2017年美赛O奖论文A题

ForofficeuseonlyT1T2T3T4TeamControlNumber68303ProblemChosenBForofficeuseonlyF1F2F3F42017MCM/ICMSummarySheetMergeBetterAfterTollSummaryWiththerapidincrementofthetrafficflow,theproblemofmergingafterthetollbarriershasrisenpublicconcern.Inourpaper,weaimtoconstructamodeltofindabetterdesignoftheareafollowingthetollbarrier.First,weclassifytheareafollowingthetollbarrierwhichmayalreadybeimple-mentedintoeightkindsaccordingtothedifferentshapes,sizes,andmergingpatternsoftheareabasedonthetollplazasinreality.Second,weuseVISSIMtodothesimulationofthetypicaleightmodelsoftheareafollowingthetollbarrier.Throughsettingthenecessaryobservationpoints,weobtainthedataofthroughput,lengthofqueuesandtheaveragetimeofdelayweneedinthefollowingevaluationmodel.Third,webuildacomprehensiveevaluationmodelbasedonPCAtoevaluatetheeighttypicalmodelsandtheoptimummodelwebuild.Consideringtheselectionoftheindex,wechoosethenumberofmergingpointstoindicateaccidentpreventionofthearea,thelengthofqueues,thethroughputandtheaveragetimeofdelaytoindicatethetrafficcapacityofthearea,andtheheightofthetrapezoidareatoindicatethecon-structioncostofthearea.Afterdatanormalization,wegetthebestmodelwhichisintheshapeofisoscelestrapezoidwithstipulatedmergingpatternandmediumsizeoftheareaamongtheeightexistingmodels.Fourth,inordertoobtainabettersolution,webuildtwomodelstoobtaintheopti-mumsolution.Thefirstoneisadifferentialequationmodelaimedatacquiretheopti-mumheightofthetrapezoidareaandtheoptimumnumberoftollbooths.Thesecondoneisalinearprogrammingmodelwhichcancalculatetheoptimummergingpatternwhilemaximizingthethroughputofthearea.Lastbutnotleast,weanalyzetheperformanceofourmodelundervariouscondi-tions,andmodifyourmodeltoaccommodatetothoseconditions.Also,weuseLingotoconstructsensitivityanalysisofthelinearprogrammingmodel.Tosumup,ourmodelisafeasibleandreasonablemodelwhichcanaccommodatetovarioussituations.Team#68303Page1of20Contents1Introduction21.1Background....................................21.2RestatementoftheProblem...........................21.3OverviewofOurWork..............................21.4GeneralAssumptions...............................32ClassifytheDesign33SimulationModel44EvaluationModel74.1Indexvariables..................................74.2PCAModel....................................84.3AnalysisandResult................................85FindtheOptimumSolution95.1Overview......................................95.2DifferentialEquationModel...........................95.3LinearProgrammingModel...........................125.4ResultandModelTesting............................136EffectsandAdjustment146.1LightandHeavyTraffic.............................146.2AddAutonomousVehicles............................146.3CompositionsofTollbooths...........................157SensitivityAnalysis167.1ReducedCost...................................167.2ChangeRangeofVariables............................168Conclusion178.1Strengths......................................178.2Weakness......................................18Team#68303Page2of201Introduction1.1BackgroundThemajorproblemsfacingmotoristsontoday’shighwaysarecongestion,accidents,andcosts-toomanyautomobilestravelingtothesameplaceatthesametime;toomanyautomobiles,trucks,buses,bicycles,andpedestriansattemptingtousethesamespace;toomanymotoristslosingtimeunnecessarily;toomanyaccidentsoccurring;andtoomanydecisionsbeingmadeonhighwayimprovementswithoutadequateanalyticaltools[1].Asanimportantpartofthehighway,thetollplazaistoblameformostofthecon-gestionsandaccidentshappenaroundit.Sincethereareusuallymoretollboothsthanthereareincominglanesoftraffic,vehiclesmustfaninfromlargernumberoftollboothegresslanestothesmallernumberofregulartravellanes.Inotherwords,vehiclesneedtomergeaftertoll.Trafficcongestionnormallyhappenswhenmergingpointsaremet[2],whichmayre-sultinlongtrafficqueuesontheroad.Whendesigningmergingareaofthetollplaza,shape,sizeandmergingpatternoftheareashouldbetakenintoconsideration.More-over,thedesignshouldreducetheriskofaccident,thecostofroadconstructionandincreasethethroughputasmuchaspossible.1.2RestatementoftheProblemWearerequirednotonlytoanalyzetheperformanceoftheareafollowingthetollbar-rierwithdifferentshapes,sizes,andmergingpatternsthatmayalreadybeimplementedontheaspectofaccidentprevention,throughput,andcost,butalsotodetermineiftherearebettersolutionsthananyincommonuseandevaluatetheperformanceofthemun-derdifferentcircumstances.Theproblemcanbeanalyzedintofourparts:Analyzetheexistingdesignoftheareafollowingthetollbarrierwithdifferentshapes,sizesandmergingpatterns.Buildasimulationmodeltosimulatethetrafficconditionofdifferentdesignsoftheareafollowingthetollbarrier.Buildanevaluationmodeltoratetheperformanceofdifferentdesignsoftheareafollowingthetollbarrier.Findasolutionwhichcanperformbetterthananyincommonuse.1.3OverviewofOurWorkWiththeincrementoftrafficflow,thetrafficcongestionhappensmoreandmorefre-quentlyonthehighway,asitgraduallybecomesthemaincauseoftrafficaccidents.Theproblemofmergingaftertollhasbecomethecommonconcernofthesociety.Team#68303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