Congestion derivatives for a traffic bottleneck

Historically, congestion pricing is considered to be an efficient mechanism used to decrease total social cost by charging users' true costs including congestion externalities. Congestion pricing under uncertainty has been relatively little studied. In this paper, we review the literature on deterministic congestion pricing and introduce possible sources of uncertainty for a simple bottleneck. We show that, when prices involve exogenous uncertainty that is independent of the central authority and of individual drivers, total social cost may be expressed in closed form as a function of departure time and uncertainty. We also show that there is a class of financial derivatives based on congestion that have the potential to reduce total social cost. In particular, such derivatives are shown to have the potential to alter drivers' departure behavior and reduce drivers' risks of high variance in trip costs, including congestion tolls. Finally, numerical formulations and examples are given to justify the robustness of our results with respect to more general congestion uncertainty.