方格网络上用户均衡行为效率损失研究

The Research of Efficiency Loss for User Equilibrium Behavior in Grid Traffic Networks

针对用户出行时追求费用最短的路径,而不考虑其它用户如何选择路径,在一般网络中导致系统费用较高的问题,从实际出发,本文重点讨论特殊网络-方格网络上纳什均衡流与系统最优流之间的关系,研究了用户均衡行为的效率损失。研究结果表明,在方格网络上,当路阻函数是系数非负的线性函数和二次函数时,用户均衡行为的效率损失分别是0和0.35,而一般网络中用户均衡行为的效率损失分别是1/3和0.626,说明方格网络具有较好传送流量的功能。该研究为道路建设部门进行道路改造和增加新道路设计提供理论依据。

For the problem that users purse the time-shortest path to assign flow ignoring other users＇ ways of choosing their paths so that the behavior lead to the higher system cost in general network, the relation between user equilibrium flow and system optimization flow is discussed, and the efficiency loss of user equilibrium behavior is analyzed in grid traffic networks in this paper. The efficiency loss in grid traffic networks are and if the cost functions are linear functions and quadratic functions with nonnegative coefficient respectively, which are better than the efficiency loss and in general traffic networks. The research in this paper can give a help in theory aspect to the government in expanding the road network.