国赛A题全国一等奖论文英文版文档格式.docx
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国赛A题全国一等奖论文英文版文档格式.docx
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wecanintroducetheconceptoftheequivalentqueuelengthtodealwiththereallinelengthwhichmaybequitecomplicated.AndthenweclassifyallthevehiclerunningstatesintotwoequivalentlybasedontheTwoFluidTheory.Thisprocessingmethodhelpsusachievetheexpressionoftheequivalentqueuelength.Herewelisttheexpression
.Atlastweexamineourmodelbythemeansofthecomputersimulationandtheinspectionresultsareshownasbelow:
time
16:
48:
00
49:
50:
51:
52:
53:
54:
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
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
Ø
Theeventthatvehiclesarrivedattheaccidentsiteisindependent.
Thestandardcarequivalentnumberthroughtheupstreamcross-sectionalobeysthePoissonDistribution.
Ignoringtheinfluenceontheactualtrafficflowstatisticswhicharisesfromnon-standardvehicleontheroad;
Thevehiclesreachintothesectionwheretheaccidenthappensataconstantspeed.
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.
It’svitalforustobuildanexpressionabouttheequivalentqueuelengthandtime.Accordingtotheanalysisofquestion3,whatweneedisjustmakesomeappreciatechangesformodelofquestion3.Thenwecangettheanswerofquestion4.Forthemodifiedmodel,weanalyzethevalueofeachparameterandultimatelysolvetheequationbasedontheassumptionofthetitle.Thefinalsolutionistheunknownquantityt.Finally,wetestedtherationalityandvalidityofthemodelbycomparingtheactualrecordeddatawiththedataoftheoreticalanalysis.
5.Preparationsforthemodel
5.1Determiningthecrosssectionoftheactualtrafficcapacity
Consideringtheactualtrafficflow,theroadiscontrolledbythetrafficlightattheupstreamintersection.Ifvehiclesarereleasedbythefirstphasestoppedbythesecondphase,wecanseetheroad’strafficappearsascyclicaltrends.Besidesboththetimeoffirstandsecondphaseare30seconds,therefore30secondscanbetakenasatimeinterval.Throughtheanalysisofvideo1and2,werecordedevery30sof
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