User Equilibrium with Recourse

Abstract

The focus of this work is to develop a convex mathematical program for static user equilibrium under uncertain link states where users learn the actual state of the arc when they traverse the network and update their route choice in an online manner. The proposed model accounts for one step information where users learn the cost functional form of the links when they reach the upstream node. Two variations of information learning is considered: one where all users reaching a particular node see the same arc states, and another where different users learn different arc states. A convex mathematical programming formulation is proposed and a solution methodology based on the Frank-Wolfe algorithm is provided. Properties of the equilibrium such as existence and uniqueness are discussed. Numerical experiments are conducted on two networks: Nguyen Dupuis and Sioux Falls. Even though the focus of this paper is primarily traffic networks, the fundamental equilibrium model can be applied to other network models where commodities receive information about the state of the network as they traverse the network.