美赛数学建模比赛论文模板.docx

1、美赛数学建模比赛论文模板 The Keep-Right-Except-To-Pass RuleSummaryAs for the first question, it provides a traffic rule of keep right except to pass, requiring us to verify its effectiveness. Firstly, we define one kind of traffic rule different from the rule of the keep right in order to solve the problem clea

2、rly; then, we build a Cellular automaton model and a Nasch model by collecting massive data; next, we make full use of the numerical simulation according to several influence factors of traffic flow; At last, by lots of analysis of graph we obtain, we indicate a conclusion as follow: when vehicle de

3、nsity is lower than 0.15, the rule of lane speed control is more effective in terms of the factor of safe in the light traffic; when vehicle density is greater than 0.15, so the rule of keep right except passing is more effective In the heavy traffic. As for the second question, it requires us to te

4、stify that whether the conclusion we obtain in the first question is the same apply to the keep left rule. First of all, we build a stochastic multi-lane traffic model; from the view of the vehicle flow stress, we propose that the probability of moving to the right is 0.7and to the left otherwise by

5、 making full use of the Bernoulli process from the view of the ping-pong effect, the conclusion is that the choice of the changing lane is random. On the whole, the fundamental reason is the formation of the driving habit, so the conclusion is effective under the rule of keep left. As for the third

6、question, it requires us to demonstrate the effectiveness of the result advised in the first question under the intelligent vehicle control system. Firstly, taking the speed limits into consideration, we build a microscopic traffic simulator model for traffic simulation purposes. Then, we implement

7、a METANET model for prediction state with the use of the MPC traffic controller. Afterwards, we certify that the dynamic speed control measure can improve the traffic flow . Lastly neglecting the safe factor, combining the rule of keep right with the rule of dynamical speed control is the best solut

8、ion to accelerate the traffic flow overall.Key words：Cellular automaton model Bernoulli process Microscopic traffic simulator model The MPC traffic controlContent1. IntroductionAs is known to all, its essential for us to drive automobiles, thus the driving rules is crucial important. In many countri

9、es like USA, China, drivers obey the rules which called “The Keep-Right-Except-To-Pass (that is, when driving automobiles, the rule requires drivers to drive in the right-most unless they are passing another vehicle)”.2. Analysis of the problemFor the first question, we decide to use the Cellular au

10、tomaton to build models, then analyze the performance of this rule in light and heavy traffic. Firstly, we mainly use the vehicle density to distinguish the light and heavy traffic; secondly, we consider the traffic flow and safe as the represent variable which denotes the light or heavy traffic; th

11、irdly, we build and analyze a Cellular automaton model; finally, we judge the rule through two different driving rules, and then draw conclusions.3. AssumptionIn order to streamline our model we have made several key assumptionsThe highway of double row three lanes that we study can represent multi-

12、lane freeways.The data that we refer to has certain representativeness and descriptive Operation condition of the highway not be influenced by blizzardor accidental factorsIgnore the drivers own abnormal factors, such as drunk driving and fatigue drivingThe operation form of highway intelligent syst

13、em that our analysis can reflect intelligent systemIn the intelligent vehicle system, the result of the sampling data has high accuracy.4. Symbol Definition The number of vehicles The time5. ModelsBy analyzing the problem, we decided to propose a solution with building a cellular automaton model.5.1

14、 Building of the Cellular automaton modelThanks to its simple rules and convenience for computer simulation, cellular automaton model has been widely used in the study of traffic flow in recent years. Let be the position of vehicle at time , be the speed of vehicle at time , be the random slowing do

15、wn probability, and R be the proportion of trucks and buses, the distance between vehicle and the front vehicle at time is:, if the front vehicle is a small vehicle., if the front vehicle is a truck or bus. 5.1.1 Verify the effectiveness of the keep right except to pass rule In addition, according t

16、o the keep right except to pass rule, we define a new rule called: Control rules based on lane speed. The concrete explanation of the new rule as follow: There is no special passing lane under this rule. The speed of the first lane (the far left lane) is 120100km/h (including 100 km/h)；the speed of

17、the second lane (the middle lane) is 10080km8/h (including80km/h)；the speed of the third lane (the far right lane) is below 80km/ h. The speeds of lanes decrease from left to right.Lane changing rules based lane speed control If vehicle on the high-speed lane meets , , , the vehicle will turn into t

18、he adjacent right lane, and the speed of the vehicle after lane changing remains unchanged, where is the minimum speed of the corresponding lane.The application of the Nasch model evolutionLet be the lane changing probability (taking into account the actual situation that some drivers like driving i

19、n a certain lane, and will not take the initiative to change lanes), indicates the distance between the vehicle and the nearest front vehicle, indicates the distance between the vehicle and the nearest following vehicle. In this article, we assume that the minimum safe distance gap safe of lane chan

20、ging equals to the maximum speed of the following vehicle in the adjacent lanes.Lane changing rules based on keeping right except to passIn general, traffic flow going through a passing zone (Fig. 5.1.1) involves three processes: the diverging process (one traffic flow diverging into two flows), int

21、eracting process (interacting between the two flows), and merging process (the two flows merging into one) 4.Fig.5.1.1 Control plan of overtaking process(1) If vehicle on the first lane (passing lane) meets and , the vehicle will turn into the second lane, the speed of the vehicle after lane changin

22、g remains unchanged.5.1.2 Numerical simulation results and discussion In order to facilitate the subsequent discussions, we define the space occupation rate as, where indicates the number of small vehicles on the driveway, indicates the number of trucks and buses on the driveway, and L indicates the

23、 total length of the road. The vehicle flow volume is the number of vehicles passing a fixed point per unit time, where is the number of vehicles observed in time duration.The average speed , is the speed of vehicle at time . Take overtaking ratio as the evaluation indicator of the safety of traffic

24、 flow, which is the ratio of the total number of overtaking and the number of vehicles observed. After 20,000 evolution steps, and averaging the last 2000 steps based on time, we have obtained the following experimental results. In order to eliminate the effect of randomicity, we take the systemic a

25、verage of 20 samples 5.Overtaking ratio of different control rule conditions Because different control conditions of road will produce different overtaking ratio, so we first observe relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control condit

26、ions.(a) Based on passing lane control (b) Based on speed control Fig.5.1.3Fig.5.1.3 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.It can be seen from Fig. 5.1.3: (1) when the vehicle density is less than 0.05, the overtakin

27、g ratio will continue to rise with the increase of vehicle density; when the vehicle density is larger than 0.05, the overtaking ratio will decrease with the increase of vehicle density; when density is greater than 0.12, due to the crowding, it will become difficult to overtake, so the overtaking r

28、atio is almost 0.(2) when the proportion of large vehicles is less than 0.5, the overtaking ratio will rise with the increase of large vehicles; when the proportion of large vehicles is about 0.5, the overtaking ratio will reach its peak value; when the proportion of large vehicles is larger than 0.

29、5, the overtaking ratio will decrease with the increase of large vehicles, especially under lane-based control condition s the decline is very clear. Concrete impact of under different control rules on overtaking ratioFig.5.1.4Fig.5.1.4 Relationships among vehicle density, proportion of large vehicl

30、es and overtaking ratio under different control conditions. (Figures in left-hand indicate the passing lane control, figures in right-hand indicate the speed control. is the overtaking ratio of small vehicles over large vehicles, is the overtaking ratio of small vehicles over small vehicles, is the

31、overtaking ratio of large vehicles over small vehicles, is the overtaking ratio of large vehicles over large vehicles.).It can be seen from Fig. 5.1.4: (1) The overtaking ratio of small vehicles over large vehicles under passing lane control is much higher than that under speed control condition, wh

32、ich is because, under passing lane control condition, high-speed small vehicles have to surpass low-speed large vehicles by the passing lane, while under speed control condition, small vehicles are designed to travel on the high-speed lane, there is no low- speed vehicle in front, thus there is no need to overtake.Impact of different control rules on vehicle speed Fig. 5.1.5 Relationships among vehicle density, proportion of large vehicles and av