Efficiency loss of mixed equilibrium associated with altruistic users and logit-based stochastic users in transportation network

Abstract

The efficiency loss of mixed equilibrium associated with two categories of users is investigated in this paper. The first category of users are altruistic users (AU) who have the same altruism coefficient and try to minimize their own perceived cost that assumed to be a linear combination of selfish component and altruistic component. The second category of users are Logit-based stochastic users (LSU) who choose the route according to the Logit-based stochastic user equilibrium (SUE) principle. The variational inequality (VI) model is used to formulate the mixed route choice behaviours associated with AU and LSU. The efficiency loss caused by the two categories of users is analytically derived and the relations to some network parameters are discussed. The numerical tests validate our analytical results. Our result takes the results in the existing literature as its special cases.