美国数学建模提交论文模板.docx

美国数学建模提交论文模板.docx

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美国数学建模提交论文模板

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2014MathematicalContestinModeling（MCM）SummarySheet

Summary

TheKeep-Right-Except-To-PassRulehasgotalonghistoryinmostcountriesandthescientificevaluationoftherulehasnotbeenexplicit.Inthispaper,threemodelsareconstructedtostudythetrafficflow,security,speedandthemutualinfluenceamongthemunderthisrule.Asaresult,wegetdifferentoutputsbychangingthethreefactors.Atlast,basedontheseoutputsweevaluatehowtheruleinfluencesthetrafficperformance.Furthermoreweputforwardabetterrulebycomparingdifferentrules.

Inmodel1,animprovedsafetyperformancefunctionisestablished.First,weanalyzehowtrafficsafetyrelatetoovertakingbyusingtheminimumsafetyspacingandanimprovedsafetyindex.Thenwegettherateofcollision.Aninfluentialcoefficientisproposedtoassesshowdrivingontherightinfluencestrafficsafety.Thetrafficsafetycoefficientiscalculatedbyusingthefuzzymathematicsbasedinterval-valuedfuzzysettheory.Atlastweaddthesafetycoefficientintothesafetyperformancefunctionandgetanimprovedsafetyperformancefunction.Basedontheimprovedsafetyperformancefunction,wegetsomeconclusions.Thatis,inlighttraffic,theaccidentfrequenciesincreasewiththeincreasingoftrafficflowwhileinheavytraffic,theaccidentfrequenciesdecreasewiththeincreasingoftrafficflow.

Model2dealswiththerelationshipbetweenthetrafficflowandtrafficspeed.Thebasisofthemodelisthetrafficsafety.Anequationisestablishedaboutthetrafficflowandtrafficspeedusingthebasicmodeloftrafficflow.Byanalyzingthepropertyoftheperformancefunction,weobtainthatthetrafficspeedincreaseswiththeincreasingoftrafficflowinlighttraffic.However,inheavytraffic,thetrafficspeeddecreaseswiththeincreasingoftrafficflow.

Model3combinesmodel1andmodel2.Basedonmodel1and2webuildathree-dimensionalmodeloftrafficsafety,trafficspeedandtrafficflow.Bychangingthethreefactors,wegetsomeresults.First,undertheKeep-Right-Except-To-PassRule,abetterpointcanbeobtainedwherethetrafficflowandspeedisrelativelyhighandtheaccidentfrequencyislow.Thenwechangetherulefromrighttoleft,wefindthatthevalueoftheinfluentialcoefficientincreases,whichindicatestheincreasingoftheaccidentfrequency.Meanwhilethetrafficflowincreasesinlighttrafficbutdecreasesinheavytraffic.Asfortheintelligenttrafficsystem,wegivesomequalitativeanalysis.

Finally,theadvantagesanddisadvantagesoftheabovemodelsarediscussedandsomefutureimprovementsareproposed.

Drivingontherightorleft

Summary

TheKeep-Right-Except-To-PassRulehasgotalonghistoryinmostcountriesandthescientificevaluationoftherulehasnotbeenexplicit.Inthispaper,threemodelsareconstructedtostudythetrafficflow,security,speedandthemutualinfluenceamongthemunderthisrule.Asaresult,wegetdifferentoutputsbychangingthethreefactors.Atlast,basedontheseoutputsweevaluatehowtheruleinfluencesthetrafficperformance.Furthermoreweputforwardabetterrulebycomparingdifferentrules.

Inmodel1,animprovedsafetyperformancefunctionisestablished.First,weanalyzehowtrafficsafetyrelatetoovertakingbyusingtheminimumsafetyspacingandanimprovedsafetyindex.Thenwegettherateofcollision.Aninfluentialcoefficientisproposedtoassesshowdrivingontherightinfluencestrafficsafety.Thetrafficsafetycoefficientiscalculatedbyusingthefuzzymathematicsbasedinterval-valuedfuzzysettheory.Atlastweaddthesafetycoefficientintothesafetyperformancefunctionandgetanimprovedsafetyperformancefunction.Basedontheimprovedsafetyperformancefunction,wegetsomeconclusions.Thatis,inlighttraffic,theaccidentfrequenciesincreasewiththeincreasingoftrafficflowwhileinheavytraffic,theaccidentfrequenciesdecreasewiththeincreasingoftrafficflow.

Model2dealswiththerelationshipbetweenthetrafficflowandtrafficspeed.Thebasisofthemodelisthetrafficsafety.Anequationisestablishedaboutthetrafficflowandtrafficspeedusingthebasicmodeloftrafficflow.Byanalyzingthepropertyoftheperformancefunction,weobtainthatthetrafficspeedincreaseswiththeincreasingoftrafficflowinlighttraffic.However,inheavytraffic,thetrafficspeeddecreaseswiththeincreasingoftrafficflow.

Model3combinesmodel1andmodel2.Basedonmodel1and2webuildathree-dimensionalmodeloftrafficsafety,trafficspeedandtrafficflow.Bychangingthesethreefactors,wegetsomeresults.First,undertheKeep-Right-Except-To-PassRule,abetterpointcanbeobtainedwherethetrafficflowandspeedisrelativelyhighandtheaccidentfrequencyislow.Thenwechangetherulefromrighttoleft,wefindthatthevalueoftheinfluentialcoefficientincreases,whichindicatestheincreasingoftheaccidentfrequency.Meanwhilethetrafficflowincreasesinlighttrafficbutdecreasesinheavytraffic.Asfortheintelligenttrafficsystem,wegivesomequalitativeanalysis.

Finally,theadvantagesanddisadvantagesoftheabovemodelsarediscussedandsomefutureimprovementsareproposed.

Keywords:

roadtraffic,performancefunction,trafficflow,trafficspeed,trafficsafety,fuzzymathematics

Introduction

Withthedevelopmentofsociety,theproblemofthetrafficsystemhasbeenabigproblemandtheestablishmentofthetrafficsystemhasbeeninbadlyneed.InAmericathetrafficspeeddecreasedtonomorethan

duetohightrafficdensityduringpeak-houronthefreewayin1990s.Asaresulttheproblemcausedgreateconomiccost.[1][2]Toimprovethetrafficperformancewestudyhowthetrafficperformanceisinfluencedbysomefactorsbasingonthekeep-right-except-to-passtrafficrule.

Inmostcountriesdrivingontherightistheruleandinothercountriesdrivingontheleftistherule.Sodrivingruleslikethismayhaveaninfluenceontrafficperformance.Theinfluencefactorsincludethetrafficflow,thetrafficsafetyandtrafficspeedwhichisrelatedtothetrafficspeedlimits.Basingonthesefactorsweshouldanalyzethemutualeffectamongthemandgettheevaluationofthetrafficperformance.Themodelisconstructedbasedontheruleofdrivingright,sowhentheruleischanged,weshouldanalyzetheresultsandfindabetterrulewhichcanimprovethetrafficflow.Furthermorewhenthetrafficsystemisintelligent,theresultsaredifferentbasedthemodelwehavebuilt.

Nowtherearemanystudiesabouttrafficperformanceincludingsomesystemsoftrafficsafety,lanechangingmodelsandsoon.Howeverthesestudiesnearlyneglecttheinfluenceofthetrafficrulessuchasthekeep-right-except-to-passtrafficrule.Soourmodeltakethetrafficruleintoconsiderationandthatistosayweconstructmodelsbasingonthisrule.

Inaddition,tosimplifyourmodelweonlyconsidertrafficsafety,trafficflowandtrafficspeed.Weusesomeindextoquantifyallthefactorsinordertoassessthetrafficperformance.Soourmodelcanhelppeopletofindabettertrafficperformancebasedondifferentrules.

Assumptions

●Wedonottakethevehicletypeintoconsiderationwhenweconstructmodels.

●Wedonotconsidertheinfluenceofthebadnaturalenvironmentonthetraffic.

●Theroadconditionisnormal.

Model1：

showingtherelationshipbetweentrafficsafetyandflow.

Weknowthetrafficsafetyisacomplexsystemanditisinfluencedbymanyfactors.Hereweuseexpectedaccidentfrequenciestorepresenttrafficsafety.Theexpectedaccidentfrequencymeansthenumberofaccidentsbytype,expectedtooccurontheentityinacertainperiod,perunitoftime[3].Tosimplifythefollowingdiscussions,weassumethat:

●Trafficflowisthemaincasualfactorswhichaffectaccidentfrequencies.Butwealsoconsidersomesmallfactorsincludingtrafficspeed,overtaking,anddrivingrules.

●Whenweanalysistheovertakingbehavior,weonlyconsidertwocars.Thatistosaytherearenoothercarswhichinfluencethem.

●Whenweconsiderovertakingbehavior,wethinklane-changingandmergingbehaviorissymmetric.MeanwhilewethinkwhenOovertakeBtheminimumsafetydistanceisnomorethanthedistanceoflane-changing[4].

●Tosimplifycalculating,weassumethatOisinthestateofuniformlyacceleratedmotionwhenitchangslanesandBisinthestateofuniformmotion.

Step1:

consideringhowovertakinginfluencestrafficsafety.

Table1

Notations

Parameters

Meaning

Q

Thetrafficflow

Theminimumsafetydistance

Thedistancebetweenthetwocar

TheinitialvelocityofcarO

TheinitialvelocityofcarB

TheexpectedvelocityofcarO

Under-postedspeedlimit

Over-postedspeedlimit

ThemaximumbrakeaccelerationofcarB

TheinitialaccelerationspeedofcarO

Figure1theprocessofovertaking

Theovertakingbehaviorincludesthreestepswhicharelane-changing,passingandmergingbehavior.Accordingtotheassumptions,weonlyconsiderlane-changing.Hereweusetheminimumsafetydistancetoanalyzethesafety.

Inthemodeloflane-changingthatisputforwardbyUniversityofSouthernCalifornia,theminimumsafetydistanceis[5]

（1）

Where

meanstheaccelerationspeedofcarOatcertainmoment.

meanstheaccelerationspeedofcarBatcertainmoment.

Accord