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ITS technologies that aim to improve, and ideally optimize, the utilization of the transportation network require accurate and efficient traffic models and algorithms. For many applications, these models must solve the dynamic traffic assignment problem - i.e., to find the optimal path choices for all vehicles in the network - within a reasonable margin of error in the shortest possible time. This paper presents an iterative algorithm for the dynamic (time dependent) user-optimal assignment problem. The algorithm produces time-dependent assignments which, when used in a traffic simulation model, result in experienced path travel times that approximately satisfy user-optimal conditions. The model is tested on a small but challenging network, for which convergence (to equilibrium) results are compared with those obtained using a variant of the method of successive averages (MSA). The model results are also examined in detail by comparison with the exact equilibrium queue lengths determined analytically. The proposed model is found to perform very well under these tests, and to converge faster than the MSA.