A Computable Theory of Dynamic Congestion Pricing

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dynamic congestion pricing, dynamic user equilibrium, differential variational in-equality, optimal control


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. We describe how an infnite dimensional mathematical programming perspective may be employed to create an algorithm for the DOTPEC. A numerical example is provided.

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Citation / Publisher Attribution

A Computable Theory of Dynamic Congestion Pricing, in R.E. Allsop, M.G.H. Bell & G.H. Benjamin, Transportation and Traffic Theory 2007, p. 1-26