Dynamic Equilibrium Assignment Convergence by En-route Flow Smoothing

An essential feature in many dynamic traffic assignment (DTA) models used for planning purposes is to compute the (dynamic) equilibrium assignment, where travellers follow user-optimal routes, leading to minimal experienced route travel times. To compute these time-varying route flows in the equilibrium assignment, an iterative procedure is typically required, in which usually either the route flows or the route costs are averaged over successive iterations in order for the assignment to converge. To speed up this convergence, several methods have been proposed and tested. This paper proposes a new method using enroute route flow smoothing to efficiently derive the dynamic equilibrium assignment. At the same time, the newly proposed method aims at solving potential problems due to grid-locks. When grid-locks (are about to) occur, and consequently travel times increase on these road sections, travellers are rerouted (i.e., take a detour) thereby resolving the grid-lock conditions. These higher travel costs – due to detours and penalties for deviating from their initial route – will lead to different pre-trip route choice decisions, such that in the end an equilibrium still can be determined (where the equilibrium situation does not have grid-lock or circular routes). The method is described and tested on the Sioux Falls network. The application section shows that en-route smoothing indeed resolves grid-locks and speeds up the convergence rate. In the application, when applying en-route smoothing, approximately half the number of iterations is needed to find an assignment yielding an equal duality gap. Some explanations are given for this, and suggestions are made to further investigate how the method can be improved.