Efficient Implementation of Method of Successive Averages in Simulation-Based Dynamic Traffic Assignment Models for Large-Scale Network Applications

The method of successive averages remains by far the most widely used solution heuristic in simulation-based dynamic traffic assignment. Its simplicity and the nonrequirement of derivative information for the flow-cost mapping function are the main reasons for its widespread use, especially in the realm of dynamic traffic assignment (DTA). However, its convergence properties in real-life networks have been inconclusive, especially because (a) simulation-based models typically are not well behaved mathematically, and therefore their solution properties are not guaranteed, and (b) predetermined step sizes do not exploit local information in searching for a solution and therefore tend to have sluggish performance properties. An effort was made to improve on the performance of the method of successive averages heuristic for user-equilibrium and system-optimal DTA problems on large congested networks through novel implementations that derive their efficiency from exploiting local information made available in the results of vehicle-based simulation models used to provide the mapping between a feasible path flow assignment and the experienced travel cost in a DTA solution framework. The results of extensive numerical tests on actual networks are reported, confirming the performance improvements attainable with the new approach.