Bi-objective network equilibrium, traffic assignment and road pricing

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 modelling 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 maximum 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.