Inside the queue: hypercongestion and road pricing in a continuous time - continuous place model of traffic congestion

Abstract

This paper develops a continuous time - continuous place model of road traffic congestion, based on car-following theory. The model fully integrates two archetype representations of traffic congestion technology, namely "flow congestion", originating in the works of Pigou, and "vertical queuing" models, pioneered by Vickrey. Because a closed-form analytical solution of the formal model does not exist, its behaviour is explored in a numerical exercise. In a setting with endogenous departure time choice and with a bottleneck halfway the route, it is shown that "hypercongestion" can arise as a dynamic - transitional and local - equilibrium phenomenon. Also dynamic toll schedules are explored. It is found that a toll rule based on an intuitive dynamic and space-varying generalization of the standard Pigouvian tax rule can hardly be improved upon. A naïve application of a toll schedule based on Vickrey´s bottleneck model, in contrast, performs much worse and actually even reduces welfare.