不完全信息下城市交通量分配研究

Research of Traffic Routing with Incomplete Information in a City

由于缺乏信息,用户在出行时实际上并不能确切知道出发点处的交通量,由于城市私家车越来越多,用户往往会过高的估计出发地的交通量。本文假设所有用户总是悲观的预期即认为出发地有M≥r单位的交通量,其中r表示实际的交通量,悲观流就是所有用户悲观预期交通量时产生的流量。当费用函数是系数非负的线性函数时,证明了用户均衡流总费用不小于悲观流的总费用;当费用函数是系数非负、最大度数为d的多项式函数时,证明了用户均衡流的总费用不超过悲观流总费用的1/τd倍,其中1≥τ=r/M。研究结果表明,当用户过高估计交通量出行时,会改善交通状况,是因为部分用户绕行到费用更大的路径上,缓解了交通压力,改善了交通状况。

Traffic is foregone in the previous research,and users,in fact,don＇t know the exact traffic when they choose their paths at some time owing to lack of information,so they often overestimate the traffic for cars become more and more.In this paper,we assume that all users think havingM≥runits traffic pessimistically and the corresponding flow is named pessimistic flow in the network,where r is the real traffic.We give a tight upper bound about the ratio between the cost of user equilibrium flow and pessimistic flow,which indicates that pessimistic flow is better than user equilibrium flow if the latency function is linear functions with nonnegative coefficient.Meanwhile,a lower bound1/τd is given between the cost of user equilibrium flow and that of pessimistic flow in network with polynomial latency functions,where1≥τ=r/M and d is the most degree of latency functions.The results indicate that some users detour when they have more traveling time so that the performance of network is improved.