2014年美赛数学建模A题论文

Team # 31725 Page 9 of 25

And the equation of maximum safe speed:

vm?127Rh(?h?ah)=127?Rh(0.4?0.015)=48.895Rh （8） Finally we get the equation of performance index from equation(4)(7)and (8)

w?k

vmt （9）

W represent performance index.., k :random number ?v?v1?v2

?v is the speed difference between the passing car and the passed car .

Finally we get the relationship of w??v from MATLAB .The trend chart is shown as below ;

Explanation of the image:

As the picture show us, ?v is abscissa and w is ordinate,the upper and lower side of the picture represent the traffic performance index in light and heavy condition.

Then we can get the result that the performance of Keep-Right-Except-To-Pass in light traffic is steadily effective but poor effect and unsteadiness in heavy traffic .

3.6 Without the rule of Keep-Right-Except-To-Pass

We use the calculation method deduced in Model One to represent the traffic

performance of the case of without the previous rule .

Without the rule of Keep-Right-Except-To-Pass meaning that the vehicles drive in the lane one by one.There is the idealized pattern graph below:

Team # 31725 Page 10 of 25

B A B’

The simple figure of overtaking route:

In this case ,the vehicle route will be a line .

t1t?1?I?2??(vB?)??a?()2??vB?t??a?t2

222?4?vC the speed of passing vehicle C

a the accelerometer of passing vehicle C

Then we can get the expression of passing time :

2?(vB?vA)?(vB?vA)2?2ast?

aThe passing time :t'???I vBAnd the expression of maximum safe speed in the case of no rule :

w'?k?vm k is random number t'?v2?vB?vA ?v is the speed difference between the passing car and the passed car .

Finally we get the relationship of ?v?w from MATLAB .The trend chart shown as below ;

Team # 31725 Page 11 of 25

The explanation of the image:

As the picture show us, ?v is abscissa and w is ordinate,the upper and lower side

of the picture represent the traffic performance index in light and heavy condition.Then we can get the result that the performance in both the light and heavy conditions have poor effect without the rule of Keep-Right-Except-To-Pass.

3.7 Result:

Compare the traffic performance of rule have with not have :

In conclusion,compare the traffic performance of rule have with not have,it’s obvious to

show that the traffic performance within the rule is better than the traffic performance without the rule.What’s more ,the performance of Keep-Right-Except-To-Pass in light traffic is steadily effective but being poor effect and unsteadiness in heavy traffic .

IV. The Model of New Rule According

to

the

analysis

of

Model

One,the

performance

of

Keep-Right-Except-To-Pass in light traffic is steadily effective but being poor effect and unsteadiness in heavy traffic.We improve the original rules to increase the overall traffic capacity of roads.The rule we suggest would improve the speed of the vehicle and road usage to overall enhance the traffic capacity efficiently .

4.1 The Expression Of New Rule

Our new rule requires drivers to drive in the right lane ,when they are passing another

vehicle just move to the left.It’s permitted to drive in the left lane if the drivers want to keep in high speed.But they have got to return to the right lane if there is coming a faster vehicle . Here the schematic diagram is :

Team # 31725 Page 12 of 25

Case 1:

C’ C B A B’ C’

C A B

CASE I: Vehicle C is the one which will pass the former one named A,B is the driving in the left lane but not as fast as C.So when C is passing A, vehicle B have to return to the right lane to be sure C would keep in speedy .

Case 2:

C A B B’ C’

CASE II: Vehicle C and B are both driving in the left lane till B realize C is the faster one .So B have to return to the right lane to be sure C could keep in speedy .

As the first case ,we will get the performance index -w calculated from the formulas developed in Model One .

w the performance index