2017年美赛O奖论文B题

ForofficeuseonlyT1________________T2________________T3________________T4________________TeamControlNumber69427ProblemChosenBForofficeuseonlyF1________________F2________________F3________________F4________________2017MCM/ICMSummarySheetOptimalDesignofTollPlazaBasedonMinimumRiskMaximumFlowThedesignofhighwaytollplazaiscrucialtothetrafficflowandtollboothsoperationefficiency.Westudytheoptimaldesignprogramoftollplazafromthreeaspects：accidentrate,trafficflowandconstructioncost.Atthesametime,wegivethedesignfiguresandmergingpatternoftollplaza.Thefirststage,wedeterminethenumberoftollboothsbyassumingthatthetrafficconditionisnormal.Thenumberoftolllanesisdecidedbytrafficcapacity,trafficflowandservicelevel.Weestablishafunctionmodeloftollboothsthroughtheabovethreeindexes.Whenthenumberoflanesis3,weknowthatthenumberofsingle-waytolllanesshouldbe7bycalculatingthetrafficdatafromthehighwaytollboothsof417highwayinFlorida.Wefindinthesensitivityanalysisthatthetrafficflowispositivelyrelatedtothenumberoftolllanes.Thesecondstage,theoptimalmodelofthemergingpatternbasedonminimumriskandmaximumthroughputisestablished.Thismodelisonaccountoftheanalysisoftheperformanceoftheexistingtollplazatooptimizeitsdesignprogram,andweregardthedecelerationshuntandaccelerationmergingofthewholetollplazaasadirectedandweightednetworkflow.Similarly,byusingthedataofthehighwaytollboothsof417roadinFlorida,weobtaintheprogramofmergingpattern(ShowninFig.5).Themaximumtrafficflowofthisprogramcanreach1375vehiclesperhour,theaccidentratecanbereducedto0.9%.Thethirdstage,takingintoaccountthevehicle'svariablemotioninthetollplaza,weemploythedrivingdistancebetweenthefrontandrearvehiclesandthebrakingdistanceoftherearvehicletodeterminethesizeofthetollplaza,andestablishaoptimizationmodeltominimizetheconstructioncost.Likewise,usingthedatafromthehighwaytollboothsof417roadinFlorida,weobtainthesmallesttollplaza(ShowninFig.6)whoseareaabout4650.1875squaremeters.Remarkably,wetestthemodelindetail.Thetrafficflowandtheaccidentratearelowerinlighttrafficflow.Whenthetrafficflowislarger,theaccidentrateisincreasedby0.05%comparedwiththeslighttrafficflow,thatis,thesizeoftrafficflowonthetollplazadesignisnotsignificant.Afterexaminingtheimpactofaddingautonomousvehiclesintomixedtraffic,weadd500autonomousvehiclesintothetrafficflowbasedonunittrafficflowonHighway95inNewJersey.Andtheaccidentratewasreducedby0.83%.Inviewoftheproportionofthethreetollbooths,thegreatertheproportionofautomatictollbooths,thesmallertheentiretollarea,thesmallerthenumberoftollbooths,thestrongerthecapacityofthetollbooths.Finally,weapplythemodeltostudytheoptimaldesignofthehighwaytollplazainNewJersey.WeselecttheNewJerseyHighwayNo.95astheresearchobject,andwegetitsshapeabouttollplazaandthefigureofmergepattern(SeeFig.12).Thenumberoftolllanesis10,andtheproportionsofthethreetollboothsis5:3:2,theareaofthetollplazais9614.562m.Lastbutnotleast,writingalettertotheNewJerseyTurnpikeAuthorityaboutthedesignscheme．Contents1Introduction.............................................................................................................................................11.1Background.......................................................................................................................................11.2PreviousResearch.............................................................................................................................11.3OurWork...........................................................................................................................................22AnalysisofOverallandKeyPoints........................................................................................................22.1OverallAnalysis................................................................................................................................22.2KeyPointsAnalysis..........................................................................................................................32.2.1AnalysisofTollboothNumber...............................................................................................32.2.2PerformanceAnalysisofTollPlaza........................................................................................32.2.3CostAnalysisofTollPlazaDesign........................................................................................33AssumptionsandJustification.................................................................................................................34SymbolsandDefinitions.........................................................................................................................45TheModel...............................................................................................................................................45.1ModelI:TheDeterminationoftheTollLaneNumberB..................................................................55.1.1ModelingIdeas.................................................................................................