汕头大学学报（自然科学版）

本文是对2013年全国大学生数学建模竞赛A题的解答.通过参考国家标准的道路通行能力评价体系,建立了准确求解道路在发生交通事故后的实际通行能力的数学模型;同时,基于交通流二流理论建立了排队长度分析模型,评估其与各影响因素之间的关系.在问题1中,以红绿灯导致的车流量周期性变化规律为依据,引入相关修正系数对模型进行修正,得出求解实际通行能力的模型.在问题2中,对统计数据进行加权平均后计算出道路的实际通行能力,再对比所堵车道的车流量,分析得车道车流量与通行能力的关系.在问题3中,根据交通流二流理论和流量稳定方程建立排队长度的分析模型,再运用控制变量法和MATLAB制图定性分析车辆排队长度与事故断面实际通行能力、事故持续时间和路段上游车辆数间的灵敏度.在问题4中,利用问题3建立的当量排队模型进行适当推导,即得排队长度达到140 m的时间估算模型.

In this paper, a solution is presented for the Problem A of Contemporary Undergraduate Mathematical Contest in Modeling in 2013. A model was built for calculating the passing capacity of city roads after traffic accidents,with reference to the traffic capacity of the national standard evaluation system. Meanwhile, a model of queuing length was built to figure out the relation between factors from the traffic flow second-rate theory. Based on cyclic variation of traffic flow and by adding correction factors, a model for calculating actual passing capacity was built in Question 1. In Question 2, the relation between traffic flow and passing capacity was figured out by taking a weighted average of the actual passing capacity of the road and comparing the traffic flow at different times. A model was built to evaluate the effect of queuing length,incident duration and the amount of vehicles on the upstream section to actual passing capacity during traffic accidents,according to the traffic flow second-rate theory and flow stability equation. In Question 4,the time when the queuing length is 140 meters was figured out via using the model of Question 3.