2017美赛B题O奖论文56731中英对照版

2017MCM/ICMSummarySheet(Yourteam'ssummaryshouldbeincludedasthefirstpageofyourelectronicsubmission.)Typeasummaryofyourresultsonthispage.Donotincludethenameofyourschool,advisor,orteammembersonthispage.ANewTypeofTollPlazaBasedonBionics-HoneycombSummaryInthispaper,weanalyzetheperformanceofcommonlyusedtollplazabasedonourproposedmathematicalmodel.Anewimprovedtollplazaisproposedtoreducethecost,decreasetheprobabilityofcollisionatthemergingpointandincreasethethroughput.Thedistributionofourproposedtollboothsresemblesthehoneycomb.Atthecenterofeachregularhexagonalhoneycomb,therearetwotollbooths,whichservetwoseparatedvehiclestreams.Thevehiclesinthesetwoseparatedstreamsaremergedinadvancebeforetheycontinuetheirjourneyonthehighway.Duetothespecificpatternofthenewtollplaza,thetotalareacanbereducedsignificantly.Meanwhile,theaveragewastedtimecausedbyqueuingcanbediminished,whichmeansthatthethroughputwillberaised.Additionally,bysplittingthemergingprocedureintotwostages,thepossibilityofaccidentscanalsobedecreased.Themaincontributionsofthispaperareasfollows:(1)Thenewdesignedcellulararchitecturecangreatlyreducetheconstructionareacomparedwithtraditionallineardistributedtollgates.(2)Weanalyzethethroughputoftollplazasbymeansofthequeuingtheory.Toverifyourtheory,wesimulatethebehaviorofthelargenumberofvehiclespassingthetollplazawiththehelpofPTV-VISSIM.Simulationresultsshowthattheidealcellulardistributedtollboothshavebetterresultscomparedwithtraditionaltollstations,especiallywhenthetrafficflowisheavy,theaveragetraveltimereducedbyabout55%andtheaveragedelaytimeofeachlaneisreducedbyabout70%.(3)Weanalyzetheinfluenceoftheproportionsofdifferenttypesoftollboothstoourdesign.Accordingtorelevantdocuments,theimpactofexact-changetollboothsissimilartomanualtollbooths,soweonlyconsidertwokindsoftollbooths:human-staffedtollboothsandE-ZPasstollbooths.PTV-VISSIMsimulationresultsshowthatfullETCtollboothis8timesfasterthanfullMTCtollbooth.(4)Wesimulatetheperformanceofthecellulartollplazaunderdifferenttrafficthroughput.Simulationresultsshowthattheaveragetransittimeremainsatabout11secondsunderdifferentthroughputsfrom0to2000(Unit:veh/h).Wecaninferthatthismodelisnotsensitivetotrafficflowvariationsandhasstrongrobustnesswhichissuitableforpracticalconstruction.(5)Tofurtherreducethepossibilityofaccident,weimprovethecellulartollboothconceptmodel:makethetransitionzonemoresmoothandarrangedifferentkindsoftollboothsmoreequitable.(6)Forself-drivingvehicles,inthecenterofthetollplaza,wereservespecialE-ZPasstollbooths,whichmatchthecharacteristicsofautonomousvehicles:saferandfaster.Electronictollcollectionandautonomousvehiclesarethetrendsofmoderntransportation,ournewdesignedmodelcanimprovetheperformanceoftollplazaintheaspectsofcost,throughputandaccidentprevention.ForofficeuseonlyTeamControlNumber56731ProblemChosenBForofficeuseonly一种基于仿生蜂窝的新型收费广场概要在本文中，我们基于我们提出的数学模型分析了常用收费广场的表现。提出了一种新的改进的收费广场，以降低成本，降低在合并点的碰撞概率，提高吞吐量。我们建议的收费站的分布类似于蜂窝。在每个正六边形蜂窝的中心，有两个收费站，为两个分离的车流提供服务。这两条分开的河流中的车辆在高速公路上继续前行之前被合并。由于新收费广场的具体模式，总面积可以大大减少。同时，排队造成的平均浪费时间可以减少，这意味着吞吐量将会提高。另外，通过将合并过程分成两个阶段，也可以减少事故的可能性。本文的主要贡献如下：（1）与传统的线性分布式收费站相比，新设计的蜂窝式架构可以大大减少建筑面积。（2）通过排队论分析收费广场的吞吐量。为了验证我们的理论，我们在PTV-VISSIM的帮助下模拟了通过收费广场的大量车辆的行为。仿真结果表明，理想的蜂窝分布式收费站比传统收费站效果更好，特别是在交通流量大的情况下，平均出行时间减少了约55％，平均每个车道延误时间减少了约70％。（3）分析不同类型收费站的比例对我们设计的影响。根据有关文件，精确改造收费站的影响与手动收费站类似，所以我们只考虑两种收费站：人力收费站和E-ZPass收费站。PTV-VISSIM仿真结果显示，完整的ETC收费站比完整的MTC收费站快8倍。（4）模拟不同业务吞吐量下蜂窝收费广场的性能。仿真结果表明，在0〜2000的不同吞吐量下，平均通过时间约为11秒（单位：veh/h）。我们可以推断出这个模型对交通流量变化不敏感，具有很强的鲁棒性，适用于实际建设。（5）为进一步降低事故发生的可能性，我们改进了蜂窝收费站的概念模型：使过渡区更加顺畅，并使不同种类的收费站更加平等。（6）对于自驾车辆，在收费广场中央，我们预留了符合自动驾驶汽车特点的特殊E-ZPass收费车：更安全，更快捷。电子收费系统和自动驾驶汽车是现代交通运输的趋势，新设计的模式可以提高收费广场在成本，吞吐量和事故预防方面的性能。Team#56731Page2of22I.Introduction1.1ProblemBackgroundWiththenumberofvehiclesincreasing,expresswayisconfrontedwithgreattrafficpressure,especiallyatthetollplaza.Thecongestionproblematthetollstationbecomesmoreandmoreseriousduetotheoutdateddesign.Relatedresearchfoundthat36%ofthetotaltraveltimeinChinaisdelaytimecausedbytolling[1].Inaddition,asavehicle-intensiveplace,tollplazahasbecomeanaccident-pronesectionbecauseofthedrivers'improperoperation[2].WiththewidespreaduseofElectronicTollCollection(ETC)andE-ZPass,theefficiencyoftollcollectionhasbeenimprovedsignificantlyandfurtherthecongestionatthetollplazaisreleased.However,duetothehighspeedofthevehiclespassingthroughthetollplaza,theprobabilityofcollisioninthemergingzoneisincreased.Moreover,theconstructionoffuturetollplazaisveryexpensive.Consideringabovefactors,itisnecessarytodesignnewtollplazatoimproveitsthroughput,reducethecostofconstructionanddecreasethepossibilityofcollisioninthemergingzone.Inthispaper,wedesignatollstationmodelbasedonbionics-honeycombasshowninFigure1.1.Thehexagonaltilingcreatesapartitionwithequal-sizedcells,whileminimizingthetotalperimeterofthecells.Knowningeometryasthehoneycombconjecture,thiswasgivenbyJanBrożekandprovedmuchlaterbyThomasHales[3].CellularStructureiswidelyusedinmanyaspectsoflife.Forexample,thebasestationsofmobilecommunicationsaredistributedlikethehoneycomb.Inourn