Dynamic congestion pricing models for general traffic networks

In this paper we develop two types of dynamic congestion pricing model, based on the theory of marginal cost pricing. The first model is appropriate for situations where commuters have the ability to learn the best route choices through day-to-day explorations on a network with arc capacities and travel demands that are stable from day to day. The second model is appropriate for situations where commuters optimize their routing decisions each day on a network with arc capacities and travel demands that fluctuate significantly from day to day. We show that two types of time-varying congestion tolls can be determined by solving a convex control formulation of the dynamic system optimal traffic assignment problem on a network with many origins and many destinations. We also show that the dynamic system optimal traffic assignment is an equilibrium for commuters under the tolls in both cases.