Endogenous Trip Scheduling: The Henderson Approach Reformulated and Compared with the Vickrey Approach

Two approaches to modeling peak-period congestion that account for travelers' scheduling behavior have made their way into the economics literature. On the demand side of both approaches, travelers trade off a cost of travel delay against a cost of being early or late at destination in scheduling their trip. On the supply side, the Vickrey approach uses a queuing-congestion technology; the Henderson approach uses a flow-congestion technology, assuming that the travel time for any traveler is determined by the departure flow he departs with at origin. But the Henderson approach is found to have problems. This paper illustrates these problems; shows that they can be eliminated by assuming that the travel time for any traveler is determined by the arrival flow he arrives with at destination; and compares the behavior of the Vickrey and reformulated Henderson approaches both analytically and using simulations. The paper finds that the behavior of the reformulated Henderson approach varies with its elasticity of travel delay with respect to traffic flow, while the Vickrey approach lacks such a flexibility; and that the behavior of the Vickrey approach is the limit of that of the reformulated Henderson approach as the elasticity of travel delay goes to infinity.