The paper considers a dynamic traffic assignment model with deterministic queuing and rigid demand for travel between each origin-destination (OD) pair in the network. Traffic flows and costs are functions of within-day time, which is regarded a continuous. Day-to-day time is modelled as continuous and the day-to-day dynamical system is derived naturally from the usual user equilibrium condition, ie travellers make decisions aimed at reducing their own travel costs. Perceived cost is the actual cost experienced by a traveller traversing a given route and travellers cannot change their route once they have departed from the origin. Bottleneck queuing is shown to be Fist-in-first-out (FIFO) at each link, ie traffic cannot exit a link earlier than other traffic entering the link earlier than it. The route cost vector is shown to be a Lipschitz continuous function of the route flow vector using an implicit function theorem. This continuity is sufficient for existence of dynamic user equilibrium. Unlike much of the previous analysis of the bottleneck model that has required certain restrictive assumptions regarding the network structure, this existence result is applicable to all networks. Finally, the set of equilibria is shown to be convex provided that the route cost vector is a monotone function of the route flow vector and strict monotonicity is shown to be sufficient for uniqueness of equilibrium.(A) Reprinted with permission from Elsevier. For the covering abstract see ITRD E134766.
Abstract