2014年全国大学生数学建模竞赛A题

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T4 ________________ 31527 Problem Chosen For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________ A

2014 Mathematical Contest in Modeling (MCM) Summary Sheet

Keep-Right-Except-To-Pass Rule

Summary

In this paper, we analyze the impact of the right rule for traffic from three parts.

Part one:

First, simplify the right line rules affect on traffic capacity into the overtaking impact on traffic performance and divide its impact into the vehicle flowrate and security to discuss. For the vehicle flowrate problems, based on road capacity and road space share, this paper proposes a calculating method of additional share of road space by overtaking behavior, introduces correction factor of road capacity impact, and built the vehicle flowrate model about it.

For security issues, first through the kinematics analysis of the overtaking, we deduced solution algorithm of overtaking longitudinal distance between vehicles, obtained the minimum safe distance of overtaking and establish a relation function between overtaking and safety distance. Considering the stability of overtaking, we established the curvature limit model on the longitudinal and lateral distance and the curvature radius[1]. Considering a lot of human factors involved in the overtaking process, the model was improved by the establishment of a driver’s reliability model.

Then the above model is improved and simulated, by the results of simulation, the right line rule is modified as follows[2]:

First, change traffic flow by changing traffic rules, when the number of one-way lanes is 4 or less, the free travel rules is implemented. When more than 4, the right line rules is implemented. Thus the vehicle flowrate is increased.

Second, affect the safety factor of the vehicle driving by changing the speed difference between the overtaking and overtaken cars, that is, reducing speed difference between the overtaking and overtaken cars, we can improve the safety factor of the vehicle driving.

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Team #31527 Page 2 of 33 Part two:

From the principle of the human engineering, considering driver's perspective and both hands’ reaction time, we discuss the changes of the reaction time and the following distance. Combining them with the vehicle flowrate, we draw the conclusion that traffic flow changed little between the right line rule and left line rule. Finally using simulation software to simulate, the results can be verified. Thus we can get that the right line rule can be directly used to the left line.

Part three:

In the intelligent control system, we take road correction factor as the index and use fuzzy comprehensive evaluation method to weigh the original parameters of the model. It is concluded that, compared with driving a car, intelligent control cars not only improve the traffic flow but also improve security. But with the increase in the number of lanes, intelligent advantage is not obvious and with the increasing of the passing time, the security decreased, tends to be stable.

Key words: Overtaking model, Vissim Simulation, Curvature limit model, Right Rule,

Correction coefficient

Contents

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Team #31527 Page 3 of 33

1 Restatement and Analysis of the Question ................................................................................................... 3

2 Model Assumption ....................................................................................................................................... 4

3 Symbols ........................................................................................................................................................ 4

4 Model of right-line rules on traffic performance .......................................................................................... 5

4.1 The relationship between congestion-sparse and the traffic total volume ........................................ 5

4.2 Indicators Conversion of Right-line Rules ....................................................................................... 5

4.3 Relational Model of Overtaking Behavior and Traffic Flow ............................................................ 6

4.4 Relational model of overtaking behavior and traffic safety ............................................................ 10

5 Improved Model of right line rule’s impact on traffic capacity.................................................................. 20

5.1 Rules of Improving Traffic ............................................................................................................. 20

5.2 Case of Covering 40 Miles and Supporting 10,000 Users .............................................................. 25

5.3 Conclusion ...................................................................................................................................... 25

6 Test and Improvement of the Model under left Rule ............................................................................... 25

6.1 Comparison of Left Rule and Right Rule ....................................................................................... 25 6.2 the simulation test ........................................................................................................................... 27

6.3 Concluion ....................................................................................................................................... 28

7 Discussion of intelligent electronic control model ..................................................................................... 29

7.1 Impact on traffic flow model .......................................................................................................... 29

7.2 The impact on traffic safety model ................................................................................................. 31

7.3 The conclusion ................................................................................................................................ 32

8 References .................................................................................................................................................. 32

1 Restatement and Analysis of the Question

In countries where driving automobiles on the right is the rule, that is, drivers are required

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Team #31527 Page 4 of 33 to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left , pass and return to their former travel lane. In this rule, we investigate its effect on freeway capacity.

First, to analyze the performance of overtaking traffic rules in light and heavy traffic, we need to consider the following factors in the model: traffic and safety trade-offs, the speed limit is too high or too low, other factors, this problem may occur in the statement. Through the study of the above factors, one may explore whether the rule is effective in improving traffic flow. If not, an alternative proposed and analyzed.

Secondly, for the left-country, to explore whether these programs are still applicable, or require some additional needs.

Finally, the above rules rely on human judgment, if the same rules of transportation are entirely under the control of intelligent systems, then, to what extent, this will modify the results of the above analysis.

2 Model Assumption

1. Assuming the freeway segments basically straight, road conditions of each lane is similar no large entrances and exits.

2. Assuming drivers follow traffic rules,and there is on accidences.

3. Assuming all left countries have right driving seats and all right countries have left driving seats.

4. Assuming the smart car can recognize and understand the traffic situation around the vehicle. Ignore the reaction time of the intelligent system.

3 Symbols

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Team #31527 Page 5 of 33 4 Model of right-line rules on traffic performance

4.1 The relationship between congestion-sparse and the traffic total volume Related terms are explained as follows:

Total Traffic: the total number of vehicles passing a certain way you want in a certain time, with the representationQT

Traffic Flow: the number of vehicles per unit time passed, and traffic total volume on the

dQtime derivative, with the representation I I?T dt

Sparse traffic and congestion depends on two factors:

(a)the total number of vehicles passing a certain way you want in a certain time

(b) the maximum total number of vehicles on the road during that period of time that can pass. Through the analysis of the correlation between the total traffic, traffic flow and congestion sparse, we find the light and heavy traffic can be measured by means of total volume. Because the total amount of traffic statistics are more convenient. We first establish the relationship between the total amount of traffic and the right line rules, and then based on the relationship between traffic volume and traffic flow, time derivative of traffic volume, we can get the relationships between right-line rules and traffic flow.

4.2 Indicators Conversion of Right-line Rules

China adopted the prevailing right-line rules, requiring the vehicle to return to the original lane after overtaking. When vehicles are traveling on their lanes, traffic performance is only related with the total amount of traffic. small amount, smooth road; large amount, road congestion. Right-line rules include straight driving all along and straight driving then

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