Steepest Descent Day-to-Day Dynamic Toll

Day-to-day dynamic congestion pricing schemes have been recently proposed to force the traffic system to evolve from the status quo to a stationary state of system optimum instead of user equilibrium, considering drivers’ day-to-day behavior adjustments. From the perspective of traffic management, it may be desirable to expedite the evolution process such that the total travel cost across the process can be reduced. A novel steepest descent dynamic toll scheme is proposed that minimizes the derivative of the total system cost with regard to day t or reduces the total system cost the most for each day. The problem of finding the steepest descent scheme is first formulated as a piecewise linear nonsmooth optimization problem and then transformed into a standard linear programming problem. Its mathematical properties are discussed further and a solution procedure is proposed for specifying the steepest descent pricing scheme. A numerical study of the well-known Braess network and the Sioux Falls, South Dakota, network is conducted to compare the performance of different dynamic pricing schemes.

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