Dynamic traffic assignment for urban road networks

Abstract

This paper presents a nonlinear programming formulation of the dynamic user-equilibrium assignment problem (DUE) for urban road networks with multiple trip origins and destinations. DUE is a temporal generalization of the static user-equilibrium assignment problem (SUE) with additional constraints to insure temporally continuous paths of flow. In DUE, the full assignment period of several hours is discretized into shorter time intervals of 10–15 minutes each for which trip departure matrices are assumed to be known. This formulation of DUE includes SUE as a special case in which there is only one time interval for the full assignment period. The assumption of steady-state flows allows SUE to have all linear constraints, but DUE requires nonlinear flow continuity constraints. Whereas SUE is typically solved by methods of linear combinations, these methods create temporally discontinuous flows if applied to DUE. A dynamic traffic assignment heuristic (DTA) is presented that generates approximate solutions to DUE in an efficient manner for large networks. DTA is not a convergent solution algorithm for DUE, but was designed instead to produce assignments that approximate the DUE optimality conditions. An overview of alternative dynamic assignment approaches is given, including the limitations of other optimization and simulation approaches. Test results presented in this paper show that DTA generates both static and dynamic assignments that approximately satisfy the user-equilibrium conditions of these problems.