Bounding the Efficiency Loss of Mixed Equilibrium in the Transportation Network with Selfish and Altruistic Users

Abstract

Existing research mainly focuses on the efficiency loss of homogeneous users in the transportation network while little effort has been made to explore the efficiency loss of heterogeneous users. The aim of this article is to investigate the efficiency loss of mixed traffic assignment in the transportation network with selfish and altruistic users. The selfish user chooses a travel path based on the classical user equilibrium (UE) principle and the altruistic user aims to minimize their perceived travel cost (here, the perceived travel cost of each altruistic user is a linear combination of a selfish and altruistic component). Firstly, this article establishes a Variational Inequality (VI) model to depict this mixed traffic assignment. Secondly, the upper bound of this mixed equilibrium traffic assignment is derived by analytic derivation and the relation between the upper bound and the network parameters is obtained. Finally, a numerical example is carried out to validate the analytical result. The analytical and numerical results show that the upper bound of efficiency loss is related to the maximal altruism coefficient, the minimal altruism coefficient and the link travel cost functions.