美赛a题一等奖论文.docx

美赛a题一等奖论文.docx

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美赛a题一等奖论文

ModelingontheKeep-Right-Except-To-PassRule

Summary

Inthispaper,wedevelopmodelstoanalyzekeep-right-except-to-passtrafficrule,andcarryoutin-depthresearchtostudytrafficflowandsafety,optimaltrafficrules,thedifferencebetweendrivingleftandright,aswellasthefutureutilizationofintelligenttransportationsystems（ITS）.

Firstly,weanalyzethefactorsdeterminingtrafficflow.Trafficdensityischosentodescribetrafficload,thatis,whetherthetrafficislightorheavy.Itcanbeformulatedthatthetrafficflowisaquadraticfunctionofthetrafficload.Meanwhile,weappraisethekeep-right-except-to-passrulebyroadutilityfunctionandlane-changingincidence.Then,basedontherelationshipbetweentrafficflowandsafety,webuildsafetyevaluationmodelintermsoftrafficcapacity,congestiondegreeanddrivingspeed.Lastly,weexploretheoptimaltrafficrules,withtheprecautionofsafetyandthepurposetopromotetrafficflow.Wefigureoutthattravelingonrightandleftlanes,leavingthemiddlelaneastheaccelerationlaneisthebestchoicefortwo-waysix-lanefreeway.Formore-than-eight-lanefreeway,itisbettertodistributedifferenttypesofvehiclesondifferentlanes.Differentrulesondifferentfreewaysectionisthekeyprinciplesinceallfreewaysectionsaredesignedinitiallytomeetparticulardemands.

Whenonlyphysicalfactorsaretakenintoaccount,thereisnosubstantialdifferencebetweenkeep-right-except-to-passruleandkeep-left-except-to-passrule.Whenmentalfactorsaretakenintoaccount,keep-right-except-to-passruleismorelikelytocauseaccidentsduetoindividualdifferencesinstrength,reactionspeedanddynamicvisualerror.AsforITS,wefindthatitenableshigherreliabilityandlargerflow.Itimprovestheeffectivenessandfrequencyofroadutilityassessment.Besides,wefindoutthattransportationmanagement,informationsharingandcoordinationbetweenvehiclesandroadsaredevelopingdirectionsforITS.Lastbutnotleast,wecanseethatinthefuture,thebesttrafficruleisnoruleduetothepopularityofITS.

Contents

Summary1

Background3

Problem1:

Studyonfreewaytrafficcondition4

1.1AnalysisonthetrafficflowundertheKeepRightExcepttoPassrule4

1.1.1Trafficflowcharacteristicsunderdifferentloadsonthefreeway4

1.1.2Trafficflowcharacteristicsbasedonfreewaylane-changingbehaviors7

1.2AnalysisonsafetyundertheKeepRightExcepttoPassrule11

1.2.1Therelationshipbetweenthetrafficflowandroadsafety11

1.2.2Thecomprehensiveevaluationmodeloffreewaytrafficsafetybasedontrafficflowcharacteristics13

1.3Optimizedtrafficrulesmodel17

1.3.1Trafficrulesontwo-wayfour-lanefreeways17

1.3.2Trafficrulesontwo-waysix-lanefreeways20

1.3.3Trafficrulesontwo-wayeight-lanefreewaysormore21

Problem2:

Analysisontheperformanceoftrafficofdrivingleftandright21

2.1Analysisofphysicalfactorsoftraffic23

2.2Analysisonmentalandphysiologicalfactorsofmen23

2.2.1Reliabilityanalysisonthefieldofviewonthemoveanddrivingsafety24

2.2.2Analysisonthereactionanddistributionoftheleft-handedandright-handed26

2.2.3Analysisonthedrivingfeatures27

Problem3:

AnalysisandoutlookonIntelligentTransportationSystems28

3.1AnalysisonthetrafficflowbasedonITS30

3.1.1Modelsonthebehaviourreliabilityandtrafficflow30

3.2AnalysisonthetransportationabilitybasedonITS31

3.3StudyonthesecurityofITS31

3.3.1IndexanalysisofITS32

3.4VisionforintegrationofIntelligentTransportationSystems[13]33

3.4.1Improvementofsecuritycoordinatedbyvehiclesandroads33

3.4.2Increasingtransportationmanagementlevelusinginformationtechnology.33

3.4.3Coordinationoftransportationsanditsutilityimprovementbasedoninformationsharing33

Reference35

Background

Freewayaredesignedfortwo-dimension,multilaneuseforautomobileswhichcantakefullycontrolofallvehicles,adaptingto120km/horhigherspeed.Ithasstrongcapacityoftransportation.Forinstance,thetotalmileageofthefreewayinAmericaisonly1%ofthewholemileageofthehighway,butitundertakesmorethan20%transportationofAmerica.

ItisquiteinterestingtowhendiggingintotheoriginoftheKeepRightExcepttoPasstrafficrule.InmedievalEurope,thereisaspecialstratum,thatis,knight.Accordingtotheirhabit,theyridehorse,withswordintheirrighthands,shieldandreinintheirlefthands.Iftheyrideontheleftside,theycanattackenemies’weakpoints.Astimegoesby,peopleinEnglanddriveontheleftside.AsknightsinEngland,Japanhaswarriors.Inordertoprotectthemselves,theywalkontheleftsideoftheroad.WhentheFrenchrevolutionarrived,theFrenchstartedtogoontherightside.Powerpoliticshavecloserelationshipbetweenthedrivingside.BritishCommonwealthandcoloniesofEnglandstilldriveontheleftside.ColoniesofFrancedriveontheright.Untilthesecondworldwar,becauseoftheassistingcarsfromAmericadriveontheright,ChinastarttocomplywiththeKeepRightExcepttoPasstrafficrule.ThetrafficofPakistanisquiteuniqueandinteresting,camelsgoalongtheleftanditisquitedifficulttochange.Peoplehavetofollowtheirrules.

Thisincreaseinroadtransportbringsbenefitstosocietyintermsofmobilityandaccessibility,italsohoweverhascosts.Thecostsincludenotonlythedirectcostofprovidingtransportservicessuchasinfrastructure,personnel,equipmentcostsbutalsothevariousindirectcostsintermsoftheimpactontheenvironment,mostnotablynoiseandairpollution;traveldelayduetotrafficcongestion;andthelossoflifeandpropertydamageasaresultofroadaccidents.Thegrowingnumberoftrafficaccidentshavedirecteffectsonourcountry’snationaleconomicdevelopment,threateningpeople’slifeandpropertysecurity,increasingthepressuretothesecurityandstabilityofthewholesociety.

Problem1:

Studyonfreewaytrafficcondition

1.1AnalysisonthetrafficflowundertheKeepRightExcepttoPassrule

1.1.1Trafficflowcharacteristicsunderdifferentloadsonthefreeway

Inordertodiscusstrafficflow,firstlyofall,weshouldknowexactlywhattrafficflowis.Wefindthattrafficflowcanbedescribedbythreemainparameterstheoretically:

flow,speedanddensity.Speedanddensitycanreflectthequalityofserviceacquiredfromfreeway.However,flowcandescribethedemandoftrafficfacilities.Theparametersareindependentrandomvariablesandthedistributionoftrafficflowobeysthestatisticallaws.Tomakeitclearer,thetrafficflowfollowsPoissondistribution[1].

Where:

denotesthepossibilityof

carsinacertaintimeperiod

denotesthefixedtimeperiod（

）

denotesthenumberofcarsperunitoftime,

denotestheaveragecarnumberinperiod

1.1.1.1Therelationshipbetweenspeedanddensity

Whendrivingontheroad,weallexperiencethatthelowerthedensityis,thefasterthecargoes.Whenthedensitygoeshigher,thenumberofcarsincrease.Sothatdriversareforcedtoreducespeed.Whenthetrafficisgettingheavier,carsareslowerandtheroadbecomesmorecrowdeduntilcongestionhappens.

In1933,Greenshieldsputforwardlinearmodelbetweenspeedanddensity[1].

Where:

indicatesacorrelationconstantwhichcanbeacquiredbyfittingspecificdata.

indicatesthenavigatespeedwhichisconstrainedbyroadconditionsonly

indicatesthecongestiondensity.

Themodelisintuitiveandpractical,fittingwellwithmeasureddata.When

canreachnavigatespeed

whichisthehighestspeedtheoretically.

1.1.1.2Therelationshipbetweenflowanddensity

TherelationshipcanbededucedfromGreenshieldsmodel[1].

Theformulaisapproximatelyaquadraticrelationshipwhichcanbedescribedbyparabola-likecurve.

Figure1.Therelationshipbetweentrafficflowandvehicledensity

Whenthedensityiszero,theflowiszero.Sothecurvegoesthroughthecoordinateorigin.Theflowincreasesasdensityincreasesuntilitreachesthemaximumtransportationabilityoftheroad,whichis

inFigure1.Thecorrespondingdensityisthebetterdensity

.Frompoint

on,asvehicledensityincreases,speedandflowgodownuntilitreachescongestiondensity

.Atthatpoint,thespeedandflowturnzero.Depictradiusvectorfromthecoordinateorigintothecurve.Theslopeofthevectorindicatesthemeanspeedofthecertainpointonthecurve.Theradiusvectorthroughpoint

istangenttothecurve,theslopeofwhichisthenavigatespeed

.Fordensitysmallerthan

thetrafficisnotcrowded.However,fordensitybiggerthan

thetrafficiscrowded.

Let

wecanget

correspondingto

asfollows.

Forinstance,

.

1.1.1.3Therelationshipbetweenspeedandflow.

Forinstance,

.

Wecanseefromtheformulathat,therelationcurvebetweenspeedandflowapproximatelyfollowsaparabolacurve.

Figure2.Therelationshipbetweenspeedandtrafficflow

Whenthedensityiszero,thespeedofthesmoothtrafficflowcanreachthehighestspeed

.Meanwhiletheflowiszero.Whenthedensityreaches

thespeediszero,soastheflow.Sothatthecurvegoesthroughthecoordinateorigin.

From

wedepictalineperpendiculartotheaxis.Theleftpartofthelineindicateslighttraffic,inwhichspeeddecreaseswiththeincreaseofflowuntilthemaximumflow

.Therightpartindicatesheavytraffic.Theflowandspeedgodowntogether.

Conclusion

Basedonthethreeparameters,wegetfollowingconclusions.

●Whenthedensityissmall,vehicle