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VIGRE seminar, spring 2002: Mathematical/Computational Modeling of Traffic Flow

Paul Nelson
Students enrolled
Paul Dostert, Jody Wilson (graduate mathematics students); Tongbin Qu, Lelitha Vanajakshi (graduate civil engineering students); Aaron Watson (graduate nuclear engineering student)
Topics discussed are among the following. Overview of types of models and objectives (Automated Traffic Management Systems). Traffic stream models (fundamental diagrams) -- theory. The Lighthill-Whitham model: Theory and computational techniques. Traffic stream models (fundamental diagrams) -- observational techniques and results Higher-order continuum models. Queuing models and travel times. Introduction to car-following models. Traffic stream models from car-following models. Introduction to nonlinear dynamics. Car-following models as dynamical systems. Introduction to cellular automata models. Introduction to the Prigogine-Herman kinetic model. Traffic stream and continuum models from the Prigogine-Herman kinetic model. Critique of and alternatives to the Prigogine-Herman model. Elements of recent research (largely student presentations of recent research papers), topics to be dictated by student interests.