美賽集美賽獎(jiǎng)

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SummarySheet

HighwayTrafficFlowModelwithSelf-DrivingVehiclesBasedonCellularAutomata

Summary

Withtheincreasinglackoftransportationcapacityandthegrowthofself-drivingvehicle(SDV)industry,anevaluationshouldbemadetofindouttheinfluenceontrafficwhenmoreandmorenon-self-driving-vehicles(NSDV)arereplacedbySDVswhilefewstudiesweredoneontheinteractionsbetweenSDVsandNSDVsandthecooperationsamongSDVsthemselves.

Wechoosecellularautomata(CA)modeltoevaluatethisproblemafteracarefulstudyandcom-parisonofdifferentkindsoftrafficflowmodelsinthepastfewdecades.Inordertotakethere-lationshipsofSDVsandNSDVsintoconsideration,weimprovethetraditionalCAmodelwhichemphasizesonstatusandrulesofchanges,byredesigningthesetwofactors.BeforebuildingaCAmodel,discretizationshouldbedonefirst.Bylearningtheaveragelength,speed,accelerationofrunningvehiclesonhighwayandthereactiontimeofhumanbeings,thesizeofacellandthetimelengthofaturnaredecided.Aftermakingassumptionsandsimplifyingtheproblem,twointer-relatedCAmodelsarecoveredinthispapertosimulatethechangeabletraffic:theFollowingModelandtheMultilaneTrafficModel.

TheFollowingModelisdesignedtosimulatehowavehiclefollowsanotherinasinglelane.RulesforNSDVsandSDVsaredifferentfromeachother:ForanNSDV,thedriver’sreactiontimeandpsychologicalcharacteristicsareconsidered;ForanSDV,therulesarebasedonthesharingofinformationwithotherSDVsandthejointdecisionmaking.Specifically,wecreateanewconception’SDV-Train’tosimulatethecooperationsamongSDVs.

TheMultilaneTrafficModelisbasedontheFollowingModel.Inthismodel,besidesfollowing,wetrytofindoutwhenandhowshouldavehiclechangealane.Twomainparametersareinvolvedinthismodel:Lane-ChangingMotivation(LCM)andLane-ChangingSecuirty(LCS).LCMdependsonwhetherchangingalanecanincreasethespeedandLCSshowsthewhetheritissafewhenlane-changing.OnlywhenbothLCMandLCSaresatisfied,mayavehiclechangeitslane.DetailsofthesetwoparametersvarybetweenSDVsandNSDVsconsideringthehugedifferencebetweenanautomaticcontrolsystemandahumandriver.Atwo-stepturningmethodisspeciallymadeforthismodelincorrespondencewiththerealworld.

Afterbuildingandmakingimprovementstothemodel,wewriteprogramstosimulateitandgethugevolumesofdata.WeanalyzeandvisualizethedatausingMatlab,showingstrongcorrelationsamongthreeparameters:theaveragespeed,thetrafficflowandthepercentageoftheSDVsrunningontheroad.TheincreasingnumberofSDVshasgreatinfluenceonthetrafficflowwhichalmosttripleswhenalltheNSDVsarereplacedbySDVs.Also,wefindthataspeciallaneforSDVs(SDVLane)shouldbebuiltwhenthepercentagereachesacertainlevel.

Basedonthecorrelationswegetinanalysis,weapplyourmodeltotheGreatSeattleareabycomparingtherealdataandthedatawegainfromsimulations.Wefindthatthelackoftrafficcapacityinthisareaishuge.AlthoughaddingSDVstothestreetcanreducethislack,itisnotacure.WebelieveacomprehensivemethodshouldbeappliedinthisareaincludingsettingaSDVLaneandbroadeninghighwaysinsomeparticularlynarrowparts.

Keywords:TrafficFlowModel;Self-DrivingVehicle;CellularAutomata

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Contents

1

Introduction

1

2

SimplificationsandAssumptionsoftheProblem

1

1

2

3

3

2.1

2.2

2.3

2.4

FeaturesoftheHighway....................................

FeaturesofVehicles.......................................

SpecialFeaturesofNSDVs...................................

SpecialFeaturesofSDVs....................................

3

ChoiceandBasicSettingsoftheModel

3

3

4

4

3.1

3.2

3.3

ChoiceoftheModel.......................................

Discretization..........................................

BasicSettings ..........................................

4

DetailsoftheModel

4.1 FollowingModel........................................

4

4

5

6

7

9

9

10

10

12

4.1.1

4.1.2

4.1.3

Variables.........................................

FollowingRulesforNSDVs..............................

FollowingRulesforSDVs...............................

4.2 MultilaneTrafficModel ....................................

4.2.1

4.2.2

4.2.3

4.2.4

Variables.........................................

GeneralRulesofChangingLanes ..........................

Lane-ChangingRulesforNSDVs...........................

Lane-ChangingRulesforSDVs............................

5

AnalysisoftheResultsObtainedfromtheModelSimulation

13

13

15

16

5.1

5.2

5.3

ResultsofFollowingModel..................................

ResultsoftheMultilaneTrafficModel............................

SDVLane.............................................

6

ApplianceoftheModel

17

7

SensitivityAnalysis

7.1 ChoiceoftheParametersinLCP

18

18

18

...............................

7.2 DifferentSpeedLimit.

.....................................

8

Conclusions

19

9

Strengthsandweaknesses

9.1 Strengths.............................................

19

19

19

9.2 Weaknesses

...........................................

10

ALetter

20

Appendices

22

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1 Introduction

Builtinthe20thcentury,manyhighwaysweredesignedtomeetthetransportationdemandsatthattime.Withtheboomofpopulation,urbanizationandeconomy,theneedoftransportationgrowsrapidlyinthenewcentury.Nowadays,highwaysintheGreatSeattleareacannolongermeetpeople’sneedandtrafficdelayscanbeseeneverywhereduringpeakhours.However,atthistimebuildingmoreroadsoraddinglanesinthisareaisextremelydifficultandexpensive.Inordertoincreasethecapacityofhighwayswithoutincreasingthenumberoflanesorroads,allowingself-drivingvehicles(SDVs)torunontheroadshouldbetakenintoconsideration.AmodelisneededtoevaluateSDVs’influenceonthetrafficflow.

Weproposedtodecomposethisproblemintothreeparts:

?

BuildamodelthatcansimulatethetrafficflowindifferentpercentageofSDVsandnon-self-drivingvehicles(NSDVs),numberoflanesandtrafficvolume.

Usethemodeltofindtheequilibriaortippingpointsandapplythemodeltotheprovideddata.

Basedonthedata,decidewhethertherearesomeconditionswherelanesshouldbededicatedtoSDVsandhowthepolicyshouldbechanged.

?

?

Firstly,weusecellularautomata(CA)tosimulatethetrafficflowwhenthereisonlyonelane.ThismodeliscalledtheFollowingModel.Inourmodel,werulethewayeachcellbehavesbysimplifyingthebehaviorsofvehiclesinreallife,likewhenavehiclewillslowdownorspeedup.WeusedifferentrulesforSDVsandNSDVsinourmodeltosimulatethecooperationsamongSDVs,interactionsbetweenSDVsandNSDVs,unpredictabilityofhuman-beingsandotherfactors.

BasedontheFollowingModelwebuilt,weputseparateparrellanestogetherandaddnewrulestosimulatethetrafficflowonamultilanehighway.ThisistheMultilaneTrafficModel.Aftersimplifyingthebehaviorsofrealvehicles’changinglanes,wemakerulesonwhenandhowacellmoveacrosslanes.Boththemotivationandthesafetyconcernareconsidered.Furthermore,wemakespecialrulestosimulatehumanbehaviorsandcooperationsamongSDVsincludingtheformofachainofSDVscalledtheSDV-Train.

Secondly,usingreal-lifeparameters,weruntheCAmodelandgetalargenumberofdata.Byanalyzingthedata,wefindseveralinterestingfeaturesofthemixedtrafficflow.Thecorrelationsamongtheaveragespeed,thetrafficflowandthepercentageofSDVsarestrong.Thesethreepa-rametersinfluenceeachotherintheirownway.Whentherearemanylanes,thesituationchangesandmoreinterestingphenomenaarefoundincludingtherelationshipsbetweentheefficiencyofeachlineandthepercentageofSDVs.Aftercomparison,wefindoutwhenandhowtobuildaspeciallaneforSDVs(SDVLane).

Thirdly,wecomparedourdatawithrealdataintheGreatSeattlearea.Wefindthatthereisindeedagreatlackoftrafficcapacityinthisarea.AfterchangingNSDVstoSDVs,thetrafficcapacityincreasesandeventriplesbutwebelievethetrafficsituationinthisareaisstillnotabundant.MoremethodsincludingbroadenafewpartsofthecurrenthighwayandsettingaSDVLaneshouldbetakenintoconsideration.

SimplificationsandAssumptionsoftheProblem

FeaturesoftheHighway

StraightRoad

Ahighwayinthismodelshouldbestraightoritsdegreeofcurvaturecanbeignored[1].A

vehicle’sspeedandotherconditionsdoesnotchangebecauseoftheshapeoftheroad.

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2.

3.

4.

Thenumberoflanesshouldremainconstantforalongperiod.

Thehighwayisingoodconditionandthetrafficflowisnotaffectedbytheroughroad.

Nopedestrian,animaloranyformofobstaclecanbefoundonthehighwaysothetrafficflowwouldnotbeblocked.

Weatherchangesandilluminationdifferenceduringdifferenttimeisnottakenintoconsid-eration.

RulesforSDVLane

5.

6.

?

IfaSDVLaneisset,allSDVsshouldruninthislinewhilenoneoftheNSDVsmayruninit.

OnlyoneSDVLanecanbesetinourmodelconsideringthewidthofthehighwayislimited.

TheSDVLanewillbeplacedontheedgeoftheroadtopreventaseparationoflanesforNSDVs.

?

?

7.

8.

Thewidthofeachlaneis12feet.

Thespeedlimitofallhighwaysis60mph.

2.2

1.

FeaturesofVehicles

Inthismodel,onlyaveragelength,speed,accelerationandotherfeaturesofvehiclesareused.Althoughthereisagreatdiversityamongdifferentvehicles,thisdifferencecanbeignoredandtheresultofthemodelwouldnotbegreatlyaffected.

Allvehiclesobeytrafficlaws.Theviolationoftrafficlawsdoesgreatharmtothedriver’shealth,publicsecurityaswellasthespeedoftotaltrafficflow.Asaresult,thesecircumstanceswouldnotoccurinourmodel:

2.

?

?

?

?

avehicleexceedsthespeedlimit;avehiclestopsfornoreason;

avehiclerunsinanemergencylaneorontheshoulderfornoreason;avehiclechangesitslanebut

itsturninglightisnotturnedoninadvance;

thevehiclebehinditshowsitsintentiontochangethelane;twovehiclesrunsidebysideinonelane;

thedistancebetweentwovehiclesinthesamelaneistooshort.

?

?

3.

Trafficaccidentisnottakenintoconsideration.DetailsofitsinfluencewillbediscussedinSection9.2.

Averagedailytrafficflowisusedinthismodel.Trafficflowvariesindifferentdays,soanaveragelevelshouldbeusedtosimplifythismodel.

Hornisnotusedinourmodel.Onhighway,theinfluenceofahornislimitedbecausethedistancebetweentwovehiclesistoolongforacomplicatedsoundsignaltobeheardandunderstoodclearly.

4.

5.

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2.3

1.

SpecialFeaturesofNSDVs

Uncertaintyoftheestimationofdistanceandspeed

Comparedwithcomputersystems,humandriversaremorelikelytomakemistakes,especiallywhenitcomestotheevaluationofdistanceandspeed.Therefore,humandriverstendtoslowdownthevehicleandchoosenottochangealanewhentheycannotestimatethedistanceclearlyevenwhenothervehiclesareoutoftheminimumsafedistance.

Longerreactiontime

Humandriversneedmoretimetodecelerateandstarttheirvehiclecomparedwithself-drivingonesespeciallyonthehighway[2].

2.

2.4

1.

SpecialFeaturesofSDVs

Shortreactiontime

SDVsarecontrolledbycomputersystemswhichrunfastandcanstayactiveforthewholetime.Withmoderntechnology,itiseasyforanSDVtoperceivetheoutsideworldandmakereactionsaccordinglyinashorttime.

CooperationsamongSDVs

ThesystemofanSDVisconnectedtotheInternet,thereforeinformationofalltheSDVsonaroadisshared.Withmoreinformation,anetworkdecision-makingsystemcanbebuiltwhichismentionedinpreviousstudies[3].

Maturetechnology

Thetechnologyofself-drivingismatureenoughandnomalfunctionofSDVs’guiding,drivinganddecision-makingsystemistakenintoconsiderationinthismodel.IfanaccidentdoeshappentoanSDV’ssystem,thisSDVshouldbelabeledasanNSDV.

InteractionsbetweenanNSDVandanSDV

AsdiscussedinSection3,forahumandriver,thereisnodifferencebetweenanSDVandanNSDVthatheorsheencountersonthestreet,forSDVswouldmakelessmistakesthanNSDVsandwouldnotcausemoretroubletohumandrivers.

2.

3.

4.

3 ChoiceandBasicSettingsoftheModel

3.1

ChoiceoftheModel

Inthepastfewdecades,withthedevelopmentoftransportation,agreatvarietyofmodelssimu-

latingthetrafficwerebuiltandimproved,amongwhichContinuousMediummodelandCAmodelarethemostpopularones.LighthillandWhithamfirstlyputforwardtheconceptofcontinuous

mediummodel,whileshortlyafterwardsRichardsalsoputforwarditindependently,thereforeitisalsonamedLWRmodel[4].LWRmodelmainlyfocusesonthemacroscopichomogeneityandsta-bilityofthetrafficflow.However,inthisproblem,thecooperationsbetweenSDVsandthereactionsbetweenanSDVandanNSDVmustbefurtherdiscussed,whichmakesithardforustoadapttheLWRmodel,becauseLWRmodelneglectstheinteractionsbetweendifferentparticlesintheflow.Aftercarefulcomparison,wefindthattraditionalCAmodelwithmodificationscanbeusedinthisproblem.

Inreallife,theactionofavehicletakenbybothhumandriversandcomputersystemsdependsonthestatusofthevehicleitselfandthesurroundingtraffic,whichissimilartotherulesofCA,whichisoriginallydiscoveredinthe1940sbyStanislawUlamandJohnvonNeumann[5].ThebasicideaofCAisthatitstartswithasetofcellswithstatus.Asimplesetofrulesarecreatedthatthe

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statusareupdateddependingonthestatusofthecellanditsneighbors.Withmultipleiterations,CAmodelscansimulatethemovementofcomplexobjects.ChangesaremadetothestatusandtherulesoftheoriginalCAmodelinorder,ensuringthatthismodelcanworkforamixtureofSDVsandNSDVs.InordertomakeaCAmodel,discretizationshouldbedonefirsttoalmostallvariables.

3.2

Discretization

InourCAmodels,eachvehicleisregardedasacellwithitsownstatus.Besides,eachlaneisalso

dividedintocellsthatcancontainthevehicleswhiletimeisdividedintosmallunits(turns).

Sizeofacell

TheaveragelengthofvehicleinU.S.isabitlongerthan4meters.Aseverycellrepresentsavehicle,thelengthofthecellshouldbethesameastheaveragelength.Tosimplifythecalculation,weuse

1.

1cell=4m

(3.1)

2.

Timeunit

AstheresultsofTriggs,T.J.andHarris,W.G’sworkshows,theaveragereactiontimefordriversisaround1.5seconds[2].InoneturnoftheCAmodel,avehiclemakesoneaction,so

1.5secondsisagoodchoiceforourCAmodel’stimeunit.

1turn=1.5s

(3.2)

3.3

1.

BasicSettings

Speed

Thespeedlimitofroadis60mph,whichis10cellperturn,usingEqn.(3.1)andEqn.(3.2).BecauseCAmodelisdiscretized,thespeedisregardedasanaturalnumberfrom0to10inourmodel.

Acceleration

Accordingtotheassumption,thespeedofavehicleshouldchangestepbystep.Inourmodel,thespeedcanonlychange1cellinaturn.UseEqn.(3.1)andEqn.(3.2),theaccelerationofavehicleis2.67m/s2,whichisinlinewithdailyexperience.

MinimumSafeFollowingDistance(MinSFD)

Avehicleshouldnotgettooclosetothevehicleaheadtopreventaccidentwhenrunningonahighway.MinimumSafeFollowingDistance(MinSFD)isdesignedtomakesurethatanormalvehiclerunningatacertainspeedcanstopbeforecollision.

2.

3.

4 DetailsoftheModel

InourCAmodels,rulesaremadetosimulatevehicles’movement.Amongallkindsofmove-ments,twotypesofvehicle’sactionsarethemostimportantones:followingandlane-changing.TheFollowingModelandtheMultilaneTrafficModelaremadetosimulatethesetwotypesofactions.

4.1

FollowingModel

TheFollowingModelsimulatestheflowofvehiclesinasinglelaneonthehighway.Largequan-

titiesofsingle-lanetrafficflowmodelshavebeendeveloped,themostfamousoneofwhichisthe

NaSch(NS)model.KaiNagelandMichaelSchreckenbergbuiltthisCAmodelforhighwaytrafficin1992[6].Theirmodel’ssimulationsshowatransitionfromlaminartrafficflowtostart-stopwaves

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withincreasingvehicledensity.Inreallife,SDVs’behaviorisdifferentfromthenon-self-drivingones,soourmodificationsfortheNaSchmodelaremainlyfocusedontheSDVs.

4.1.1 Variables

Table1:MainVariablesUsedintheFollowingModel

Variable

Defination

Unit

di

?di

DistancebetweenvehicleNo.iandthestartpointDistancebetweenvehicleNo.iandthevehicleaheadofit

cellcell

viai

SpeedofvehicleNo.i

WhethervehicleNo.iisacceleratingornot

cell/timestepunitless

biti

StatusofthebacklightofvehicleNo.iTypeofvehicleNo.i

unitlessunitless

MinSFDbetweentwovehicleswhenthelatterone’sspeedisv

Maximumdistancebetweentwovehicleswhenthelatterone’s

Dmin(v)

cell

Dmax(v)

P1,i

cell

unitless

speedisvandtheactionoftheformeronecanbeignoredPossibilityofahumandrivertodecelerateoutofcaution

vA

A

ΔdA

BackLightOn

bi=1

BackLightOff

bi=0

SDV

NSDV

Figure1:DiagramofMainVariablesUsedintheFollowingModel

MainvariablesusedintheFollowingModelareshowninTab.4.1.1andFig.1.Specifically,Eqn.(4.3)showsthefunctionsforthestatusofthebacklightandthevehicletypeseparately:

{

0,

1,

0,

1,

thebacklightofvehicleNo.iisoffthebacklightofvehicleNo.iison

vehicleNo.iisanNSDVvehicleNo.iisanSDV

bi=

{

(4.3)

ti=

ForanNSDV,nolightsignalshowswhetheritisacceleratingornot,whichparameteraiindicates.However,thisinformationissharedamongself-drivingones,whichiswhatEqn.(4.4)shows:

{

0, vehicleNo.iisnotaccelerating

ai=

(4.4)

1, vehicleNo.iisaccelerating

A

vA

B vB

C

vC

DvD

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4.1.2

?

FollowingRulesforNSDVs

Deceleration

Aswediscussedinpart1andpart2ofSection2.4,humandriverneedmoretimetoreactandtheysometimeschoosetoslowdowntomaintainalongerfollowingdistanceoutofcaution.InthisFollowingModel,ifvehicleNo.iisNon-Self-Driving,apossibilityfunctionP1,iismadeforittosimulatethetwofactorsmentionedabove.ForanNSDVA,Eqn.(4.5)showsthefunction,inwhichBrepresentsthefirstvehiclethatisinfrontofA.

P11,P12,P13,0,

bB=1∧?dA>Dmin(vA)∧?dA<Dmax(vA)bB=0∧?dA>Dmin(vA)∧?dA<Dmax(vA)vA=0

othercases

P1,A

(4.5)

=

Incalculation,weusetheresultsgotfromperviousworks[7][8]:

(4.6)

P11=0.94,P12=0.50,P13=0.20

Inshort,thereisarateforNSDVstodecelerateundercertaincircumstances.AsshowninLane1inFig.2,foranNSDVA,everyturnarandomnumberRbetween0and1isgivenintheFollowingModel,and:

P1,A?R?vA=vA?1,bA=1

Besidesthiseffect,ifthereisanothervehiclewithinvehicleA’sMinSFD,Ahastodecelerate

andturnitsbacklighton.Thatis:

?dA?Dmin(vA)?vA=vA?1,bA=1

AndthisisLane2inFig.2.

Dmax(vA)

Dmin(vA)

Deceleration

vA

Lane1

A

B

(P1,A

R)

Lane2

vA

Deceleration

A

B

vA

Acceleration

Lane3

A

B

vA

Lane4

Acceleration

A

B

Hold

vA

Lane5

A

B

(P1,A

R)

Figure2:FollowingRulesforNSDVs

?

Acceleration

IfNSDVAdoesnotdeceleratebecauseofPA,andvehicleBis

faraway,or

notdeceleratingandoutofA’sMinSFD

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thenAwillaccelerate,whichareshownseparatelyinLane3andLane4inFig.2.Thatis:

P1,A<R∧?dA>Dmax(vA)∨bB=0∧?dA>Dmin(vA)

?vA=vA+1,bA=0

Hold

Onothercircumstances,anNSDVholdsitsspeed,whichisshowninLane5ofFig.2:

[OtherCircumstances]?bA=0.

(

))

(

4.1.3 FollowingRulesforSDVs

Accordingtothediscussioninpart1andpart2ofSection2.4,SDVshaveshortreactiontimeandtheycancooperatewitheachother.Consideringthatanaccidenthappensrightinfrontofastraightlineofvehicles,allvehiclesshoulddecelerateinordertokeeptheMinSFD.Iftheyarecontrolledbyhumanbeingswhosereactiontimecannotbeignored,vehicleswilldecelerateonebyonebutwithadelay.However,ifallvehiclesareself-drivingones,theycandecelerateatthesametime,thankstothecooperatingsystem.Itisthesamefortheaccelerationprocess,becauseaicanbeknownforallSDVs,whichismentionedinSection4.1.1.

AnotherfactoristhatthewaychangestocalculateminimumsafefollowingdistancebetweentwoSDVswhichonefollowsanotherclosely,becauseallSDVssharetheinformationofspeedandotherparametersoftheSDVsinfrontofthem,whichismentionedinpart2ofSection2.4.Asisalsoassumedinpart3ofSection2.4,malfunctionoftheself-drivingsystemisnottakenintoconsiderationinthismodel.ThetwoadjacentSDVscandecelerateatthesametimeifemergencyhappens,sothattheMinSFDforanSDVcanbecalculatedfollowingEqn.(4.7),inwhichtheBrakingDistanceoftheformercanberemoved.NocollisionbetweenSDVswillhappenwhenallinformationissharedanddecisionsaremadecooperatively.

BrakingDistanceE=Dmin(m(ax(vE?2,0))

)

(4.7)

(vA)=maxDmin(vA)?BrakingDistanceE+1,1

D

min(SDV?SDV)

InEqn.(4.7)EistheSDVaheadofA.

WiththechangeofDmin(SDV?SDV),thedistancebetweenSDVscanbeshortenedandtherefore

arowofpureSDVscanbeformed.WhenallthedistancesbetweentwoconsecutiveSDVsaretheir

Dmin(SDV?SDV),thischainofSDVscanbecalledaSDV-Train.ForanSDVA,ifitisinanSDV-

Train,letFbetheSDVinthefrontofthetrain.ThethreevehiclesinLane4fromFig.3formatypicalSDV-Train.

Dmax(vA)

Dmin(vA)

vA

B

Acceleration

A

Lane1

vA

A

C

Acceleration

Lane2

AvAvA

Acceleration

E

Lane3

Acceleration

(aF=1)

vA

A

Lane4

F

aSDV-Train

Figure3:FollowingRulesforSDVs:Acceleration

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?

Acceleration

AnSDVacceleratesunder4conditions:

itfollowsavehicleB,andtheirdistanceislongerthanDmax(vA),thatis:

?DA?Dmax(vA)?vA=vA+1;bA=0;aA=1;

1.

whichisthesituationinLane1inFig.3;

itfollowsanNSDVC,whosebacklightisoffandtheirdistanceislongerthantheMinSFDofA,thatis:

tC=0∧bC=0∧?DA?Dmin(vA)?vA=vA+1;bA=0;aA=1;

2.

whichisthesituationinLane2inFig.3;

itfollowsanSDVE,andtheirdistanceislongerthantheDmin(SDV?SDV)ofA,thatis:

tE=1∧?DA>Dmin(SDV?SDV)(vA)?vA=vA+1;bA=0;aA=1;

whichisthesituationinLane3inFig.3;

itisina’SDV-Train’,andthefirstSDVFintrainaccelerates,thatis:

3.

4.

=1?vA=vA+1;bA=0;aA=1.

?DA

=Dmin(SDV?SDV)(vA)∧aF

whichisthesituationinLane4inFig.3.

?

Deceleration

Dmax(vA)

Dmin(vA)

Deceleration

vA

C

Lane1

A

AvAvA

Deceleration

Lane2

E

vA

Deceleration

A

F

Lane3

aSDV-Train

Figure4:FollowingRulesforSDVs:Deceleration

AnSDVdeceleratesunder3conditions:

1.itfollowsanNSDVC,andtheirdistanceisshorterthantheMinSFDofA,thatis:

tC=0∧?DA?Dmin(vA)?vA=vA?1;bA=1;aA=0;

whichisthesituationinLane1inFig.4;

2.itfollowsanSDVE,andtheirdistanceisshorterthantheDmin(SDV?SDV)ofA,thatis:

tE=1∧?DA?Dmin(SDV?SDV)(vA)?vA=vA?1;bA=1;aA=0;

whichisthesituationinLane2inFig.4;

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3.itisina’SDV-Train’,andthefirstSDVFintraindecelerates,thatis:

=1?vA=vA?1;bA=1;aA=0.

?DA

=Dmin(SDV?SDV)(vA)∧bF

whichisthesituationinLane3inFig.4.

?

Hold

Onothercircumstances,anSDVholdsitsspeed:

[OtherCircumstances]?bA=0;aA=0.

TwodifferentsituationsareshowninFig.5:

Dmax(vA)

Dmin(vA)

Hold

Lane1

Hold

（aF=0）

Lane2

aSDV-Train

Figure5:FollowingRulesforSDVs:Hold

4.2

MultilaneTrafficModel

Onmultilanehighways,vehiclestendtostayonitsownlane,whichisthesameastheFollowing

ModelmentionedaboveinSection4.1.However,undercertaincircumstances,driverschangetheir

lanes.TheMultilaneTrafficModelisdesignedonthebasisoftheFollowingModeltosimulatethislane-changingaction[9].BecauseofSDVs’cooperationwitheachotherandtheformationofSDV-Trains,SDVs’rulesofchanginglanesvarywithNSDVs’.

4.2.1 Variables

Table2:AdditionalVariablesUsedintheMultilaneTrafficModel

Variable Defination

Unit

?di,j

ci

DistancebetweenvehicleNo.iandvehicleNo.jStatusoftheturninglightsofvehicleNo.i

cellunitless

NumberoflanewhichvehicleNo.iisonPossbilityofahumandriverofvehicleNo.i

unitless

li

P2,i

unitless

tochangethelanewhenconditionallows

BesidesvariableslistedinTab.4.1.1,additionalvariablesusedintheMultilaneTrafficModelarelistedinTab.4.2.1andFig.6.Specifically,Eqn.(4.8)showsthefunctionforthestatusofvehicleNo.i’sturninglights:

turninglightsofvehicleNo.iareoff

0,

ci=

1, therightturninglightofvehicleNo.iison

?1,theleftturninglightofvehicleNo.iison

(4.8)

A vA C

A vA

F

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C

vC

lC=2

ΔdA,E

1

Lane

2

Lane

BothLightsOff

ci=0

RightLightOn

ci=1

LeftLightOn

ci=-1

Figure6:DiagramofAdditionalVariablesUsedintheMultilaneTrafficModel

4.2.2 GeneralRulesofChangingLanes

Asweassumedinpart2ofSection2.2,driversonlychangetheirlanewhennecessary:

Thevehicleonthesamelaneaheadisnotfarawayandisrunningmuchslower;

Thetrafficconditiononthelanebesideisbetter.

ThisiscalledLane-Changin