国际建模A题O奖论文Three Steps to Make the Traffic Circle Go Round.docx

国际建模A题O奖论文Three Steps to Make the Traffic Circle Go Round.docx

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国际建模A题O奖论文ThreeStepstoMaketheTrafficCircleGoRound

ThreeStepstoMaketheTraffic

CircleGoRound

ZeyuanAllenZhu

TianyiMao

YichenHuang

TsinghuaUniversityBeijing,ChinaAdvisor:

JunYe

Summary

Withgrowingtraffic,controldevicesattrafficcirclesareneeded:

signals,stop/yieldsigns,andorientationsigns—aspecialsignthatwedesigned.

Wecreatetwomodels—onemacroscopic,onemicroscopic—tosimulatetransportattrafficcircles.ThefirstmodelstheproblemasMarkovchain,andthesecondsimulatestrafficbyindividualvehicles—a“cellularautomata-like”model.

Weintroduceamulti-objectivefunctiontoevaluatethecontrol.Wecombinesaturatedcapacity,averagedelay,equitydegree,accidentrateanddevicecost.Weanalyzehowbesttocontrolthetrafficcircle,intermsof:

•placementofbasicdevices,suchaslightsandsigns;

•installationoforientationsigns,toleadvehiclesintotheproperlanes;and

•self-adaptivity,toallowthetraffictoauto-adjustaccordingtodifferenttrafficdemands.

Weexaminethe6-arm-3-laneSheriffhallRoundaboutinScotlandandgivedetailedsuggestionsforcontrolofitstraffic:

Weassignlightswitha68-speriod,andweofferasampleorientationsign.

Wealsotestsmallerandlargerdummycirclestoverifystrengthandsensitivityofourmodel,aswellasemergencycasestojudgeitsflexibility.

TheUMAPJournal30（3）（2009）261–280.!

cCopyright2009byCOMAP,Inc.Allrightsreserved.Permissiontomakedigitalorhardcopiesofpartorallofthisworkforpersonalorclassroomuseisgrantedwithoutfeeprovidedthatcopiesarenotmadeordistributedforprofitorcommercialadvantageandthatcopiesbearthisnotice.Abstractingwithcreditispermitted,butcopyrightsforcomponentsofthisworkownedbyothersthanCOMAPmustbehonored.Tocopyotherwise,torepublish,topostonservers,ortoredistributetolistsrequirespriorpermissionfromCOMAP.

Introduction

Wedeveloptwomodelstosimulatetrafficflowinatrafficcircle.ThemacroscopicmodelusesaMarkovprocesstomovevehiclesbetweenjunctions,whilethemicroscopicmodelconcentratesonthebehaviorofeachvehicle,usingamodifiedcellular-automataalgorithm.TheoutcomesofthesetwoapproachesshowgreatconsistencywhenappliedtoarealscenarioinScotland.

Wecharacterizea“good”trafficcontrolmethodintermsoffivemainobjectivesandcombinethemwithanoverallmeasure.

Weemployageneticalgorithmtogeneratethefinalcontrolmethod,inparticulartodeterminethegreen-lightperiod.Wealsoconsidertheabilitytodealwithunexpectedaffairssuchasaccidentsorbreakdowns.

GeneralAssumptions

•Thegeometricdesignofthetrafficcirclecannotbechanged.

•Thethattrafficis,nogradecircleisseparationastandardstructure.one（atgrade）withalllanesontheground,

•Theflowofincomingvehiclesisknown.

•Peopledriveontheleft（sincetheexamplelaterisfromtheUK）.

•Pedestriansareignored.

•Motorcyclesmovefreelyeveninatrafficjam.

TerminologyandBasicAnalysis

Terminology

•Junction:

circle.anintersectionwherevehiclesflowinandoutofthetraffic

•TheLane:

numberpartofofthelanesroaddirectlyfortheaffectsmovementflowthroughofasinglethecirclelineofbyvehicles.limitingentranceandexitofvehicles.However,sinceboththeconventionaldesignandreal-timephotossuggestthatvehiclesexiteasily,ourmodelignoresrestrictionsonoutwardflow.

•l0:

thenumberoflanesinthetrafficcircle.

•Section:

partofthetrafficcirclebetweentwoadjacentarms.

•Yield/stopofway;astopsigns:

signAasksyielddriverssignaskstocomedriverstoatofullslowstopdownbeforeandmerging.giveright

•Orientationsign:

asignindicatingthelaneforvehiclestotakeaccordingtotheirdestination.

•Trafficlight:

asignalingdeviceusingdifferentcolorsoflighttoindicatewhentostopormove.Atrafficlightwithdirectionarrowsperformsmuchbetter[HubacherandAllenbach2002],soweareinclinedtousesuchalight.However,comparedtoyield/stopsigns,trafficlightsslowvehiclemovement.Atthesametime,however,evenataremotemotorwaytrafficcirclewithfewpedestrians,aatraffic-lightmalfunctionwillprobablyleadtoanaccident[Picken2008].

•Cycleperiod:

thetimeinwhichatrafficlightexperiencesexactstagesofallthreecolors.Anoptimalcycleperiodiscriticalwhenevertrafficlightsareemployed.ThemethodweuseiscalledtheWebsterequation[GarberandHoel2002].Thevaluethatweuseinourmodeliscalculatedas68s.

•Green-lightperiod:

thetimethatatrafficlightkeepsgreeninonecycle.

•Timestamps:

asequenceofcharactersdenotingthestart/endtimeofred/greenlights.

AGlanceatSheriffhallRoundabout

Figure1.TheSheriffhallRoundabout.Source:

GoogleEarth.

Onecharacteristicofthistrafficcircle（Figure1）isthatthearmsinthesouthwest（6）a