Bounding the inefficiency of selfish route choice behavior is a very interesting research topic and has received much attention in the transportation community. Existing studies have shown that the efficiency loss of deterministic user equilibrium (UE) against system optimum (SO) has an upper bound which is independent of network topology. This paper makes a contribution to the literature by bounding the travel time inefficiency of the logit-based stochastic user equilibrium (SUE) under tradable credit scheme (TCS). The network flow patterns of SUE with TCS (SUE-TCS) may deviate from that of traditional SUE, thus the efficiency loss may also vary accordingly. Since the traveler's perception error is considered in the SUE context, two system performance indexes can be defined: the traditional SO which minimizes the actual total travel time (ATTT) of all travelers, and the stochastic system optimum (SSO) which minimizes the perceived total travel time (PTTT) of all travelers. Therefore, there are two ways to define the inefficiency of Logit-based SUE under TCS, i.e. to compare SUE-TCS with SO in terms of ATTT, or to compare SUE-TCS with SSO in terms of PTTT. This paper establishes the upper bounds of the inefficiency of Logit-based SUE-TCS in the two situations respectively, and their relationships with the existing results are discussed. It is found that a properly designed TCS can reduce the efficiency loss to a large extent in both situations, and several existing inefficiency bounds can be viewed as the special cases of this study.

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