgapafterthevehicleConsideringnormaldrivingspeedisunder200km/hinrealityanddrivers’acceptancegapisusuallylargerthanthetheoreticalsafevalue,andforthesakeofsimplicityofcomputerimplementation,weapproximateGs,asafunctionofpresentspeedV,tobelineartoV.Figure1:Relationshipbetweensafe-gapandWesetG0tobe10meters,anduse0.7asthefrictioncoefficient.ThelinearrelationshipwegetisGs=10+2.8×Whenchanginglanesforovertaking,avehiclesparepartofitsaccelerationtochangethedirectionandtherestaccelerationistocopewiththe2014MCMOutstandingWinnersTeam#Page12ofFigure2:Velocitywhen2014MCMOutstandingWinnersTeam#Page12ofFigure2:Velocitywhenfacingemergency.Sotheassessmentofsafetyforlane-changingshouldbedifferentfromthatforvehicle-following.Asisshowninthefigure2,V0denotesthevelocitybeforeovertaking,denotesthevelocityintheovertakingprocess,andaistheaccelerationovertaking.Empirically,V1=V−4m/s(decelerationduringlane-changing0cedureforsafetyconcern).Vehiclesfinishlane-changingin1s,andWecalculatethecomponentparalleltothelaneofa:ap=V0−V1·cos(arcsin(V1Then,thedecelerationavailable 2a=6.86−a=6.86−(V−2Vdp00ThevaluesoftheavailabledecelerationadchangesslightlyasV0varies,sowesetadto5.76m/s2forsimplicity.Gschangesto10+3.4Vaccordingly.Wecreateafunctiontoassessthedangercoefficientofavehicleinunit0 ifGs−Gr<dGs−,ifGs−Gr≥WhenG≥Gs,weassumethedangerissmallenoughtoneglect,sothercoefficientissetto0.WhenGr<Gs,weusethedifferenceofGsandGrtostateofthevehicletobemoredangerous.Thedangercoefficientsofvehicle-followingaresimilarinvariousroadandruleconditions,soweconsideronlythedangercoefficientsofovertakinginfurtherdiscussion.2014MCMOutstandingWinnersTeam#Page13ofNow2014MCMOutstandingWinnersTeam#Page13ofNowwedefinethedangerindextoindicatetheriskofacertainroadunderacertainrule.LetDbethesumofdangercoefficientsofovertakingeventshappenedin300stime:D A·1,whenpassingfrom3,whenpassingfromAAccordingtoresearches,ifaleft-handdrivevehicle(thevehiclecontrolslo-catedonthelefthandside)triestopassfromtherightside,driver’ssightwillgetrestrictedandthusincreasingthedangerindex.Weassumethatthedangerindexofpassingfromtherightsideisthreetimeshigherthanthatofpassingfromtheleftside.SowesetAto1whenpassingfromtheleft,andsetAto3whenfromtheright.ThedangerindexDweintroducedhereisthebasistoevaluatethesafetyoftheroadinourmodel. TwoSetsofRulesforCAKeepRightExcepttoPassWeanalyzetheperformanceoftheKeepRightexcepttoPassrulebycom-paringtheoutcomesfromthemodelunderthisruleandthemodelwithoutsuchrestriction.ApplyingthisruledemandssomerulesfortheCellularAutomata:(Therulesarelistedindescendingpriority,thatis,ifthefirstruleissatisfied,thefollowingonesaretobeneglected.)•••IfthegapGintherightlaneislargerthanGs,changetotherightIfthecurrentgapGislargerthanGs,applythefreedrivingrulesetinvehicle-followingIfthegapGintheleftlaneislargerthanGs,applytheovertakingmodelwithprobabilityPo,andapplythefollowingmodelwithprobability1−Po.2014MCMOutstandingWinnersTeam#Page14of2014MCMOutstandingWinnersTeam#Page14ofLikewise,whenweimplementthemodelwithoutsuchrestriction,anothersetofrulesisneeded:(Therulesarelistedindescendingpriority,thatis,ifthefirstruleissatisfied,thefollowingonesaretobeneglected.)IfthecurrentgapGislargerthanGs,followfreedrivingruleemployedinvehicle-followingmodel;Iftheovertakingconditionsaresatisfied,andthegapGintheleftlaneislargerthanGs,applytheovertakingmodeltopassfromtheleftsidewith••probabilityP,andapplythevehicle-followingmodelwithprobability1oIftheovertakingconditionsaresatisfied,andthegapGintherightlaneislargerthanGs,applytheovertakingmodeltopassfromtherightsidewith•probabilityP,andapplythevehicle-followingmodelwithprobability1o SupplementaryAnalysisontheDesignoftheAccelerationandDecelerationProbabilityDis-Thedesignoftheaccelerationanddecelerationprobabilitydistributionsweintroducedinthevehicle-followingmodelsimulatesthechangeinvelocitydur-ingthedrivingprocess.Thesystemcanself-adjusttheaveragevelocityaccord-ingtothedensity.Whenthedensityissmall,theaveragevelocityofthetrafficflowisclosetotheaveragespeedofafree-drivingcarwhichfollowstheprob-abilitydistribution.Whenthedensityislarge,slowcarsontheroaddeceleratethefollowingcars.Inotherwords,slowercarsinthelanedeterminetheaveragevelocity.Whenthefreewayisrelativelycrowded,theexpectationoftheslowestspeeddecreasesandthusaffectstheaveragevelocityoftheroad.DesigntoAvoidWhilesimulatingheavytraffic,wedesignrulestoavoidcarcrashes.Normal-ly,afreewaylimitsthelowerspeed,butwhenavehiclefindsitselftooclosetotheoneahead,itcanbraketoavoidcollisionregardlessofthelowerspeedlimit.2014MCMOutstandingWinners2014MCMOutstandingWinnersTeam#Page15ofWhenthefreewayiscrowded,thefrequencyofdecelerationtoavoidcollisionrises,sotheaveragevelocitygoesbelowthelowerlimitofspeed. ModelImplementationwithBasedontheCellularAutomatamodelandMonteCarloalgorithm,weim-plementourmodelsuccessfullyviaMATLAB.Startingfromasimplesituation,wefirstsimulateafreewayof2lanesundertheKeep-rightrule.Thenwithasmallchangetotherules,wehavetheunrestricted2-lane-freewaymodelforcomparison.Weworkontoextendthemodeltosimulateafreewayof3lanesandbothruleconditionsarerealized.Moreover,trafficunderakeep-leftrule,withdifferentspeedlimitsaswellastransportationdirectedbyanintelligentsystemisalsoemulated.Wetestthesemodelswithdifferentinflowratesinor-dertoseetheinfluenceoftrafficheaviness.Supportedbysufficientsimulateddata,weareabletoevaluateaccuratelytheperformanceoftheKeeprightex-cepttopassruleinlightandheavytraffic,includingthetradeoffsbetweenflowandsafety,theaveragespeed,thetrafficdensityandtheovertakingfrequency.Andwefurtherdiscusstheimpactofakeep-leftruleandthatofanintelligentsystem.Figurespatiotemporaldiagramofvehicles,expectationofinflowrate0.5veh/s,theratioofsmallercarstolargervehiclesis1,three-lane.Thedi-agramrecordspositionsofallthevehiclesineverytimecycle.Redrepresentssmallercarsandgreenrepresentslargervehicles.Everythreecolumnsstandforthefreewaystateofonetimecycle.Figure3:Tempo-SpatialDistributionof2014MCMOutstandingWinnersTeam#2014MCMOutstandingWinnersTeam#Page16of DataAnalysisandModelAveragelocityofthevehicleflowtoreflectthetrafficefficiency.Weanalyzethestatisticsfromthetwo-lanemodelandthethree-lanemodel,bothunderthekeep-rightruleandunrestricted.Therelationshipsbetweentheaveragespeedandthein-flowrateinvariousconditionsareshowninthefigure4andfigure5.Figure4:AverageVelocityunderDifferentFigure5:AverageVelocityunderRules(2Rules(3lanesIt’sclearthatinthetwo-lanemodel,thekeep-rightruleyieldsfasteraveragevelocityingeneral.Whenitcomestothefreewayofthreelanes(bystatistics)ormore(bydeduction),thekeep-rightruledoesn’timprovetheaveragevelocity.Wecanseethatwhenthevehicle-generationrateisover0.75veh/s,theunre-strictedruleoutperformthekeep-rightruleaccordingtothefigure.Highinflowratemaytriggertrafficjam,aswecanlearnfromthefigure.Whentheinflowrateishigherthan1.8veh/s,theaveragevelocityinbothmod-elsgoesbelowthelowerspeedlimitofthefreeway.Iftheinterferenceofothervehiclesisneglected(thatis,avehicledrivesonanemptyfreewayunderthefree-drivingrule),theaveragespeed,orwecallittheidealspeed,ofslowvehiclesis19.44m/s,andtheidealspeedoffastcarsis25.88m/s.(ThedatacomefromourMATLABsimulation.)Wecanseefromfigure4and5thatwhentheinflowrateislow,thekeep-rightrulecanalmostreachtheidealspeed,buttheunrestrictedrulegivesaworseperformance.Wecanconcludefromtheanalysisthatonathree-lanefreeway,theKeeprightexcepttopassrulepromotestheaveragevelocityofvehicleflowinlighttrafficbutmakesnoimprovementontrafficefficiencyinheavytraffic.However2014MCMOutstandingWinnersTeam#Page172014MCMOutstandingWinnersTeam#Page17ofonatwo-lanefreeway,theKeeprightexcepttopassrulepromotestheaveragevelocityofvehicleflowprominently.AverageVelocityofFastWecalculatedtheaveragevelocityoffastercarsinthethree-lanemodel.Wemainlyfocusonthefastercarstostudythattowhatextentthefastercarisblockedbyslowervehicles.ThegeneraltendencyisgoingdownforthefollowingLargevehicles(slower)mayblocktheroadresultinginthelimitedofsmallThemorecrowdedthefreewayis,themorewilltheaveragespeedbefectedbytheslowestThevelocitygoesupwhentheinflowrateisrelativelylow.Thatisbecauseatthebeginning,theinflowrateissolowthatcarshavealmostnocompanionstoovertake,whichmakesthemmoveinthefree-drivingstyle.Asinflowrategoeshighinthelowerrange(0-0.5veh/s),carshavemorechancetoovertakesothat2014MCMOutstandingiP2014MCMOutstandingiPofTeam#eveesctirnsiefFigure7:DensityofTrafficinEachLanes(2Figure8:DensityofTrafficinEachlanes,Figure9:DensityofTrafficinEachLanes(3Figure10:DensityofTrafficinEachlanes,thatthekeep-rightrulecausestheunbalanceduseoftheroad,whichmayresultindifferentdegreesofwearinthelanesinreality.Sotherepairfordifferentlanescanbestaggeredwhichreducestheharmduetosuspensionofthelaneunderrepair.2014MCMOutstandingWinnersTeam#2014MCMOutstandingWinnersTeam#Page19ofOvertakingmodelinfiveminutes.Figure11:PassingEventsWithDifferentRules(3lanes,Undertheunrestrictedrule,overtakingfromtheleftandfromtherightareequivalentinpriority,sotheratesonbothsidesareapproximatelythesame.Underthekeep-rightrule,mostvehiclesdriveintherightlaneifpossible,andvacatetheleftlane,thusmakingtheovertakingrequirementseasiertomeetandcausingthesumofpassingeventstobemuchmorethanthatoftheunre-strictedleftlane.Highpassingratekeepsfastercarsfromthelimitproducedbyslowervehicles,whichincarnatesthequicknessofthekeep-rightrule.Besides,toomanypassingeventsontherightlaneharmthesafetygreatly.ThesedataisveryimportantforustoevaluatethedangerindexoftheroadDangerInlighttr
温馨提示
- 1. 本站所有资源如无特殊说明,都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
- 2. 本站的文档不包含任何第三方提供的附件图纸等,如果需要附件,请联系上传者。文件的所有权益归上传用户所有。
- 3. 本站RAR压缩包中若带图纸,网页内容里面会有图纸预览,若没有图纸预览就没有图纸。
- 4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
- 5. 人人文库网仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对用户上传分享的文档内容本身不做任何修改或编辑,并不能对任何下载内容负责。
- 6. 下载文件中如有侵权或不适当内容,请与我们联系,我们立即纠正。
- 7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。
最新文档
- 工程退场清算协议书大全
- 二零二四年度云服务合同:餐饮业云服务协议(04版)
- 保密协议在保护商业机密中的法律效力
- 住宅买卖简易协议书
- 迟到的悔过与未来承诺
- 水马购买协议合同格式样本
- 合作延续协议书
- 建筑公司员工管理表格
- 连锁加盟店合同的解除条件
- 精挑细选装饰公司合同
- 2024家庭宽带业务完整协议
- 微电子技术专业教学资源库申报书
- 投标人履行合同能力承诺函
- JTG-QB-003-2003公路桥涵标准图钢筋混凝土盖板涵
- 叙事团体辅导方案
- 部队体能训练计划制定方案
- 园艺植物组织培养-形考作业3-国开-参考资料
- 荷花淀公开课省公开课一等奖全国示范课微课金奖课件
- 环境艺术设计发展现状分析报告
- 企业微信指导手册管理员版
- 2024年公路交通运输技能考试-公交车笔试参考题库含答案
评论
0/150
提交评论