美国数学建模提交论文模板.docx

1、美国数学建模提交论文模板For office use onlyT1_T2_T3_T4_Team Control Number24889 Problem ChosenAFor office use onlyF1_F2_F3_F4_2014 Mathematical Contest in Modeling (MCM) Summary SheetSummary The Keep-Right-Except-To-Pass Rule has got a long history in most countries and the scientific evaluation of the rule has

2、 not been explicit. In this paper, three models are constructed to study the traffic flow, security, speed and the mutual influence among them under this rule. As a result, we get different outputs by changing the three factors. At last, based on these outputs we evaluate how the rule influences the

3、 traffic performance. Furthermore we put forward a better rule by comparing different rules. In model 1, an improved safety performance function is established. First, we analyze how traffic safety relate to overtaking by using the minimum safety spacing and an improved safety index. Then we get the

4、 rate of collision. An influential coefficient is proposed to assess how driving on the right influences traffic safety. The traffic safety coefficient is calculated by using the fuzzy mathematics based interval-valued fuzzy set theory. At last we add the safety coefficient into the safety performan

5、ce function and get an improved safety performance function. Based on the improved safety performance function, we get some conclusions. That is, in light traffic, the accident frequencies increase with the increasing of traffic flow while in heavy traffic, the accident frequencies decrease with the

6、 increasing of traffic flow. Model 2 deals with the relationship between the traffic flow and traffic speed. The basis of the model is the traffic safety. An equation is established about the traffic flow and traffic speed using the basic model of traffic flow. By analyzing the property of the perfo

7、rmance function, we obtain that the traffic speed increases with the increasing of traffic flow in light traffic. However, in heavy traffic, the traffic speed decreases with the increasing of traffic flow. Model 3 combines model 1 and model 2. Based on model 1 and 2 we build a three-dimensional mode

8、l of traffic safety, traffic speed and traffic flow. By changing the three factors, we get some results. First, under the Keep-Right-Except-To-Pass Rule, a better point can be obtained where the traffic flow and speed is relatively high and the accident frequency is low. Then we change the rule from

9、 right to left, we find that the value of the influential coefficient increases, which indicates the increasing of the accident frequency. Meanwhile the traffic flow increases in light traffic but decreases in heavy traffic. As for the intelligent traffic system, we give some qualitative analysis. F

10、inally, the advantages and disadvantages of the above models are discussed and some future improvements are proposed.Driving on the right or leftSummary The Keep-Right-Except-To-Pass Rule has got a long history in most countries and the scientific evaluation of the rule has not been explicit. In thi

11、s paper, three models are constructed to study the traffic flow, security, speed and the mutual influence among them under this rule. As a result, we get different outputs by changing the three factors. At last, based on these outputs we evaluate how the rule influences the traffic performance. Furt

12、hermore we put forward a better rule by comparing different rules. In model 1, an improved safety performance function is established. First, we analyze how traffic safety relate to overtaking by using the minimum safety spacing and an improved safety index. Then we get the rate of collision. An inf

13、luential coefficient is proposed to assess how driving on the right influences traffic safety. The traffic safety coefficient is calculated by using the fuzzy mathematics based interval-valued fuzzy set theory. At last we add the safety coefficient into the safety performance function and get an imp

14、roved safety performance function. Based on the improved safety performance function, we get some conclusions. That is, in light traffic, the accident frequencies increase with the increasing of traffic flow while in heavy traffic, the accident frequencies decrease with the increasing of traffic flo

15、w. Model 2 deals with the relationship between the traffic flow and traffic speed. The basis of the model is the traffic safety. An equation is established about the traffic flow and traffic speed using the basic model of traffic flow. By analyzing the property of the performance function, we obtain

16、 that the traffic speed increases with the increasing of traffic flow in light traffic. However, in heavy traffic, the traffic speed decreases with the increasing of traffic flow. Model 3 combines model 1 and model 2. Based on model 1 and 2 we build a three-dimensional model of traffic safety, traff

17、ic speed and traffic flow. By changing these three factors, we get some results. First, under the Keep-Right-Except-To-Pass Rule, a better point can be obtained where the traffic flow and speed is relatively high and the accident frequency is low. Then we change the rule from right to left, we find

18、that the value of the influential coefficient increases, which indicates the increasing of the accident frequency. Meanwhile the traffic flow increases in light traffic but decreases in heavy traffic. As for the intelligent traffic system, we give some qualitative analysis. Finally, the advantages a

19、nd disadvantages of the above models are discussed and some future improvements are proposed.Keywords: road traffic, performance function, traffic flow, traffic speed, traffic safety, fuzzy mathematicsIntroduction With the development of society,the problem of the traffic system has been a big probl

20、em and the establishment of the traffic system has been in badly need.In America the traffic speed decreased to no more thandue to high traffic density during peak-hour on the freeway in 1990s.As a result the problem caused great economic cost.12To improve the traffic performance we study how the tr

21、affic performance is influenced by some factors basing on the keep-right-except-to-pass traffic rule. In most countries driving on the right is the rule and in other countries driving on the left is the rule.So driving rules like this may have an influence on traffic performance.The influence factor

22、s include the traffic flow,the traffic safety and traffic speed which is related to the traffic speed limits.Basing on these factors we should analyze the mutual effect among them and get the evaluation of the traffic performance.The model is constructed based on the rule of driving right,so when th

23、e rule is changed,we should analyze the results and find a better rule which can improve the traffic flow.Furthermore when the traffic system is intelligent, the results are different based the model we have built. Now there are many studies about traffic performance including some systems of traffi

24、c safety ,lane changing models and so on.However these studies nearly neglect the influence of the traffic rules such as the keep-right-except-to-pass traffic rule.So our model take the traffic rule into consideration and that is to say we construct models basing on this rule. In addition, to simpli

25、fy our model we only consider traffic safety,traffic flow and traffic speed. We use some index to quantify all the factors in order to assess the traffic performance.So our model can help people to find a better traffic performance based on different rules. Assumptions We do not take the vehicle typ

26、e into consideration when we construct models. We do not consider the influence of the bad natural environment on the traffic. The road condition is normal. Model 1：showing the relationship between traffic safety and flow. We know the traffic safety is a complex system and it is influenced by many f

27、actors.Here we use expected accident frequencies to represent traffic safety.The expected accident frequency means the number of accidents by type, expected to occur on the entity in a certain period,per unit of time3. To simplify the following discussions,we assume that: Traffic flow is the main ca

28、sual factors which affect accident frequencies.But we also consider some small factors including traffic speed,overtaking,and driving rules. When we analysis the overtaking behavior,we only consider two cars.That is to say there are no other cars which influence them. When we consider overtaking beh

29、avior,we think lane-changing and merging behavior is symmetric.Meanwhile we think when O overtake B the minimum safety distance is no more than the distance of lane-changing4. To simplify calculating,we assume that O is in the state of uniformly accelerated motion when it changs lanes and B is in th

30、e state of uniform motion. Step 1: considering how overtaking influences traffic safety.Table 1NotationsParametersMeaningQThe traffic flowThe minimum safety distanceThe distance between the two carThe initial velocity of car O The initial velocity of car BThe expected velocity of car OUnder-posted s

31、peed limitOver-posted speed limitThe maximum brake acceleration of car BThe initial acceleration speed of car O Figure 1 the process of overtaking The overtaking behavior includes three steps which are lane-changing,passing and merging behavior.According to the assumptions,we only consider lane-chan

32、ging.Here we use the minimum safety distance to analyze the safety. In the model of lane-changing that is put forward by University of Southern California,the minimum safety distance is5 (1)Where means the acceleration speed of car O at certain moment.means the acceleration speed of car B at certain moment. Accord