美赛A题论文Word文件下载.docx

美赛A题论文Word文件下载.docx

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T3

T4

TeamControlNumber

27400

ProblemChosen

A

F1

F2

F3

F4

2014MathematicalContestinModeling（MCM）SummarySheet

（Attachacopyofthispagetoyoursolutionpaper.）

Typeasummaryofyourresultsonthispage.Donotinclude

thenameofyourschool,advisor,orteammembersonthispage.

Summary

TheaimofthispaperistoevaluatetheperformanceofthechanginglanerulenamedKeep-Right-Except-To-Passandcompareotherruleswe’veconstructedwiththegivenone.

Theperformanceofchanginglanerulesmainlymanifestinsafetyandtrafficflow.Meanwhile,safetyisinfluencedbypostedspeedlimitsandtrafficdensityandtrafficflowisinfluencedbyaveragespeed.

FirstweconstructModel1todescribetherelationshipbetweenpostedspeedlimits,trafficdensityandsafety,notingthatsafetyhasnegativecorrelationwithcollisiontimesandcanbefullyexpressedbyit.ThereforeweuseMatlabtoimitatethechanginglaneandcollisionprocess.ThenweconstructModel2todescribetherelationshipbetweentrafficflowandaveragespeed.CombiningtheresultofModel1and2,wecanconcludethatthehigherthepostedspeedlimitsandthelowerthetrafficdensity,thehigherlevelsafetyantrafficflowcouldreach,andtheKeep-To-Right-Except-To-Passrulehasthebestperformance.

ThenweconstructModel3tocomparesomenormalchanginglaneruleswiththegivenoneandwitheachother.Thusweimitatealltherulesusingalgorithmgivenbymodel1.WeintroduceanewconceptnamedStandardTimetoexpresstrafficflowandstillcollisiontimestoexpresssafety.Theresultisthatwhenafreewayroadcontains2lanes,thegivenruleshowsthebestperformance.Andwhenthenumberoflanesbecomes3,thentheChoose-Speedrule,averycommontrafficruleactsthebest.

Asfortheleft-drivingcountries,wefirstchoosethebestrulesandmirrorsymmetricallymodifythem.ThenusethemethodofModel2toimitateperformancesoftheserules.Wehaveobservedthatthesetwobestrulescanbesimplycarriedover.

Finally,wehaveashortdiscussionabouttheintelligentsystem.Sincespeedcanbefastestandchanginglanescanbewellplanned,weregardthissystemasabsolutelysafetrafficwhichhasthelargesttrafficflow.

1.Introduction

1.1Analysistotheproblem

Thisproblemcanbedividedinto4requirementsthatwemustmeet,listedasfollows:

（1）BuildamathematicalmodeltodemonstratetheessenceofKeep-Right-Except-To-Passruleinlightandheavytraffic;

（2）Showtheeffectsofotherreasonablechanging-lanerulesorconditionsbyusingthemodifiedmodelbuiltintheformerrequirement;

（3）Determinewhethertheleft-side-drivingcountriescanusethesamerule（s）withsimplemirrorsymmetricmodification,ormustaddsomerequirementstoguaranteethesafetyortrafficflow;

（4）Constructanintelligenttrafficsystemwhichdoesnotdependonhumans’compliance,andthencomparetheeffectswithearlieranalysis.

Therefore,thisproblemrequiresustoevaluatetheperformancesofseveralchanging-lanerules,especiallytheKeep-Right-Except-To-Passrulewhileperformancesmainlymanifestintrafficflowandsafety.Itisobviousthatspeedlimitandthenumberofcarsinfluentcars’speedandthentheperformancesofthoserules.

Tosolverequirement

（2）,wewillusethesamemethodasabove.Butallrulesweconstructedshouldbediscussed,imitatedandcomparewitheachother.

Todiscusstheleft-drivingcountries,wewillconcludethebestrulesfromrequirement2andapplytothosecountries.Thencompareresultswiththatofright-drivingcountries.Iftheresultsaretotallythesame,thenthoserulescanbesimplycarriedoverwithsimplechange.Ifnot,additionalrequirementareneeded.

Asfortheintelligentsystem,weassumenocollisionwillhappen.Soasimplediscussionisfeasible.

1.2Crucialmethodfortheproblem

Toimitatetheprocessofchanginglanesandcollision,wewillconstructanalgorithmnamedChanging-lineandCollision.Thiswillshowthestateofanumberofcaronthesamestretchoffreewayroad,includinggoingstraight,changinglanetopassandtrafficcollision.TheimitationprocesswillbedeliveredonMatlab;

2.Symbolsanddefinition

Symbol

Definition

Unit

FLO

TrafficFlow

\

MU,

AverageSpeed

miles/h

StandardDeviationofSpeed

85%PercentileofNormalDistribution

70%PercentileofNormalDistribution

TrafficDensity

（Note:

expressedbythenumberofcars）

StandardTime

CollisionTimes

3.Generalhypothesesforallmodels

（1）Allfreewayroadscontaineithertwoorthreelanes.

（2）