Abstract

We discuss a simple probabilistic cellular automaton (CA) which emulates the flow of cars along a highway. Our Traffic CA captures the essential features of several more complicated algorithms, studied numerically by K. Nagel and others over the past decade as prototypes for the emergence of traffic jams. By simplifying the dynamics, we are able to identify and precisely formulate the self-organized critical evolution of our system. This talk focuses on the Cruise Control case, in which isolated cars move deterministically at maximal speed. An inessential symmetry assumption then leads to a two-parameter model, described in terms of acceleration and braking probabilities. We map out the phase diagram, identifying three qualitatively distinct varieties of traffic which arise, and we give rigorous bounds to establish the existence of a phase transition from free flow to jams. Several other results and conjectures will be presented. From a phenomenological perspective, Traffic CA provides local, particle-conserving, one-dimensional dynamics which cluster, and converge to a mixture of two distinct equilibria. (Joint work with Lawrence Gray, University of Minnesota)