数学中国国际赛论文参考模版Word格式.docx

数学中国国际赛论文参考模版Word格式.docx

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TITLE

Abstract:

Keywords:

Contents

1.Introduction...................................................................................................................................................3

1.1Whydoestollwaycollectstoll?

………………………………………….…………………….3

1.2Tollmodes………………………………………………………………………………………………3

1.3Tollcollectionmethods……………………………………………………………………….……3

1.4Annoyanceintollplazas………………………………………….………….…………………….3

1.5Theoriginofthetollwayproblem……………………...……………………………………...3

1.6Queuingtheory…………………………………………………………………………………...…...4

2.TheDescriptionofProblem….............................................................................................................5

2.1Howdoweapproximatethewholecourseofpayingtoll?

............................................5

2.2Howdowedefinetheoptimalconfiguration?

........................…………….………….5

2.2.1Fromtheperspectiveofmotorist…………………………………….………………….5

2.2.2Fromtheperspectiveofthetollplaza…………………………………………………6

2.2.3Compromise…………………………………...……………………………………...………..6

2.3Overalloptimizationandlocaloptimization……………………………..……………….…6

2.4Thedifferencesinweightsandsizesofvehicles………………………………………..…7

2.5Whatifthereisnodataavailable?

..............................................................................................7

3.Models……………...........................................................................................................................................7

3.1BasicModel.............................................................................................................................................7

3.1.1SymbolsandDefinitions………………………………..…...……………………………...7

3.1.2Assumptions……………………………………………………………….……..……………..8

3.1.3TheFoundationofModel………………………………………………………………….9

3.1.4SolutionandResult……………………………………………………………….………...11

3.1.5AnalysisoftheResult……………………………………………….………………………..……….….11

3.1.6StrengthandWeakness………………………………………………….…………….…..13

3.2ImprovedModel.................................................................................................14

3.2.1ExtraSymbols……………………………………..………………………...…………………......................14

3.2.2AdditionalAssumptions………………………………………………...…..…………………………..14

3.2.3TheFoundationofModel………………………………..…………………………………………….14

3.2.4SolutionandResult………………………………………….……………………………..……………...15

3.2.5AnalysisoftheResult…………………………………………….……………………..…………….….18

3.2.6StrengthandWeakness……………………………………………….……………….…..19

4.Conclusions..................................................................................................................................................19

4.1Conclusionsoftheproblem……………………………………..……………..19

4.2Methodsusedinourmodels…………………………………...……………………..…………19

4.3Applicationofourmodels…………………………………………………..………………..….19

5.FutureWork..............................................................................................................................................19

5.1Anothermodel………………………………………………………………………………………19

5.2Anotherlayoutoftollplaza………………………………………………………..……………23

5.3Thenewly-adoptedchargingmethods………………………………………..……………23

6.References...................................................................................................................................................23

7.Appendix......................................................................................................................................................23

Programsandcodes………………………………………………………………..……………………24

I.Introduction

Inordertoindicatetheoriginofthetollwayproblems,thefollowingbackgroundisworthmentioning.

1.1

1.2

1.3

1.4

1.5

1.6

II.TheDescriptionoftheProblem

2.1Howdoweapproximatethewholecourseofpayingtoll?

●

1）Fromtheperspectiveofmotorist:

2）Fromtheperspectiveofthetollplaza:

3）Compromise:

2.3Thelocaloptimizationandtheoveralloptimization

●Virtually:

2.4Thedifferencesinweightsandsizesofvehicles

III.Models

3.1BasicModel

3.1.1Terms,DefinitionsandSymbols

Thesignsanddefinitionsaremostlygeneratedfromqueuingtheory.

●

3.1.2Assumptions

3.1.3TheFoundationofModel

1）Theutilityfunction

●Thecostoftollplaza:

●Thelossofmotorist:

●Theweightofeachaspect:

●Compromise:

2）Theintegerprogramming

Accordingtoqueuingtheory,wecancalculatethestatisticalpropertiesasfollows.

3）Theoveralloptimizationandthelocaloptimization

●Theoveralloptimization:

●Thelocaloptimization:

●Theoptimalnumberoftollbooths:

3.1.4SolutionandResult

1）Thesolutionoftheintegerprogramming:

2）Results:

3.1.5AnalysisoftheResult

●Localoptimizationandoveralloptimization:

●Sensitivity:

Theresultisquitesensitivetothechangeofthethreeparameters

●Trend:

●Comparison:

3.1.6StrengthandWeakness

●Strength:

Indespiteofthis,themodelhasprovedthat.Moreover,wehavedrawnsomeusefulconclusionsabout.Themodelisfitfor,suchas

●Weakness:

Thismodeljustappliesto.Aswehavestated,.That’sjustwhatweshoulddointheimprovedmodel.

3.2ImprovedModel

3.2.1ExtraSymbols

Signsanddefinitionsindicatedabovearestillvalid.Herearesomeextrasignsanddefinitions.

3.2.2AdditionalAssumptions

●AssumptionsconcerningtheanteriorprocessarethesameastheBasicModel.

3.2.3TheFoundationofModel

1）Howdowedeterminetheoptimalnumber?

AswehaveconcludedfromtheBasicModel,

3.2.4SolutionandResult

1）Simulationalgorithm

Basedontheanalysisabove,wedesignoursimulationarithmeticasfollows.

●Step1:

●Step2:

●Step3:

●Step4:

●Step5:

●Step6:

●Step7:

●Step8:

●Step9:

2）Flowchart

Thefigurebelowistheflowchartofthesimulation.

3）Solution

3.2.5AnalysisoftheResult

3.2.6StrengthandWeakness

TheImprovedModelaimstomakeupfortheneglectof.TheresultseemstodeclarethatthismodelismorereasonablethantheBasicModelandmuchmoreeffectivethantheexistingdesign.

.Thusthemodelisstillanapproximateonalargescale.Thishasdoomedtolimittheapplicationsofit.

IV.Conclusions

4.1Conclusionsoftheproblem

4.2Methodsusedinourmodels

4.3Applicationsofourmodels

V.FutureWork

5.1Anothermodel

5.1.1Thelimitationsofqueuingtheory

5.1.2

5.1.3

5.1.4

1）

2）

3）

4）

5.2Anotherlayoutoftollplaza

5.3Thenewly-adoptedchargingmethods

VI.References

[1]

[2]

[3]

[4]

VII.Appendix