BECS Collaborative Research: Modeling the Dynamics of Traffic User Equilibria Using Differential Variational Inequalities

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The goal of this project is to employ a novel mathematical paradigm, known as a differential variational inequality (DVI), to study two fundamental problems in transportation analysis, namely, the continue-time dynamic user equilibrium with flow propagation and delays, and the problem of traffic disequilibrium in the face of network disruption. Our aim is to develop a nonlinear dynamical system theory that combines classical ordinary differential equation (ODE) methods with contemporary mathematical programming advances to study the equilibrium of short-time (e.g. within-day dynamics) and the equilibration process of longer-time (e.g. transient dynamics) traffic flows, answering questions such as: how to compute dynamic user equilibria, how traffic evolves from a disequilibrium state, due to network disruptions, toward an equilibrium, and how close the current traffic state is to an equilibrium. Results from this study will lead to a new paradigm integrating traffic network analysis methods with recent advances in mathematical science, and bridge the gaps between current practice of traffic analysis and the needs to consider short-term and long-term traffic dynamics in a holistic manner. The research will be the first step to develop a mathematical framework for traffic dynamic analysis that, in a long term, has the potential to revolutionize the traditional way of conducting transportation analyses such as network signal optimization, dynamic congestion pricing, emergency management after disruptions, among others. Since equilibrium analysis and system dynamics are widely used in other science and engineering fields, the concepts and methodologies developed in this research can also provide new perspectives for equilibrium based analysis in these fields. The research team plans to integrate research findings to undergraduate and graduate courses, and involve undergraduate and graduate students with multidisciplinary backgrounds in this research. The team also plans to reach out to policy makers and practitioners at various transportation management agencies for whom findings from the proposed research will enable them to better manage transportation systems.