2017美赛B题优秀论文

Thenumberoftollboothsisalwaysmorethanthenumberoflanesonthehighway.Afterpassingtollbooths,vehiclesenterlanesthroughamergingarea.Theshape,sizeandmergingpatternofthemergingareacanaffectitscapacityofaccidentprevention,throughputandcost.Afteraperformanceanalysisofamergingareafollowingthetollbarrier,asolutionisputforward.Thesolutionconsiderscapacityofaccidentprevention,throughputandcost.Thentheoptimaldesigningofmergingareaisobtained.Furthermore,theperformancesofsolutionsinthesituationofdifferenttrafficflowareevaluated.Asmoreautonomous(self-driving)vehiclesareaddedtothetrafficmix,thesolutionwillbeinfluenced.Firstly,theperformancesofmergingareasisanalyzedbythecapacityofaccidentprevention,throughoutandcost.Theresultindicatesthatthecapacityofaccidentpreventionisinverselyassociatedwithgradientofmergingarea;thecostofconstructionisdirectlyproportionaltotheareaoftollplazas;throughputdeterminesthemergingpatternoftollplazafollowingthetollbarrier.Secondly,inordertodeterminetheshape,sizeandmergingpatternofthemergingarea,amulti-objectiveoptimalmodelisproposedbasedondualobjectivefunction,wherethedecisionvariableisthelengthoftollplazafollowingthetollbarrier,theobjectivefunctionsareconstructioncostandthecapacityofaccidentprevention.Then,themodelissimplifiedtoaSingle-objectiveoptimalmodel.Inthisway,thelengthoftollplazafollowingthetollbarrier,thelengthofothersidesandallanglescanbeobtainedwithvaryingnumberoflanes.Andthethroughputcanbecalculatedunderdifferentmergingpattern.Thirdly,theperformanceofoursolutioninlightandheavytrafficisanalyzedandverified.Asmoreautonomous(self-driving)vehiclesareaddedtothetrafficmix,somehuman-staffedtollboothswillbereplacedbyelectronictollcollectionbooths.Underthecircumstances,thethroughputwillincreasewiththetrafficflowincreasing,thoughthetrafficefficiencywilldecrease.Taking4-tollboothinto2-laneasanexample,thetrafficefficiencyoftollmodewith2electronictollcollectionboothsand2human-staffedtollboothsdecrease2.44%.Fourthly,thethroughputwillalsoincreaseastheproportionsofhuman-staffedtollbooths,automatedtollboothsandelectronictollcollectionboothschange.ThespecificvaryingcircumstanceislistedinPage13.Finally,weofferthenon-technicalsuggestiontoNewJerseyTurnpikeAuthorityforreference.2017MCM/ICMSummarySheetENJOYAHAPPYJOURNEYSummaryForofficeuseonlyT1________________T2________________T3________________T4________________TeamControlNumber63650ProblemChosenBForofficeuseonlyF1________________F2________________F3________________F4________________Contents1Introduction21.1Background...................................21.2RestatementoftheProblem..........................32AssumptionsandNotations32.1GeneralAssumptions..............................32.2Notations.....................................43ModelOne43.1EstablishingtheModel.............................43.1.1EvaluationModel............................43.1.2OptimizationModel..........................73.2CalculatingtheModel.............................73.2.1OptimizationModel..........................73.3OurOptimizationScheme...........................94ModelTwo104.1EstablishingtheModel.............................104.1.1PerformanceAnalysisModelofLightandHeavyFlow......104.1.2TheImpactofTollboothsProportionsontheSolution.......104.2CalculatingtheModel.............................114.2.1TheImpactofTollboothsProportionsontheSolution.......115SensitivityAnalysis146EvaluationoftheModel147StrengthsandWeaknesses147.1Strengths.....................................157.2Weaknesses...................................158Conclusions15Team#63650Page2of161Introduction1.1BackgroundWiththerapiddevelopmentofthenationaleconomy,thehighwaytransportationin-dustryofAmericahasmadeconsiderableprogress.Asthemostbasictransportationfacilities,highwayhasbecomeanimportantpillarofnationaleconomicdevelopment.Highwaytollstationisasignificantservicefacilitiesonthehighway,whoseserviceleveldirectlyaffectsthehighwaycapacity.Thedesignofhighwaytollstation,asavitalpartofthehighwaytrafficmanage-mentservicefacilities,obtainsmoreandmoreattentionfromtheconstructionsector.Obviously,withthecontinuousprogressofthesocialeconomy,thehighwaytrafficflowisgrowing.Itisobservedthatsomesectionsoftheactualtrafficflowgrowthrateisfargreaterthanpredicted.Thecapacityoffreewaytollstationsareoftennotsosatisfyingandthetrafficcapacityoftheexpressway,resultingintrafficcongestion,oftenoccursinthetollstation.HighwaytollstationhasbecomeakeyimpactaspectsoftheExpresswaylogisticscirculation,thetraveltimeofvehiclesandthetrafficcost.Figure1:ATollHighwayInrecentyears,withtherapiddevelopmentoftheeconomy,highwaytrafficflowincreasesrapidly,whichbringshighwaytollstationservicegreatpressure.Somemoderntollfacilitiesrequireallpaymenttobemadebyelectronictranspon-der,sothatvehiclesdonothavetoslowdowninordertopaythetoll.Butonmanyoldertollwaysmovingtoall-electronicpaymentisnotanoption,whilemountingcon-gestionmeansthatplannersarefacedwiththeproblemofconfiguringtheirexistinginfrastructuretoprovidethebestpossibleservice.Therefore,itisaneffectivewaytoimprovetheleveloftrafficca