城市道路拥挤收费下路径选择的演化博弈分析

Evolutionary Game Analysis of Route Choices Under Urban Road Congestion Charging

在城市道路拥挤收费条件下研究出行者出行路径的选择,为政府管理部门提供相关参考。将驾车者划分为高时间价值者和低时间价值者,且居住地和工作地间存在一个包含直达和绕行道路的最简单网络,直达道路在早晚高峰期将征收拥挤费。采用演化博弈的思想,建立了出行者路径选择的效益矩阵,根据雅克比矩阵分析了演化博弈过程的稳定状态,并根据参数的不同分5种情况进行了相应的讨论,最后以算例验证了理论模型的适用性。结果表明,在不征收拥挤费和拥挤费较低时,若拥挤损失大于绕行损失,高、低时间价值者将分别选择直达和绕行道路,反之均倾向于选择直达道路;而在拥挤费较高的情况下,低时间价值者倾向选择绕行以规避直接出行成本的增加,高时间价值者将依然选择直达道路。

The commuters’ travel route choices were studied under urban road congestion so that to provide a reference for the management department of government. The drivers were divided into high VOT（ value of time） and low VOT,there existed a single flat network which contained a direct way and a detour way between residence place and employment place,and direct way in morning and evening rush hours would be imposed congestion toll. The research adapted the idea of evolutionary game,established the beneficial matrix of commuters’ travel route choices. The Jacobi matrix was then used to analyze the steady state of evolutionary game process,discussion was conducted according to parameters from five different situations. Finally,a numerical example was given to demonstrate the applicability of the theoretical model. The experimental results show that high VOT commuters would choose direct way while low VOT commuters would choose detour way if congestion loss was greater than rounded loss when the road was free and congestion toll was low,however,if rounded loss was greater than congestion loss,all commuters were inclined to choose direct way. On the contrary,when congestion toll was high,low VOT commuters would choose detour way to avoid increased direct cost while high VOT commuters would still choose direct way.