美赛论文翻译翻译.docx
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美赛论文翻译翻译.docx
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美赛论文翻译翻译
2009ContestProblems
MCMPROBLEMS
PROBLEMA:
DesigningaTrafficCircle
问题A:
设计一个道路的圆形交叉路口
Manycitiesandcommunitieshavetrafficcircles—fromlargeoneswithmanylanesinthecircle(suchasattheArcdeTriompheinParisandtheVictoryMonumentinBangkok)tosmalloneswithoneortwolanesinthecircle.Someofthesetrafficcirclespositionastopsignorayieldsignoneveryincomingroadthatgivesprioritytotrafficalreadyinthecircle;somepositionayieldsigninthecircleateachincomingroadtogiveprioritytoincomingtraffic;andsomepositionatrafficlightoneachincomingroad(withnorightturnallowedonaredlight).Otherdesignsmayalsobepossible.
很多城市和社区有一些道路的圆形交叉路口----大的有很多路口(例如巴黎的ArcdeTriomphe和Bangkok的VictoryMonument),小的有一两个路口。
一些圆形交叉路口在每个进口处设置停止或让路标识,使已经在环形交叉路口的车辆拥有优先权;有的在进口处只设置停止标识(在红灯时不允许右转)。
许多城市和社区有环形交叉口。
大的环形交叉口有许多小路,比如说巴黎的凯旋门和曼谷的胜利纪念碑。
小的环形交叉口只有一或者两条小道。
一些环形交叉口在每个来路上作为停止或让路标记,给在环形内的车辆以优先进入权。
一些在来路上只作为让路标记,给来往车辆以优先权。
一些在来路上作为交通灯的作用(红灯不能右转)也有一些其他的设计作用。
Thegoalofthisproblemistouseamodeltodeterminehowbesttocontroltrafficflowin,around,andoutofacircle.Stateclearlytheobjective(s)youuseinyourmodelformakingtheoptimalchoiceaswellasthefactorsthataffectthischoice.IncludeaTechnicalSummaryofnotmorethantwodouble-spacedpagesthatexplainstoaTrafficEngineerhowtouseyourmodeltohelpchoosetheappropriateflow-controlmethodforanyspecifictrafficcircle.Thatis,summarizetheconditionsunderwhicheachtypeoftraffic-controlmethodshouldbeused.Whentrafficlightsarerecommended,explainamethodfordetermininghowmanysecondseachlightshouldremaingreen(whichmayvaryaccordingtothetimeofdayandotherfactors).Illustratehowyourmodelworkswithspecificexamples.
这个题目的要求是用模型决定环形交叉口内外的交通流动。
清晰的说明你设计的模型中最理想的选择和影响这一选择的原因。
包括一份技术摘要。
用来向工程师解释如何使用你的模型来选择能适用于任何精确环形交叉口的交通流动的控制方案。
总结各种交通控制方案的条件。
当使用交通灯时,解释每个交通灯需要保持绿灯的秒数(由每天的时间和其他因素的变化而变化)阐述你的模型如何应用于特定的例子。
字数要求:
2页,双倍行距
AtopictodesignAtrafficcircle
Inmanycitiesandcommunitiesareestablishingtrafficcircle,boththemultiplelargeroundaboutdriveway(suchasthearcDEtriompheinParisandBangkok'svictorymonumentintersection),andthereareoneortwosmallcircleofthedriveway.Somearoundtheislandattheentranceisequippedwiththemark"stop"ortogiveway,itspurposeistoprovidethepriorityofdrivingvehiclestohaverolledaroundtheisland;Andinsomeoftheislandintothereversesideofthemouthistogivewaysigntoofferisrolledaroundtheisland'svehicledrivingpriority;Therearealsosomewillaroundtheislandattheentrancetosetupthetrafficlightsturnright(theredlightwillbeabanonvehicle);Mayalsohaveotherdesign.
Thepurposeofthisdesignistouseamodeltodeterminehowtooptimallycontrolinsidetheisland,aswellastheexternaltrafficflowaroundthem.Thepurposeofthisdesignistousemodelstomakethebestschemeselectionandanalysisofmanyfactorsaffectingchoice.Solutionneedstobeincludedinanomorethantwopages,double-spacedtypedtechnologyinthispaper,itcanguidethetrafficengineersuseyourmodelforanyspecialislandproperflowcontrol.Themodelcanbesummedupinwhatcircumstancesusewhichkindoftrafficcontrolmethodfortheoptimal.Whenconsideringusingtrafficlightwhenagreenlight,arelongcontrolmethod(accordingtothespecifictimeandotherfactorstocoordinatedaily).Lookingforsomespecialcases,toshowthepracticabilityofyourmodel.
Summary
Ourgoalisamodelthatcanaccountforthedynamicsofvehiclesina
trafficcircle.Wemainlyfocusontherateofentryintothecircletodetermine
thebestwaytoregulatetraffic.Weassumethatvehiclescirculateinasingle
laneandthatonlyincomingtrafficcanberegulated(thatis,incomingtraffic
neverhastheright-of-way).
Forourmodel,theadjustableparametersaretherateofentryintothe
queue,therateofentryintothecirde(servicerate),themaximumcapacity
ofthecircle,andtherateofdeparturefromthecircle(departurerate).We
useacompartmentmodelwiththequeueandthetrafficcircleascompartments.Vehiclesfirstenterthequeuefromtheoutsideworld,thenenterthe
trafficcirclefromthequeue,andlastlyexitthetrafficcircletotheoutside
world.Wemodelboththeservicerateandthedeparturerateasdependent
onthenumberofvehiclesinsidethetrafficcircle.
Inaddition,weruncomputersimulationstohaveavisualrepresentation
ofwhathappensinatrafficcircleduringdifferentsituations.Theseallow
ustoexaminedifferentcases,suchasunequaltrafficflowcomingfrom
thedifferentqueuesorsomeintersectionshavingahigherprobabilityof
beingavehicledestinationthanothers.Thesimulationalsoimplements
severallife-likeeffects,suchashowvehiclesaccelerateonanemptyroad
butdeceleratewhenanothervehicleisinfrontofthem.
Inmanycases,wefindthatahighservicerateistheoptimalwayto
maintaintrafficflow,signifyingthatayieldsignforincomingtrafficis
mosteffective.However,whenthecirclebecomesmoreheavilytrafficked,
TneUMAPJournal3O(3)(2009)247-260.@)Copyright2009byCOMAP,Inc.Allrightsreserved.
Permissiontomakedigitalorhardcopiesofpartorallofthisworkforpersonalordassroomuse
isgrantedwithoutfeeprovidedthatcopiesarenotmadeordistributedforprofitorcommercial
advantageandthatcopiesbearthisnotice.Abstractingwithcreditispermitted,butcopyrights
forcomponentsofthisworkownedbyothersthanCOMAPmustbehonored.Tocopyotherwise,
torepublish,topostonservers,ortoredistributetolistsrequirespriorpermissionfromCOMAP.
248TheUMAPJournal30.3(2009)
Figure1.Asimpletrafficcircle.Trafficcirclesmayhavemorethanonelaneandmayhavea
differentnumberofintersections.
alowerserviceratebetteraccommodatestraffic,indicatingthatatraffic
lightshouldbeused.Thus,alightshouldbeinstalledinmostcircleimplementations,withvariabletimingdependingontheexpectedamountof
traffic.
Themainadvantageofourapproachisthatthemodelissimpleand
allowsustoseeclearlythedynamicsofthesystem.Also,thecomputer
simulationsprovidemorein-depthiniformationabouttrafficflowunder
conditionsthatthemodelcouldnoteasilyshow,aswellasenablingvisual
observationofthetraffic.Somedisadvantagestoourapproacharethatwe
donotanalyzetheeffectsofmultiplelanesnorstoplightstocontrolthe
flowoftrafficwithinthecircle.Inaddition,wehavenowayofanalyzing
singularsituations,suchasvehiclesthatdrivefasterorslowerthantherest
ofthetrafficcircle,orpedestrians.
Introduction
Trafficcircles,oftencalledrotaries,areusedtocontrolvehicleflow
throughanintersection.Dependingonthegoal,atrafficcirclemaytake
differentforms;Figure1showsasimplemodel.Acirclecanhaveoneor
morelanes;vehiclesthatenteratrafficcirclecanbemetbyastopsign,a
trafficlight,orayieldsign;acirclecanhavealargeorsmallradius;acircle
canconfrontroadscontainingdifferentamountsoftraffic.Thesefeatures
affectthecostofthecircletobuild,thecongestionthatavehicleconfronts
asitcircles,thetraveltimeofavehicleinthecircle,andthesizeofthequeue
ofvehicleswaitingtoenter.Eachofthesevariablescouldbeametricfor
evaluatingtheefficacyatrafficcircle.
Ourgoalistodeterminehowbesttocontroltrafficentering,exiting,
andtraversingatrafficcircle.Wetakeasgiventhetrafficcirclecapacity,the
OneRingtoRuleThemAll249
arrivalanddepartureratesateachoftheroads,andtheinitialnumberof
vehidclescirculatingintherotary.Ourmetricisthequeuelength,orbuildup,at
eachoftheenteringroads.Wetrytominimizethequeuelengthbyallowingthe
rateofentryfromthequeueintothecircletovary.Foravehicletotraverse
therotaryefficiently,itstimespentinthequeueshouldbeminimized.
Wemakethefollowingassumptions:
"*Weassumeacertaintimeofday,sothattheparametersareconstant.
"*Thereisasinglelaneofcirculatingtraffic(allmovinginthesamedirection).
"*Nothingimpedestheexitoftrafficfromtherotary.
"*Therearenosingularities,suchaspedestrianstryingtocross.
"*Thecirculatingspeedisconstant(i.e.,avehicledoesnotaccelerateor
deceleratetoenterorexittherotary).
"*Anytrafficlightinplaceregulatesonlytrafficcomingintothecircle.
TheModels
ASimplifiedModel
Wemodelthesystemasbeingcontinuous;ourapproachcanbethought
ofasmodelingthevehiclemassdynamicsofatrafficcircle.Thesimplest
modelassumesthattherateofarrivaltothebackoftheenteringqueueand
therateofdeparturefromthequeueintothetrafficcircleareindependent
oftime.Thus,therateofchangeinthelengthofthequeueis
dQ-ai--si,(1
dt
whereQjisthenumberofcarsinthequeuecominginfromtheithroad,
aiistherateofarrivalofvehiclesintotheithqueue,ands,istherateof
removal,alsocalledtheservicerate,fromtheithqueueintothetrafficcircle.
Weintroducetheparameterdi,therateatwhichvehiclesexitthetraffic
circle.WeletCbethenumberofvehiclestravelinginthecircle.Then
wemodelthechangeintrafficintherotarybythedifferencebetweenthe
influxandoutfluxofvehicles,wheretheoutfluxofvehiclesdependsonthe
amountoftrafficintherotary:
d=CE_Cdi.
(2)C-Ft•'•
250TheUMAPJournal30.3(2009)
AnIntermediateModel
Themodelabovesimplifiesthedynamicsofatrafficcircle.Themostglaringsimplificationsarethatthereisnowaytoindicatet
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