A Computable Theory of Dynamic Congestion Pricing

The advent of new commitments by municipal, state and federal governments to construct and operate roadways whose tolls may be set dynamically has brought into sharp focus the need for a computable theory of dynamic tolls. By a computable theory we mean a mathematical representation which is detailed enough to capture the key behavioral and technological considerations relevant to dynamic tolling and which is nonetheless numerically tractable enough to obtain accurate approximations of optimal dynamic toll trajectories. It is clear from the policy debates that surround the issue of dynamic tolls that pure economic efficiency is not the sole or even the most prominent objective of any dynamic toll mechanism that will be implemented. Rather, equity considerations as well as preferential treatment for certain categories of commuters must be addressed by such a mechanism. Accordingly, we introduce in this paper the dynamic optimal toll problem with user equilibrium constraints whose acronym will be DOTPEC. We provide a proof of existence for plausible regularity conditions. We also present two algorithms and test both on a numerical example.