美赛A题论文Word文件下载.docx

1、T3T4Team Control Number27400Problem ChosenAF1F2F3F42014 Mathematical Contest in Modeling （MCM） Summary Sheet（Attach a copy of this page to your solution paper.） Type a summary of your results on this page. Do not includethe name of your school, advisor, or team members on this page. SummaryThe aim o

2、f this paper is to evaluate the performance of the changing lane rule named Keep-Right-Except-To-Pass and compare other rules weve constructed with the given one.The performance of changing lane rules mainly manifest in safety and traffic flow. Meanwhile, safety is influenced by posted speed limits

3、and traffic density and traffic flow is influenced by average speed.First we construct Model 1 to describe the relationship between posted speed limits, traffic density and safety, noting that safety has negative correlation with collision times and can be fully expressed by it. Therefore we use Mat

4、lab to imitate the changing lane and collision process. Then we construct Model 2 to describe the relationship between traffic flow and average speed. Combining the result of Model 1and 2, we can conclude that the higher the posted speed limits and the lower the traffic density, the higher level saf

5、ety an traffic flow could reach, and the Keep-To-Right-Except-To-Pass rule has the best performance.Then we construct Model 3 to compare some normal changing lane rules with the given one and with each other. Thus we imitate all the rules using algorithm given by model 1. We introduce a new concept

6、named Standard Time to express traffic flow and still collision times to express safety. The result is that when a freeway road contains 2 lanes, the given rule shows the best performance. And when the number of lanes becomes 3, then the Choose-Speed rule, a very common traffic rule acts the best.As

7、 for the left-driving countries, we first choose the best rules and mirror symmetrically modify them. Then use the method of Model 2 to imitate performances of these rules. We have observed that these two best rules can be simply carried over.Finally, we have a short discussion about the intelligent

8、 system. Since speed can be fastest and changing lanes can be well planned, we regard this system as absolutely safe traffic which has the largest traffic flow.1. Introduction1.1 Analysis to the problemThis problem can be divided into 4 requirements that we must meet, listed as follows:（1） Build a m

9、athematical model to demonstrate the essence of Keep-Right-Except-To-Pass rule in light and heavy traffic;（2） Show the effects of other reasonable changing-lane rules or conditions by using the modified model built in the former requirement;（3） Determine whether the left-side-driving countries can u

10、se the same rule（s） with simple mirror symmetric modification, or must add some requirements to guarantee the safety or traffic flow;（4） Construct an intelligent traffic system which does not depend on humans compliance, and then compare the effects with earlier analysis.Therefore, this problem requ

11、ires us to evaluate the performances of several changing-lane rules, especially the Keep-Right-Except-To-Pass rule while performances mainly manifest in traffic flow and safety. It is obvious that speed limit and the number of cars influent cars speed and then the performances of those rules. To sol

12、ve requirement （2）, we will use the same method as above. But all rules we constructed should be discussed, imitated and compare with each other.To discuss the left-driving countries, we will conclude the best rules from requirement 2 and apply to those countries. Then compare results with that of r

13、ight-driving countries. If the results are totally the same, then those rules can be simply carried over with simple change. If not, additional requirement are needed.As for the intelligent system, we assume no collision will happen. So a simple discussion is feasible.1.2 Crucial method for the prob

14、lem To imitate the process of changing lanes and collision, we will construct an algorithm named Changing-line and Collision. This will show the state of a number of car on the same stretch of freeway road, including going straight, changing lane to pass and traffic collision. The imitation process

15、will be delivered on Matlab;2. Symbols and definition SymbolDefinitionUnitFLOTraffic FlowMU, Average Speedmiles/hStandard Deviation of Speed85% Percentile of Normal Distribution70% Percentile of Normal DistributionTraffic Density（Note: expressed by the number of cars）Standard TimeCollision Times3. General hypotheses for all models（1） All freeway roads contain either two or three lanes.（2）