Analysis of Price of Anarchy in Traffic Networks With Heterogeneous Price-Sensitivity Populations

In this paper, we investigate how the scaled marginal-cost road pricing improves the price of anarchy (POA) in a traffic network with one origin-destination pair, where each edge in the network is associated with a latency function. The POA is defined as the worst possible ratio between the total latency of Nash flow and that of the socially optimal flow. All players in the noncooperative congestion game are divided into groups based on their price sensitivities. First, we consider the case where all players are partitioned into two groups in a network with two routes. In this case, it is shown that the total latency of the Nash flow can always reach the total latency of the socially optimal flow if the designed road price is charged on each link. We then analyze the POA for general case. For a distribution of price sensitivities satisfying certain conditions, a road pricing scheme is designed such that the unique Nash flow can achieve the social optimal flow, i.e., $\text {POA}=1$ . An algorithm is proposed to find the price scheme that optimizes the POA for any distribution of price sensitivities and any traffic network with one origin-destination pair. Finally, the results are applied to a traffic routing problem.