Efficiency loss of the multi-class stochastic traffic equilibrium assignment with fixed demand

There exists efficiency loss when introducing a user equilibrium traffic assignment in comparison with the system optimization assignment. Seeking the upper bound of the efficiency loss has attracted many scholars' attentions. The existing researches mainly focus on single user class and deterministic traffic assignment, few on stochastic user equilibrium (SUE) assignment with multiple user classes. In this paper, the authors investigate the upper bound of this SUE's inefficiency. Two decision making criteria are used in the SUE, namely, time-based and monetary-based. It is shown that the upper bound of efficiency loss caused by the time-based SUE depends on the type of link travel time function, the network complexity, the travel demand, and the degree of users' perception error to travel cost. The upper bound of efficiency loss caused by the monetary-based SUE depends on the value of time of user classes besides the aforementioned factors.