用户均衡与系统最优原则下交通分配模型的建立与分析

Establishment and analysis of traffic assignment model under the user equilibrium and system optimization principle

为了更加深入地理解用户均衡(UE)和系统最优(SO)原则之间的差别与联系,从理论上推导出以路径费用函数为基础的UE模型,并且证明了该模型与Wardrop第一原则等价性。基于这一模型,研究了路段与路径费用函数关系。计算发现,路径费用函数可以由该路径所通过路段的费用函数来建立,并且SO原则下,路径费用函数只是UE原则下路径费用函数的一个特例。分别从物理意义和几何意义上解释了UE和SO模型,通过构造不同的道路费用函数使它们之间可以相互转换。经过对比研究表明,所推导的模型可以为交通流分配算法提供新思路、新方法。

In order to better understand the difference and connection between the user equilibrium （UE） and system optimization （SO） principle, the UE model based on route cost function derived by mathematical theory is established. The equivalence of this model to Wardrop first principle is also proved. Based on this model, the relationship between link and route cost function is studied. Through calculating, we find that route cost function can be created by link cost function which is passed by route. Com- pared to route cost function of UE principle, route cost function of SO principle is just a special case. The UE model and SO mod- el are interpreted from physical and geometric points of view of. By constructing different link cost functions, the UE model and SO model can be converted into each other. These results show that the derived model can provide new perspectives and new methods for traffic assignment algorithm.