Multiclass Continuous-Time Equilibrium Model for Departure Time Choice on Single-Bottleneck Network

Commuters may react to structural congestion on urban roads and freeways by adjusting their departure time. Single-bottleneck models enable direct insight into the mechanisms of departure time choice. The interaction of user equilibrium departure time choice processes for multiple user classes in continuous time is studied in the situation in which all users have to pass a common bottleneck. The study draws on the bottleneck approach introduced by Vickrey and provides a generic algorithm that solves the departure time choice equilibrium problem given heterogeneous departure time preferences, arbitrary origin-bound and destination-bound rescheduling cost functions, and arbitrary queuing cost functions. For all user classes, the (generalized) queuing costs have a travel duration–dependent component and a travel cost–dependent component. First, a solution is provided for the elastic-demand case. It is shown that the equilibrium departure rates per user class can be calculated directly by calculating the acceptable travel times per user class. Second, a solution is provided for the fixed-demand case. The fixed–demand problem is formulated as a minimization problem that is solved using the Nelder–Mead procedure. The algorithm is illustrated with an example showing the effects of a flat peak-hour road pricing scheme on the departure time choice and total incurred costs per user class.