美国数学建模.docx

美国数学建模.docx

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美国数学建模

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TheKeep-Right-Except-To-PassRule

Abstract

Inthispaper,wetakeChinesegeneraltwo-waysixlanehighwayforexample,withoutconsideringtheimpactontrafficsafetylane.Therefore，itcanbeseenasathetwinfour-lanehighways.

Forquestion1,firstlytherewereestablishedtwolanecellularautomatontrafficflowmodel,oneisonmanagedcontrolrules,theotherhasnocontrolled,foundthatWhenvehicledensityislowerthan0.14,andtheproportionoflargevehiclesisfrom0.37to1,thetrafficflowofthetwocontrolconditionsarebasicallythesame.Exceptthat,thetrafficflowofthetwocontrolconditionsisslightlylarge.

Fortrafficsafetyissues,withthevehiclemodelandlanechangingmodelconsideredseparately,trafficsafetyindicatorswereestablished.Whenthevehicleflowothers,Securityrelatedtothedistancebetweentheadjacenttwovehicle;whenlanechanging,itisassociatedwiththeclosestdistance,whichthespacebetweenadjacentlanesbeforeandafterthevehicle.AccordingtoThesetwomodelsofsafetyindicatorsweighted,foundingthefinalrateofovertaking:

，where

.

Insummary,atlowload,theimpactoftrafficflowandsafetyarenotmuchdifferenceinthetworules;Withtheincreaseofload,althoughrighttrafficrulesisonlyslightlybiggerthanthetrafficwithoutrules,butsafetyisobviouslyimproved.

Forquestion2,thesolutionofquestion1alsoappliedtocountriesdriveontheleft,justputthefirstandsecondlanesexchange.

Forquestion3,inacompletelyunderthecontroloftheintelligentsystem,fromthemacroscopic,dynamiccharacteristicsofhighwayandtrafficflow,thetrafficflowmacromodelandthetrafficflowcontrolmodelwereestablished,andthenproposealow-densityareaofvariablespeedcontrol,medium-densityareaofvariablespeedlimitandrampcontrolmodel,andgivestheoptimalsolutiontosolvetheproblem,canbetterrealizethesafety,rapidityandcomfortoffreewaytrafficflow.

Keywords：

CellularAutomataSafetyindicatorsMacroscopictrafficmodelDynamicProgramming

Contents

1Introduction1

2Assumptions1

3Symbols2

4ModelsandResultsaboutQuestionone2

4.1Cellularautomatonmodel2

4.1.1two-laneunregulatedcellularautomatatrafficflowmodels3

4.1.2Twolanecontrolcellularautomatontrafficflowmodel[1]4

4.2results6

4.2.1Impactofdifferentcontrolconditionsonovertakingratio[2]6

4.2.2Impactofdifferentcontrolconditionsonvehiclespeed[3]7

4.2.3Effectofdifferentcontrolconditionsontrafficflow[4]8

4.2.4Effectofproportionoftrucksandbusesontrafficflow9

4.3Modelsofsecurityissues9

4.3.1Withthecar’ssafetyindicators10

4.3.2safetyindicatorsbetweenthetwovehicleswhenchanginglanes10

4.3.3Safetycompositeindicator11

4.3.4Conclusions11

5TheModelofQuestion311

5.1TrafficFlowMacroscopicModel11

5.2TrafficFlowControlModel13

5.2.1on-rampcontrolmodel13

5.3Theobjectivefunction[7]14

5.3.1ServiceFlow14

5.3.2Traveltime14

5.3.3Traveltimedelays14

5.3.4PerformanceIndicators15

5.4OptimalControl15

5.4.1optimalproblemofvariablelimitcontrolledspeedinLow-densityarea[9]15

5.4.2Optimalissueofthevariablespeedlimitinmiddle-densityareaandthejointcontrolonon-ramp15

5.4.3Theoptimalproblemoftheon-rampadjustinHigh-densityareaandexit-rampdiversionadjustmentcontrol16

References16

1Introduction

Incountrieswheredrivingautomobilesontherightistherule（thatis,USA,ChinaandmostothercountriesexceptforGreatBritain,Australia,andsomeformerBritishcolonies）,multi-lanefreewaysoftenemployarulethatrequiresdriverstodriveintheright-mostlaneunlesstheyarepassinganothervehicle,inwhichcasetheymoveonelanetotheleft,pass,andreturntotheirformertravellane.Inthecaseofvehicledensityisrelativelyhigh,overtakingproblemsnotonlyaffectsthetrafficflowandlikelytocauseaccidents,soweshouldbeovertakingundersafetyconditions.

Figure1keeprightexcepttopass

Inthispaper,tosolvethetrafficproblemscausedduetoovertaking,theapplicationofcellularautomatatomodeltoanalyzetheimpactofdifferentrulesunderthecontrolofthetrafficflowandtrafficsafetycausedbytherealizationofthefinalbuilddynamicmodelsofreal-timeintelligenttrafficcontrol

WetakeChinesegeneraltwo-waysix-lanehighwayforexample,ignoredthesafetylane.Specificallyaddressthefollowingissues:

Question1:

Undertheprincipleofmulti-lanehighwaytofollow,setamathematicalmodeltoanalyzetheperformanceofthistrafficconditionsatdifferentfactors.Proposedaprogramsthatcanimprovetrafficflow,safetyfactorsoralternatives（includingnosuchlaw）.

Question2:

Discussiontheconclusionsofquestion1,makingsomechangestoapplythecountriesdriveontheleft.

Question3:

Ifvehicletransportationonthesameroadwaywasfullyunderthecontrolofanintelligentsystem–eitherpartoftheroadnetworkorimbeddedinthedesignofallvehiclesusingtheroadway–tochangetheresultsconcludedofquestion1and2.

2Assumptions

Inordertoensurethatourmodelsremainvalidundervariouspotentialconstraints,wemakeanumberofassumptionsasfollowsbeforesteppingintodetailsaboutourapproaches.

1）Thehorizontalwidthoflanescanbeignored.

2）Theoverallcharacteristicsofthedriver'sinfluencecanbeignored

3）Doesnotconsiderthecurve

4）Doesnotconsidertheimpactoflaneroadconditionsontrafficsafety.

5）Thestudyisatwo-waysix-lanedriveway,whichdoesnotconsidertheimpactontrafficsafetylaneroadconditions,whichisthetwo-wayfour-lanedriveway.

3Symbols

Parameter

Meaning

Thepositionofvehicleiattimet

Thespeedofvehicleiattimet

Themaximumspeedofthevehicle

Thelengthofroad

therandomslowingdownprobability

Vehicleswithdecelerationprobability

Intervalaveragedensity

Averagespeedofintervali

Rampflowrate

Blockingdensity

4ModelsandResultsaboutQuestionone

First,weusecellularautomatamodelingandnumericalsimulation,Studiedinthecaseofloadchangerulesbecauseoftherightlineandspeedcausedtrafficrulesandsafetychangesandappliedtotheleft-rule.Finally,theuseofdynamicprogrammingmodelhasbeenestablishedunderdifferenttrafficflowmodelsreal-timeintelligenttrafficloadcontrol.Thefollowingissueswerediscussedtrafficflowandsafety.

4.1Cellularautomatonmodel

Cellularautomatonmodelisoneofthemicroscopictrafficmodels.Inthismodel,aroadwayismadeupofcellslikethepointsinalatticeorlikethecheckerboardandtimeisalsodiscredited.Vesiclesmovefromoncelltoanother.Thebasicruleofthetrafficflowisthateachvehiclemovevsitesateachtime.Thevelocityspeedvwilladd1ifthereisnocarsvspaceaheadandslowdownto

−1ifthereisanothervehicle

spacesahead.Thevelocitywillslowdownrandomlywiththeprobability.

4.1.1two-laneunregulatedcellularautomatatrafficflowmodels

Trafficroadsystemconsistsoftwoparallellanesinthesamedirection,namelyrecordedasthefirst,seconddriveway.WedefinethelengthofeachchainisL,andeachgridpointwillbeoccupiedoremptyateachmomentAssumingthesamemaximumspeedofthevehicleoneachlane,

.Vehiclelanefromlefttorightmovement,duetotheinteractionbetweenthevehicle,thevehiclehasaspeeddistributionofvalues​​inbetween

.

Intheevolutionofthemodel,eachstepofthetwo-stepandchangelaneswhentravelingevolution.

Figure2Overtakingunderunregulated

1）Advancingstep

Inthisstep,thevehiclebytheNSmodelruleupdatingitstravelingspeedandlocation:

（1）Updateallvehiclevelocitydistribution:

thefrontofthevehiclebasedonthecurrentspeedandthenumberofspacestoadjustitsspeed.

IF（

ELSEIF（

）

ELSEIF（

）

（2）Changethelocationofallvehicles:

Let

bethepositionofvehicleiattimet,

bethespeedofvehicleiattimet,

bethemaximumspeedofthevehicle,

bethelengthofroad,

betheVehiclespacingofvehicleiattimet,

betherandomslowingdownprobability.

2）Lanechangingsteps

Afterthevehicleistravelingoneachlane,accordingtothetravelneedswillchangelanes.Vehiclelanechangeprocess,tomeettheovertakingandsafetyprinciples.

Lanechangingrulesofthefirstlane:

If

thedriverwillgenerateawarenessoflanechanging.If

and

thevehicleinthefirstlanewillturnintothesecondlane,thespeedofthevehicleafterlanechangingremainsunchanged.

indicatesthedistancebetweenthevehicleandthenearestfrontvehicleinthefirstlane.

Indicatestheexpectationsofvehiclespeed.

indicatesthedistancebetweenthevehicleinthefirstlaneandthenearestfrontvehicleinthesecondlane.

indicatesthedistancebetweenthevehicleinthefirstlaneandthenearestfollowingvehicleinthesecondlane.

indicatesthespeedofthefollowingvehicleinthesecondlane.

Lanechangingrulesofthesecondlane:

If

thedriverwillgenerateawarenessoflanechanging.If

and

thevehicleinthesecondlanewillturnintothefirstlane,thespeedofthevehicleafterlanechangingremainsunchanged.

4.1.2Twolanecontrolcellularautomatontrafficflowmodel[1]

Inthispaper,basedontwo-lanetrafficflowunregulatedCAmodel,thefirstlaneisapassinglane,Theve