A COMPARISON OF NETWORK INEFFICIENCY BETWEEN LOGIT-BASED STOCHASTIC USER EQUILIBRIUM AND DETERMINISTIC USER EQUILIBRIUM

A traffic network without central authority often evolves efficiency loss issues, since its users try to minimize their own travel time. If users have perfect information about their accurate travel time, the traffic flow assignment becomes deterministic user equilibrium (UE), whereas the traffic flow assignment in a network whose users have incomplete information becomes logit-based stochastic user equilibrium (SUE). Results obtained from the literature provide the bounds of inefficiency of UE and SUE respectively. This study focuses on the comparison of inefficiency of UE and that of SUE. We define the relative performance ratio of a network as the ratio of its inefficiency of SUE to that of UE, and we present the lower bound and the upper bound of the relative performance ratio. Then we focus on a two-link network. We identify regions where the logit-based SUE leads to a system optimum. Furthermore, we determine a flow region in which the relative performance ratio is strictly less than one, which means SUE performs better than UE. The conditions under which the relative performance ratio reaches its lower bound are also achieved. We further extend our study of the relative performance ratio to networks with parallel routes.