The morning commute in urban areas with heterogeneous trip lengths

This paper investigates the equilibrium properties of the morning commute problem at the network level with heterogeneous trip lengths. Congestion is modeled with a Macroscopic Fundamental Diagram relating the space-mean speed of a network to the vehicular accumulation. It is shown for a large class of scheduling preferences that if users have continuously distributed characteristics, the network accumulation at equilibrium is a continuous function of time. With alpha-beta-gamma preferences and under certain conditions, a partial First-In, First-Out (FIFO) pattern emerges at equilibrium among early and late users. This FIFO pattern is strict only within families of users having heterogeneous trip lengths and identical preferences, or vice versa. Simulation results confirmed that an attracting steady-state exists for a wide range of demands and that the predicted patterns are indeed observed.