2014年美赛数学建模A题论文

Team Control Number For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________ 31725 Problem Chosen For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________ A . 2014 Mathematical Contest in Modeling (MCM) Summary Sheet Keep-Right-Except-To-Pass

Team #31725 February 7, 2014

Summary

This paper presents a new mathematical method to analyze how the traffic efficiency affected by traffic rules. The model is based on traffic flow and safety to define traffic efficiency with maximum safe speed and the passing time.By using the mathematical model reaching a conclusion that the performance of Keep-Right-Except-To-Pass is steadily effective in light traffic but poor effect and unsteadiness in heavy traffic.And the traffic efficiency is overall better than the case of without the rule.In order to overall enhance the traffic capacity efficiently ,we suggest a new rule that Slower Traffic Keeps Right--It is promoted to keep speedy on the left line but have to give way to the faster one coming behind.Compared with the former rule in traffic performance index,we conclude that the traffic efficiency of the new rule is overall higher and more stable.As for driving on the left,the rule we suggest can not adapt to those countries according to Coriolis acceleration and the human instinct.What’s more ,if the mathematical model is used in an intelligent system,the results of earlier analysis will change 3.9%.

Key words: maximum safe speed ,traffic efficiency,Slower Traffic Keeps Right,traffic performance index Team # 31725 Page 2 of 25

Contents

1. Introduction.....................................................................................4 2. The Description of Problem.......................................................... 5 3.Models...............................................................................................5 3.1Symbols.............................................................…………..……5 3.2Asumptions............................................................. ....................6 3.3 Survey of Previous Research…………….........……………6 3.4 A Mathematical Model ………………………………………… 6 3.5 Without the rule of Keep-Right-Except-To-Pass ….................. 8 3.6 Result .........................................................................................10 4 .The Model of New Rule.................................................................10 4.1 The Expression Of New Rule …………............ ....………..10 4.2Result…………………………..………..........................……13 4.3 Model Test………………………………………..………..….13 5. Application........................................................................................15 6. Evaluation and improvements..................……….........................17 6.1 Strength.............................. ................................................... 17 6.2 Weakness............................................................................... 17 6.3 Further Improvements........................................................ 17 7. References.......................... ...........................................................20

Team # 31725 Page 3 of 25

8. Appendix........................................................................................20

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I. Introduction

As we all know, car-overtaking is a common way to speed, which is the key and difficult

point in traffic safety management of high way. Therefore, research on the process of overtaking is important to understand the characteristics of traffic flow of highway. And it is also helpful to the development of traffic simulation modeling of highway.

Traffic Efficiency Safety Traffic Flow Model Traffic PerformaStability Further ImprovementDriving Left Intelligent System