Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues

This paper considers a simultaneous route and departure time choice equilibrium assignment problem in network with queues. The problem is modeled on discrete-time basis and formulated as an equivalent ‘zero–extreme value’ minimization problem, in which the first-in-first-out behavior at intersection is guaranteed by proper formulation of the dynamic link travel times. A heuristic solution algorithm is proposed, which simulates a normal day-to-day dynamic system by a route/time-swapping process, thereby reaching to an extreme point of the minimization problem. The existence of discrete-time dynamic user-equilibrium solutions is investigated. The iteration-to-iteration stability of the proposed algorithm is discussed, together with numerical results on two example networks.