User Equilibrium in a Bottleneck under Multipeak Distribution of Preferred Arrival Time

The pattern of departure times at a single bottleneck is studied under general heterogeneous preferred arrival times. Three main outputs are delivered. First, the existence of equilibrium is proved without the classical S-shape assumption of the preferred arrival time distribution–that is, that demand, represented by the flow rate of preferred arrival times, may exceed bottleneck capacity only on one peak interval. Second, a generic algorithm is given to solve the equilibrium problem for departure time choice. Finally, the graphical approach that pervades the algorithm provides insight into the structure of the queued periods, especially by characterizing the critical instants at which the entry flow switches from a loading rate (overcapacity) to an unloading rate (undercapacity) and vice versa. Numerical illustration is given.