发布时间 : 星期四 文章2014年美赛数学建模A题论文更新完毕开始阅读8747b27df78a6529657d5336
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t is the passing time t?tc?tb?1
tc the speed time of Vehicle c. tb time for b to turn to the right lane
1 reaction time of the driver in vehicle B
s safe distance vm maximum safe speed
2?(v1?v2)?(v1?v2)2?2ast? a??t?tc?tb?1
?(vC?vA)?(vc?va)2?2?ac?s?(vB?vA)?(vB?vA)2?2aBs???1
aCaBvm2?127?Rh2?(?h?ah) h2(I?Ic2)32Rh2?Ic22
122Ic1?2?(vc?tc??ac?tc)?2?v?ctc?ac?tc
2?v2?vC?vA
w?kvm k is the natural number tSo we get the performance index of case 1-w2.
In the same way ,we get the performance index of case 2 -w3.
The performance index of our own rule consist of w2,w3and w calculated in Model One .
w'?p1w?p2w2?p3w3 p is the weight factor of different case
p1?30％ p2?60％ p3?10％
4.2 Result:
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Finally ,we get the image of ?v-w to show the performance index of the rule we came up with .
Explanation of the image:
As the picture shows 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 the rule we suggested is steadily effective both in light traffic and heavy traffic.
4.3 Model Test:
Compare the new rule with the former one :
According to the figure from MATLAB ,we will accurately describe the difference between the new rule and the former one in the the upper and lower line modeled with MATLAB .
The top line the former rule ; the new rule;
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The Lowest line
the former rule the new rule
From the figure upon ,we conclude that the new rule is better than the former one since the traffic performance index of the new rule is overall higher and more stable than the former one.
All in all ,The rule we suggest can increase the overall traffic capacity of roads.
V. Application
5.1 Does the rule suggested by us can be used for the countries where drives automobiles on the left?
There are 34 percent countries driving on the left and 66 percent countries driving on the right side of the road.
The difference drive on right and left ;
Objective factors:The migration of a fast moving object can not be ignored because of Coriolis acceleration,and the directions of migration are different from place to place on the earth.so the maximum safe speed is different from place to place .
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Human factors:the biggest advantage of driving on the left is come from the human instinct,when a man meet an emergency,,he will turn to another direction in order to protect the heart.Furthermore ,if the seat is on the right of the car,it will be more convenient for the driver to observe the condition of roads .On the country driving on right ,the drivers can save time to control the car device,so it will decrease the distance of the brake.
All in all ,the traffic rules which adapt to the driving on the right countries are different from the driving on the left.The rule we suggest can not adapt to the countries which keep driving on the left .
So the answer of the question is NOT .
5.2 Is the rule suggested by us can be helpful if vehicle transportation on the same roadway was fully under the control of an intelligent system ?
During the establish of the model,we have already considered of the human factors.For example ,the influence ratio of human factors to performance index is 3.9%.And if the rule is used in the system fully under VI. Evaluation and improvements 6.1 Strength:
? In the model one,in order to effectively react the traffic influenced by the safety and
velocity speed.We use the maximum speed to represent the safety factors,and the passing time to represent vehicle speed factors.
? In model two, the stability and the traffic performance index are been improved for
considering the human subjective factors and the waste of road resources for the model one and model two,
? The model mentioned in the article can adapt to the most facts,and it also consider the
safety and traffic flow.
? Our models have both good precision and operability.