Recently day-to-day dynamic congestion pricing schemes with fixed travel demand have been proposed to approach system optimum flows instead of user equilibrium ones. This paper will study the day-to-day dynamic pricing schemes with the elastic demand counterpart to force the traffic system to evolve from the status quo to a stationary state of maximizing the social net benefit, considering a general drivers' behavior adjustment process. The paper will introduce the notion of a strong dynamic optimal toll under which the dynamic social net benefit is monotonically increasing along the day-to-day dynamic flow trajectory until day-to-day dynamic flows become stationary. The dynamic pricing schemes are general in the sense that they are formulated based upon a family of day-to-day dynamics in the literature. The paper will further discuss their mathematical properties and propose a simple solution, namely the dynamic marginal pricing scheme. A numerical study on the well-known Braess and Sioux Falls test networks is conducted to test the performance of the dynamic pricing schemes.
Abstract