Bi-objective Network Equilibrium, Traffic Assignment and Road Pricing

Abstract Multi-objective equilibrium models of traffic assignment state that users of road networks travel on routes that are efficient with respect to several objectives, such as travel time and toll. This concept provides a general framework for mod-elling traffic flow in tolled road networks. We present the concept of time surplus maximisation as a way of handling user preferences. Given a toll, users have a max-imum time they are willing to spend for a trip. Time surplus is this maximum time minus actual travel time. A rational user can be assumed to maximise time surplus, leading to the definition of time surplus maximisation bi-objective user equilibrium. We propose to use such models on the lower level of bi-level models for pricing in road networks under multiple upper level objectives such as minimising total travel time and emissions. In such a model a multi-objective optimisation problem at the upper level is combined with a multi-objective equilibrium problem at the lower level. 1 Traffic Assignment and User Equilibrium Traffic assignment models the route choice of users of a road network. Given a set of origin-destination (OD) pairs and demand for travel between these OD pairs, it determines how many users choose each of the available routes, and thereby the amount of traffic on each section of the road network. Conventional traffic assign-ment is based on the assumption that all users want to minimise their travel time, or more generally, a generalised cost function c(xp) = m(xp)+αt(xp), (1) where xp represents traffic flow on route p, t is travel time, which is dependent on flow, and m is a monetary cost comprising of tolls, vehicle operating cost etc