The ergodic theory of traffic jams (joint work w/ David Griffeath)

Lawrence Gray
University of Minnesota
School of Mathematics

A simple "particle-hopping" model for traffic will be presented. This model is related to the Nagel-Schreckenburg model, but it is mathematically more tractable. The model has several distinct ergodic (unmixed) phases, with multiple critical points. When traffic density exceeds the lowest critical value, the model produces large, persistent, well-defined traffic jams spontaneously from uniform initial conditions, somewhat like the condensation of droplets in a vapor. Between the two lowest critical values, there is a nonergodic mixture of "jammed" and "free-flowing" phases. Mathematical analysis is accomplished in part by making interesting transformations of the model. Computer simulations will be used to illustrate various phenomena.

Presentation (PDF File)

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