Bounding the Efficiency Loss of Logit-Based Stochastic User Equilibrium under Tradable Credit Scheme

Existing studies on bounding selfish route choice behavior inefficiency have shown that efficiency loss of deterministic user equilibrium (UE) against system optimum (SO) has an upper bound independent of network topology. This paper bounds travel time inefficiency of logit-based stochastic user equilibrium (SUE) under a tradable credit scheme (TCS). SUE with TCS (SUE-TCS) network flow patterns may deviate from those of traditional SUE, thus efficiency loss may vary accordingly. Since SUE considers traveler perception error, two system performance indexes can be defined: traditional SO, which minimizes actual total travel time (ATTT), and stochastic system optimum (SSO), which minimizes perceived total travel time (PTTT). Therefore, logit-based SUE-TCS inefficiency can be defined by either comparing SUE-TCS with SO in terms of ATTT or comparing SUE-TCS with SSO in terms of PTTT. This paper establishes upper inefficiency bounds of logit-based SUE-TCS in the two situations and compares them to existing results. A properly designed TCS can significantly reduce inefficiency in both situations; several existing inefficiency bounds can be viewed as special cases of this study.