In stochastic traffic assignments, if the total perceived travel cost of all users is used as the system performance index, the stochastic system optimum (SSO) assignment will then be to minimize the total perceived travel cost. In this study, we investigate the efficiency loss caused by the stochastic user equilibrium (SUE) traffic assignment against the SSO assignment. The efficiency loss is defined as the difference between these two assignments. Two variational inequality (VI) models are presented to formulate the time-based and monetary-based SUE route choice behaviors respectively, in traffic networks with multiple user classes and fixed demand. The upper bounds of the efficiency losses caused by these two kinds of behaviors are analytically derived and their relations to some network parameters are discussed.
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