Engineering studies demonstrate that traffic in dense downtown areas obeys a stable functional relationship between average speed and density, including a region of 'hypercongestion' where flow decreases with density. This situation can be described as queuing behind a bottleneck whose capacity declines when the queue is large. We combine such a variable-capacity bottleneck with Vickrey scheduling preferences for the special case where there are only two possible levels of capacity. Solving the model leads to several new insights, including that the marginal cost of adding a traveler is especially sensitive to the lowest level of capacity reached. We analyze an optimal toll, a coarse toll, and metering, showing substantial benefits from using these policies to eliminate the period of reduced capacity. Under hypercongestion, all of these policies can be designed so that travelers gain even without considering any toll revenues.
