瓶颈路段上拥挤收费水平与收费时段的优化问题

Optimization of the Tolling Level and Tolling Period for Bottleneck Model

本文主要在瓶颈路段建立单一收费方案,并且优化瓶颈路段上的拥挤收费水平和收费时段.首先,应用Greenshields模型描述了瓶颈路段上流量的演化过程,并计算每个时刻出行者的出行时间和出行费用.通过出行费用与流量的关系调整每个时刻流量的分配,得到稳定状态时排队的长度和运动部分的速度.然后,建立双层规划模型,其中上层模型是最小化最大排队车辆数和最大化运动部分的最小速度,下层模型是应用Greenshields模型模拟出行者的出行行为.应用改进的遗传算法求解双层规划模型,得到最优的收费水平和收费时段.最后,应用一个简单的算例来验证本文所建立的模型及其算法,并且通过变换参数来分析所得到的现象和结论.

This paper mainly analyzes the problem of step-toll on a bottleneck link and optimizes the level and period of congestion pricing in single- step- toll method on a bottleneck link. Firstly, based on Greenshields model, this paper describes the propagation of flow on the bottleneck link, and calculates the travel time and the travel costs of the travelers ＇departing at each time. The flows of all the time are adjusted by the relationship between total trip costs and flows until the flows reach the UE equilibrium. And Greenshields model is applied to obtain the queue length and the speed of the moving part at a stable state. Then, the bi-level programming model is established, in which the upper level is to minimize the maximal queue length and to maximize the minimal speed, and the lower programming is to simulate the travel behaviors using the Greenshields model. The bi-level programming model is solved by an improved genetic algorithm, to obtain optimal pricing level and pricing period. Finally, a simple example is given to illustrate the application of the model and the algorithm. The phenomena and conclusions are analyzed by transformation parameters based on optimal pricing level and pricing period.