Discrete-time dynamic road congestion pricing under stochastic user optimal principle

Road pricing is believed to be an effective instrument for alleviating roadway congestion. Most existing road pricing schemes are developed based on traditional static traffic equilibrium models, in which a fixed toll can be obtained to support the corresponding traffic flow pattern as an equilibrium. However, static models cannot consider the evolution process of traffic flow caused by the day-to-day fluctuations of road users' route choices. Under practical traffic conditions, the multiple traffic equilibria may exist (e.g., due to the asymmetric travel cost function). Indeed, the fixed road pricing scheme derived from the equilibrium model cannot guarantee that the dynamic traffic system can converge to the desired equilibrium state from any initial traffic state. This study, assuming that travelers follow the stochastic user optimal principle, develops a day-to-day dynamic road pricing scheme that can drive the traffic dynamic system to converge to a given stochastic user equilibrium (SUE) even when the traffic system has multiple SUE states. The characteristic of this dynamic road pricing scheme is verified by rigorous proof and numerical tests in this study.