Algorithms for Non-Separability Problems: The Departure Time Choice

Abstract

Many algorithms for choice predictions for dynamic traffic assignment (DTA), e.g. route choice or departure time choice, shift travelers from an expensive alternative to a cheaper alternative in order to find the equilibrium. These algorithms work well if the cost for the alternative is mainly dependent on the alternative itself, meaning that when adding/removing travelers to the alternative, the cost increases/decreases respectively. When this is not the case, these algorithms do not converge smoothly (Dafermos, 1980). In this abstract, some examples are given where these non-separability problems occur in DTA. A generic algorithm on how to solve this kind of problem more efficiently is sketched. We demonstrate the convergence of our approach on a simple bottleneck with departure time choice.