2014年美国大学生数学建模MCM-A题-O奖论文31333.pdf

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1、Team#31333Page1of17RulesoftheRoadUsingadaptationsofNagel-SchreckenbergCellularAutomatonTrafficSimulationstoEvaluatePassingRulesforMulti-LaneFreewaysAbstractWepresentthreeconventionsforregulatingthebehaviorofautomobilesonafreewayaspotentialalternativestothe“keep-right-except-to-p

2、ass”rulethatiscurrentlyestablishedintheUnitedStatesandinmanyothernations.TheseconventionsaretestedagainsttheestablishedconventionwithinafreewaytrafficflowmodelwehavedesignedbasedonNagel-Schreckenbergmodelsoftrafficflow.Weassumecarsremainonthefreewayandalldriversattempttoadhereto

3、therulesoftheroad,butsometimesmakemistakesthatcanleadtoaccidents.Wealsoassumethatanintelligentsystemcontrollingtheactionsofallcarsontheroadwaywouldnotmakethosesamemistakes.Thefirstofthethreealternativesproposedpresentsdriverswithnorulesgoverningtheirlane-to-lanemovement,allowing

4、themtomovetoanylanethatwillletthemgofaster,andtostaythereforexactlysolongasthatremainsthecase.Thisconventionresultsinthehighestflowrateofcarsthroughthesystem,butalsoresultsinahigheraccidentrateforatypicalthree-lanefreewaythandoesthe“keep-right-except-to-pass”rule.However,whenthe

5、numberoflanesisincreased,theaccidentratedropssignificantly.Thesecondofthethreealternativesforbidsdriversfromchanginglanesatall,andresultsinthesecondhighestflowrateseen,betweenthenoruleand“keep-right-except-to-pass”systems,butresultsinahigheraccidentratethaneithersystemfortypical

6、three-lanehighways.Thethirdmodel,mandatingthatdriversremaininthecenterlaneofathree-laneoffive-lanefreeway,exhibitedthelowestflowrateandhighestaccidentrateofanyofthefourconventionsstudied.Unfortunately,themodelusedwasseentobeverysensitivetotherategoverningaccidentprobabilityandth

7、enumberoflanesinasimulation.Thewayaccidentsweremodeledmeantthatasingleaccidenttendedtopromotetheoccurrenceofmanymore.Additionallyasoftwarelimitationinthefunctionusedtogenerateaninitialmatrixwithuniquecarlocationsmeantthatitwasimpossibletocreatetruegridlockwithinthemodel.Basedont

8、hedatafromallofthemodelsandtheuncertaintyinthea