数学建模历届赛题

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1、2009年美国数学建模竞赛赛题(MCM/ICM)2009ContestProblemsMCMPROBLEMSPROBLEMA:DesigningaTrafficCircleManycitiesandcommunitieshavetrafficcircles—fromlargeoneswithmanylanesinthecircle(suchasattheArcdeTriompheinParisandtheVictoryMonumentinBangkok)tosmalloneswithoneortwolanesinthecircle.Someofthesetrafficcirclesposi

2、tionastopsignorayieldsignoneveryincomingroadthatgivesprioritytotrafficalreadyinthecircle;somepositionayieldsigninthecircleateachincomingroadtogiveprioritytoincomingtraffic;andsomepositionatrafficlightoneachincomingroad(withnorightturnallowedonaredlight).Otherdesignsmayalsobepossible.Thegoalofthisp

3、roblemistouseamodeltodeterminehowbesttocontroltrafficflowin,around,andoutofacircle.Stateclearlytheobjective(s)youuseinyourmodelformakingtheoptimalchoiceaswellasthefactorsthataffectthischoice.IncludeaTechnicalSummaryofnotmorethantwodouble-spacedpagesthatexplainstoaTrafficEngineerhowtouseyourmodelto

4、helpchoosetheappropriateflow-controlmethodforanyspecifictrafficcircle.Thatis,summarizetheconditionsunderwhicheachtypeoftraffic-controlmethodshouldbeused.Whentrafficlightsarerecommended,explainamethodfordetermininghowmanysecondseachlightshouldremaingreen(whichmayvaryaccordingtothetimeofdayandotherf

5、actors).Illustratehowyourmodelworkswithspecificexamples.PROBLEMB:EnergyandtheCellPhoneThisquestioninvolvesthe“energy”consequencesofthecellphonerevolution.Cellphoneusageismushrooming,andmanypeopleareusingcellphonesandgivinguptheirlandlinetelephones.Whatistheconsequenceofthisintermsofelectricityuse?

6、Everycellphonecomeswithabatteryandarecharger.Requirement1ConsiderthecurrentUS,acountryofabout300millionpeople.EstimatefromavailabledatathenumberHofhouseholds,withmmemberseach,thatinthepastwereservicedbylandlines.Now,supposethatallthelandlinesarereplacedbycellphones;thatis,eachofthemmembersofthehou

7、seholdhasacellphone.ModeltheconsequencesofthischangeforelectricityutilizationinthecurrentUS,bothduringthetransitionandduringthesteadystate.Theanalysisshouldtakeintoaccounttheneedforchargingthebatteriesofthecellph