Application of a Complementarity Approach to Large Scale Traffic Equilibrium Problems

Abstract

The applied Aashtiani’s Complementarity formulation to solve a large-scale static traffic equilibrium problem. This formulation requires very weak assumptions and is capable of computing a very general form of traffic equilibrium including multi-modal, multi-class user, multi-variate demand functions, and multi-variate link performance functions equilibria. The traffic equilibrium problem for a large metropolitan area has been formulated as a nonlinear Complementarity problem and solved via decomposition and linearization techniques. A dynamic memory data structure has been introduced to accommodate the data manipulation needs for this path-based formulation. The results of this approach have been compared to that of the conventional Beckman’s formulation under various scenarios. It is shown that the Complementarity formulation not only is capable of handling real-life problems, but also outperforms the conventional Frank-Wolf algorithm. The benefits of this approach become even more eminent when the complexity of the problem increases either due to severe congestion or higher accuracy requirements.

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