Dynamic Systems, Variational Inequalities and Control Theoretic Models for Predicting Time-Varying Urban Network Flows

Abstract

In this paper, we set forth certain axioms for a positive theory of dynamic urban network flows. We then show that mathematical models which fulfill these axioms may be created by adapting and extending certain fundamental notions from microeconomics and nonlinear systems theory. We further show that models created in this fashion, using concepts of fast and slow dynamic processes, may be manipulated into a variety of mathematical forms, thereby providing a synthesis of dynamic systems, variational inequality and control theoretic perspectives for predicting dynamic urban network flows. We close with a discussion of the implications of this synthesis for route guidance and intelligent vehicle infrastructure. Throughout, our presentation is at a conceptual level; the mathematical arguments are purposely not rigorous to embrace the widest possible readership.