On Efficiency Loss of Multiclass Traffic Equilibrium Assignment with Elastic Demand

Seeking the upper bound of the efficiency loss in traffic assignment has attracted many scholars’ attentions in the last decade. The existing researches mainly focus on traffic assignment with fixed demand, few on user equilibrium (UE) assignment with elastic demand focus on single user. In this paper, the authors investigate the efficiency loss of multiclass traffic equilibrium assignment (MTEA) with elastic demand. Two decision making criteria are used in this traffic assignment problem, namely, time-based and monetary-based. The variational inequality (VI) models for MTEA under time-based decision criterion and monetary-based decision criterion are formulated. The efficiency loss caused by this two decision criterion is analytically derived and the relations to some network parameters are discussed. It is shown that the upper bound of efficiency loss caused by the time-based assignment depends on the type of link travel time function, the ratio of user benefit and the total social surplus under time-based at traffic equilibrium assignment state. The upper bound of efficiency loss caused by monetary-based assignment depends on the type of link travel time function, the value of time (VOT) of user classes, the ratio of user benefit and the total social surplus under monetary-based at traffic equilibrium assignment state, the ratio of user benefit at system optimum (SO) and the total social surplus at traffic equilibrium state under monetary –based. The numerical tests validate our analytical results.