2014美赛A题 北师O奖

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1、Team#30532Page1of29TeamControlNumberForofficeuseonlyForofficeuseonlyT1________________30532F1________________T2________________F2________________T3________________F3________________ProblemChosenT4________________F4________________A2014MathematicalContestinModeling(MCM)SummarySheet

2、WebuildasimulationandstatisticalmodeltoanalyzetheperformanceofKeep-Right-Except-To-Passruleinlightandheavytraffic.WeextendthefamousCellularAutomatonsingle-laneTrafficflowsimulationmodel(NaSchmodel)tomulti-lanemodelusingournewlane-changingrules.Thefactoranalyzemethodisemployedbyust

3、ostudythetradeoffsbetweentrafficflow,safety,maxvelocitylimitsandothermetrics.BesidestheKeep-Right-Except-To-Passrulementionedintheproblem,wealsoproposetwootherrules:Keep-Right-Or-LeftruleandHigh-Velocity-Left-Low-Velocity-Right-Except-To-Passrule.Adeepcomparebetweenthethreerulesha

4、sbedone.Theresultshowsthatwhentrafficdensity,theprobabilityoflane-changingandthevelocitylimitsarelow,Keep-Right-Or-Leftruleisabletopromotetrafficflowandsafety.Ingeneral,Keep-Right-Or-Leftruleperformsthebest,whileHigh-Velocity-Left-Low-Velocity-Right-Except-To-Passruleperformsthewo

5、rst.Incountrieswheredrivingautomobilesontheleftisnorm,ourKeep-Right-Except-To-Passmodelisalsosuitablewithasimplechangeoforientation.Consideringtheothertwomodelssetnolimitonthelaneinwhichvehiclesdrive,themodelcanbeappliedwithoutmodificationtothosecountriesdrivingtotheleft.Last,ifth

6、ewholetrafficiscontrolledbyanintelligentsystem,wewillsimulatetherandombehaviorsofthemodelparameterstooptimalparametersunderidealcircumstancesandalsoanalyzetheeffectstothethreerules.Underthecontrolofanintelligentsystem,thesafetyofthreerulesisalmostthesame.AndtheruleofKeep-Right-Exc

7、ept-To-PasspromotesthetrafficflowtheleastwhiletherangeofdifferenceisthegreatestandtheothertworulespromotethetrafficflowtoasimilardegreethatisgreaterthanthatpromotedbytheKeep-Right-Except-To-Passrule.Team#30532Page2of29SimulatingandScoringthePerformanceofTrafficDrivingRulesSimulati

8、ngandScoringthePerformanceofTraff