A Computable Theory of Dynamic Congestion Pricing

In this paper we present a theory of dynamic congestion pricing for the day-to-day as well as the within-day time scales. The equilibrium design problem emphasized herein takes the form of an MPEC, which we call the Dynamic Optimal Toll Problem with Equilibrium Constraints, or DOTPEC. The DOPTEC formulation we employ recalls an important earlier result that allows the equilibrium design problem to be stated as a single level problem, a result which is surprisingly little known. The DOPTEC maintains the usual design objective of minimizing the system travel cost by appropriate toll pricing. In addition, we present a direct dynamic generalization of the static e¢ cient toll problem and show that such a generalization involves certain ambiguities that do not arise when the DOTPEC is formed as we suggest herein. A numerical example for the DOTPEC is provided