美国数学建模竞赛赛题(MCMICM)

《美国数学建模竞赛赛题(MCMICM)》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、美国数学建模竞赛赛题(MCM/ICM)2018ContestProblemsMCMPROBLEMSPROBLEMA:DesigningaTrafficCircleManycitiesandcommunitieshavetrafficcircles—fromlargeoneswithmanylanesinthecircle(suchasattheArcdeTriompheinParisandtheVictoryMonumentinBangkok)tosmalloneswithoneortwolanesinthecircle.Someofthes

2、etrafficcirclespositionastopsignorayieldsignoneveryincomingroadthatgivesprioritytotrafficalreadyinthecircle;somepositionayieldsigninthecircleateachincomingroadtogiveprioritytoincomingtraffic;andsomepositionatrafficlightoneachincomingroad(withnorightturnallowedonaredlight).O

3、therdesignsmayalsobepossible.Thegoalofthisproblemistouseamodeltodeterminehowbesttocontroltrafficflowin,around,andoutofacircle.Stateclearlytheobjective(s)youuseinyourmodelformakingtheoptimalchoiceaswellasthefactorsthataffectthischoice.IncludeaTechnicalSummaryofnotmorethantwo

4、double-spacedpagesthatexplainstoaTrafficEngineerhowtouseyourmodeltohelpchoosetheappropriateflow-controlmethodforanyspecifictrafficcircle.Thatis,summarizetheconditionsunderwhicheachtypeoftraffic-controlmethodshouldbeused.Whentrafficlightsarerecommended,explainamethodfordeter

5、mininghowmanysecondseachlightshouldremaingreen(whichmayvaryaccordingtothetimeofdayandotherfactors).Illustratehowyourmodelworkswithspecificexamples.PROBLEMB:EnergyandtheCellPhoneThisquestioninvolvesthe“energy”consequencesofthecellphonerevolution.Cellphoneusageismushrooming,a

6、ndmanypeopleareusingcellphonesandgivinguptheirlandlinetelephones.Whatistheconsequenceofthisintermsofelectricityuse?Everycellphonecomeswithabatteryandarecharger.Requirement1ConsiderthecurrentUS,acountryofabout300millionpeople.EstimatefromavailabledatathenumberHofhouseholds,w

7、ithmmemberseach,thatinthepastwereservicedbylandlines.Now,supposethatallthelandlinesarereplacedbycellphones;thatis,eachofthemmembersofthehouseholdhasacellphone.ModeltheconsequencesofthischangeforelectricityutilizationinthecurrentUS,bothduringthetransitionandduringthesteadyst

8、ate.Theanalysisshouldtakeintoaccounttheneedforchargingthebatteriesofthecellphones,