RECENT ADVANCES IN THEORY OF DYNAMIC TRAFFIC EQUILIBRIUM ASSIGNMENTS

Abstract

This paper reviews the recent advances in the theory of dynamic traffic equilibrium assignment problems. We mainly discuss a Lagrange coordinate system approach enabling us to analyze the complex network traffic flows transparently. Two types of description of traffic within the approach—traditional fluid approximation models and emergent atomic/particle models—are explained in comparison. Based on the features and relationships of each model and the results on the mathematical properties of equilibrium solutions, the direction of future developments utilizing the superiority of both models is briefly discussed.