The Price of Anarchy of Stochastic User Equilibrium in Traffic Networks

Selfish routing in congested networks generally does not minimize total system travel time, and as its direct result, traffic equilibrium is typically inefficient. Bounding the inefficiency of selfish routing has become a recent emerging subject of researches by looking into the worst case ratio of the total cost in a deterministic User Equilibrium (UE) point to the total cost of System Optimum (SO). A central result obtained in the literature is that the inefficiency of UE is bounded, and its worst-case inefficiency or price of anarchy is independent of network topology. This study makes a contribution to the literature by establishing a bound on the inefficiency of the logit-based stochastic user equilibrium (SUE). Our results show that the bound on the inefficiency of SUE depends on the class of link cost functions as well as the degree of perception error and the network complexity, and thus it is generally larger than its deterministic counterpart. Like that an SUE flow pattern approaches deterministic UE as the travel time variability parameter approaches zero, our bounding result reduces exactly to that of the deterministic case. We also find that the network complexity in terms of number of available paths has very limited effect on the inefficiency bound or price of anarchy of SUE.