国赛A题全国一等奖论文英文版.docx

国赛A题全国一等奖论文英文版.docx

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国赛A题全国一等奖论文英文版

EffectofLaneOccupiedonTrafficCapacity

Abstract:

Thearticleaimsattheproblemhowthelaneoccupationaffectsthetrafficcapacity.Bythemeansofwaveletanalysisandtimeseriesanalysismethod,westudyontheperiodicityandstabilityoftheactualcapacitywhichvarieswithtimegoing.Meanwhile,wegettheexpressionofthevehicleequivalentqueuelengthbasedontheTwoFluidTheory.

Forthequestion1:

Firstly,consideringthatthenumberofvehicleswhicharriveatthecross-sectionintheaccidentobeyingperiodicaldistribution,wechoosethebeginningofgreensignaltimeasastartingpointandcalculatethetrafficdensityevery15secondsatthecross-section.（Averagetrafficdensitywithintherangefromtheaccidentsitetothepoint120metersawayinstead）.Secondly,accordingtotherelationshipamongthethreeparametersofthetrafficflow,wegetsaturatedtrafficflowateachtime,whichrepresentstheactualtrafficcapacityatthemomentthattheaccidenthappened.Finally,weanalyzetheperiodicityandstabilityoftheactualtrafficcapacitybyutilizingwaveletanalysisandSASsoftwaretools,whichresultintheconclusionthattheactualcapacitydecaysperiodicallyandtransitsfromastablestatetoanotherone.

Forthequestion2:

Weobtaintheactualcapacityatthesamecross-sectionwhendifferentkindsofaccidentshappeninvideo2.Throughtheanalysis,itiseasytofindthatbothvariationlawsarebasicallythesame,andthestablevalueisalsobasicallythesame,butthelatterdecaysfasterthantheformer.Therefore,weestablishexplicitequationabouttherealtrafficcapacityanddrawthefollowingconclusion:

Whentheroadcapacityisnotsaturated,theouteroneoflanesblockedbytheaccidenthasthegreaterinfluenceontheactualtrafficcapacitythantheinneronebuttheinfluencewilldisappearwhentheroadcannotbearmorecars.

Forthequestion3:

wecanintroducetheconceptoftheequivalentqueuelengthtodealwiththereallinelengthwhichmaybequitecomplicated.AndthenweclassifyallthevehiclerunningstatesintotwoequivalentlybasedontheTwoFluidTheory.Thisprocessingmethodhelpsusachievetheexpressionoftheequivalentqueuelength.Herewelisttheexpression

.Atlastweexamineourmodelbythemeansofthecomputersimulationandtheinspectionresultsareshownasbelow:

time

16:

48:

00

16:

49:

00

16:

50:

00

16:

51:

00

16:

52:

00

16:

53:

00

16:

54:

00

Relativeerror

5.27%

2.95%

33.48%

4.58%

4.54%

6.93%

6.90%

Judgingfromtheobservationofthedatainthetable,wecandrawaconclusionthatthemodelweestablishedcanpreliminarilyexplaintherelationshipamongstthefourparameters.

Forthequestion4:

Weputthedataintotheexpressioninquestion3.Andthenwegetthatthevehiclequeuelengthwillreachtheupstreamintersectionafter3.34minutes.

Keywords:

WaveletAnalysis,TimeSeriesAnalysis,ComputerSimulation,theTwoFluidTheory,theEquivalentQueueLength.

Content

EffectofLaneOccupiedonTrafficCapacity1

Abstract:

1

1.DescriptionoftheProblem3

2.Assumptions3

3.Definition3

3.1Descriptionofsymbols3

3.2Definitionofterms4

4.PrimaryAnalysis4

5.Preparationsforthemodel5

5.1Determiningthecrosssectionoftheactualtrafficcapacity5

5.2Basicrelationshipsofthreetrafficflowparameters6

6.Foundationandsolutionofmodel6

6.2Establishingandsolvingofthemodelforproblemtwo10

6.3EstablishmentandsolutiontothemodelofQuestion313

6.4EstablishmentandSolutionoftheModelfortheForthQuestion18

7.ModelTest19

8AdvantagesandDisadvantagesofthemodel19

9.Reference20

Appendix21

1.DescriptionoftheProblem

Thephenomenonoflaneoccupiedwillleadtolowerlaneorcrosssectiontrafficcapacity.Acity’strafficflowcouldhavelargeroaddensityandstrongcontinuity,whichwillreducetheroadcapacityevenifonlyonelaneisoccupied.Eventhoughthetimeisshort,itmayalsocauseaqueueofvehiclesevenatrafficjam.Andifhandledinappropriately,itwillleadtoemergentregionalcongestion.

Thevarietyoflaneoccupiediscomplicatedthough,itwillproperlyofferthetheorybasisforthetrafficmanagementifweareabletoestimatetheimpactoflaneoccupiedontheroadtrafficcapacityourcity.

Accordingtothedifferentsituationwhereoneortwolanesareblockedshowninthevideo1andvideo2,youneedtosolvethequestionsbelow.

1:

Describethechangingprocessoftheactualcapacityatthecross-sectionduringperiodfromtrafficaccidenthappenstotheend.

2:

Explainthedifferencewhenoneortwolaneisoccupiedbasedontheconclusiondrawnfromthequestion1andthevideo2.

3:

Constructamathematicalmodeltoanalyzetherelationshipamongvehiclequeuelength,lanetrafficcapacity,theongoingtimeoftheaccidentandtheupstreamtrafficflow.

4:

Trytoestimatethedurationfromthebeginningoftheaccidenttothemomentthequeuelinereachestheupstreamjunction.Assumingthatthedistancebetweenthetrafficaccidentsiteandthejunctionbecomes140meters,thedownstreamflowdemandisunchanged,roadtrafficupstreamflowis1500pcu/h,theinitialqueuelengthiszerowhenaccidenthappensandtheaccidentlastsforenoughlongtime.

2.Assumptions

ØTheeventthatvehiclesarrivedattheaccidentsiteisindependent.

ØThestandardcarequivalentnumberthroughtheupstreamcross-sectionalobeysthePoissonDistribution.

ØIgnoringtheinfluenceontheactualtrafficflowstatisticswhicharisesfromnon-standardvehicleontheroad;

ØThevehiclesreachintothesectionwheretheaccidenthappensataconstantspeed.

3.Definition

3.1Descriptionofsymbols

Theactualcapacityofroadsection

αi

Theproportionofthetrafficflowonlanei

Qi

Theupstreamtrafficlanei

Thesumofdownstreamtrafficflow

Speedofstandardcar

b

Lengthofstandardcar’sbody

Thetimethatthetrafficflowinlaneiallcrosstheaccidentroadsectionspent

Safedistanceforthevehicletraveling

d

Thetotalwidthofthethreelanecrosssection

L

Equivalentvehiclequeuelength

Q

Theaverageflow

K

Theaveragedensity

V

Averagevehiclespeed

3.2Definitionofterms

1.ThebasiccapacityW:

themaximumnumberofstandardvehicleswhichpassthroughcross-sectionallaneduringtheunittimeatthesituationwhereroad,trafficandenvironmentareideal.

2.ThesaturationcapacityQ:

themaximumnumberofstandardvehicleswhichpassthroughcross-sectionallaneduringtheunittimeatthesituationwhereroad,trafficandenvironmentareidealandtrafficflowiscontinuous.

3.Chainblock:

referringtothesituationwherethenextcyclicalvehiclesarrivebeforetheformervehiclesentirelypasstheaccidentsite.

4.PrimaryAnalysis

Thisproblemisacomprehensiveproblem,includingthechangesoftheactualcapacityatthecross-section,theinfluenceofdifferentlanesoccupied,thequeuelengthontheroadandtherelationshipamongthem.ItmayinvolvethePoissonDistribution,theComputerSimulationsandotherknowledge.

Firstly,weneedtoextractandprocessthedata.Afterresearchingthevideo1andvideo2,werecordtheactualnumberofvehiclesthroughtheaccidentsitebefore,duringandaftercartheaccident.Andthenweconvertitintothestandardvehicleequivalentnumber.

Question1istodescribethechangingprocessoftheactualtrafficcapacityintheaccidentcross-sectionduringthecaraccident.Thekeytosolvethequestionishowtodeterminethedynamicprocessofthevehicleflow.Afteranalysis,wefindthattheactualroadtrafficcapacitycanbevaluedbyreferringtothecorrelationaboutthetrafficflow,vehiclespeedandthetrafficdensity.Insuchway,wecandrawadiagramtovividlyillustratethedynamicchangingprocessoftheflow.

Question2isaproblemthataimsatcomparingthedifference.Firstly,weneedtodrawthegraphsrespectivelyabouttheflowdensityatthetwodifferentsituations.Andthenwecantellthesimilaritiesanddifferencesbetweenthetwocases.Secondly,Weneedtofindthereasoncausingthisphenomenon.Throughtheanalysis,weshoulddividetheblockageintotwostepsfromthemomentaccidenthappenstoevacuates,whicharechainblockageandpartialblockage.Duringthechainblockage,invideo1Woisaconstantvaluethesameinvideo2.However,it’scomplicatedinpartialblockage.Finally,webuildafunctionmodelusingthevehicleflowproportionalcoefficientasvariable.Obviouslywecanobtainthedifferentinfluenceonactualtrafficcapacityasaresultofdifferentoccupiedlanes.

Forthequestion4:

It’svitalforustobuildanexpressionabouttheequivalentqueuelengthandtime.Accordingtotheanalysisofquestion3,whatweneedisjustmakesomeappreciatechangesformodelofquestion3.Thenwecangettheanswerofquestion4.Forthemodifiedmodel,weanalyzethevalueofeachparameterandultimatelysolvetheequationbasedontheassumptionofthetitle.Thefinalsolutionistheunknownquantityt.Finally,wetestedtherationalityandvalidityofthemodelbycomparingtheactualrecordeddatawiththedataoftheoreticalanalysis.

5.Preparationsforthemodel

5.1Determiningthecrosssectionoftheactualtrafficcapacity

Consideringtheactualtrafficflow,theroadiscontrolledbythetrafficlightattheupstreamintersection.Ifvehiclesarereleasedbythefirstphasestoppedbythesecondphase,wecanseetheroad’strafficappearsascyclicaltrends.Besidesboththetimeoffirstandsecondphaseare30seconds,therefore30secondscanbetakenasatimeinterval.Throughtheanalysisofvideo1and2,werecordedevery30sof