20 13 highlights of the national mathematical modeling competition for college students in the Higher Education Club Cup [Description] The highlights are for reference only, and the marking groups in each competition area independently mark the papers according to their own understanding and students' answers.

The difficulty of this topic lies in obtaining traffic data through video data, and on this basis, establishing a mathematical model to analyze the relationship between the degree of road congestion and the upstream traffic flow after some lanes are occupied. When reviewing, please pay attention to the following aspects: the preparation of modeling (the extraction of traffic data in video, including the treatment of video missing and errors), the establishment, solution and analysis methods of the model, the expression of the results, the rationality analysis and expansion of the model.

Question 1.

1. 1. After the road is occupied, the actual traffic capacity needs to be obtained from the traffic data in the video, not just estimated according to the traffic road design standard;

1.2. According to the video information, the change of traffic flow in different time periods and under different conditions should be given, and the calculation method of traffic capacity and the statement or analysis of the reasons should be given;

1.3. When there is no vehicle queuing on the occupied road, the traffic capacity is equivalent to that of a single lane. However, when there are vehicles queuing on the occupied road, the traffic capacity of the road will be reduced because of the vehicles changing lanes and rushing. A good result should clearly point this out.

Question 2.

2. 1. The analysis of video 2 is the same as that of video 1. It is necessary to compare the data of video 2 and video 1 to give the difference of traffic capacity and analyze the reasons;

2.2. Due to the different traffic flow direction downstream of the accident section and the different number of vehicles allocated to each lane upstream, the probability of multi-lane queuing on the road section where the accident is located in the two cases is different, thus affecting the actual traffic capacity. It would be better if you noticed this in the model.

Question 3.

3. 1. Establish a mathematical model, and give the relationship between the queue length of vehicles caused by traffic accidents and the actual capacity of the accident section, the duration of the accident and the upstream traffic flow of the road section;

3.2. The model can take many forms, but it needs to include the above factors. This paper mainly studies the rationality of the model hypothesis, the principle of parameter determination and the computability of the model.

Question 4.

4. 1. This problem is an extension of problem 1 and problem 3, and the capacity obtained by problem 1 and the model calculation result of problem 3 can be used;

4.2. Different from 1 3, when the accident section is close to the traffic light intersection, the driver does not have enough time to adjust the lane, which will increase the multi-lane occupation and affect the traffic capacity, which should be considered in the model calculation;

See the attachment for the traffic light control scheme at the upstream intersection, which will affect the flow distribution of upstream vehicles. It would be better if students can use the attachment to give the traffic signal timing scheme and traffic organization scheme of the upstream intersection.