The Ergodic Theory of Traffic Jams
Lawrence Gray and
We introduce and analyze a simple probabilistic cellular automaton 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. We focus here on the Cruise Control case, in which isolated cars move deterministically at maximal speed. A 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 derive rigorous bounds to establish the existence of a phase transition from free flow to jams. Many other results and conjectures are 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.
(1.68MB compressed, 8.5MB in Postscript with extensive graphics)
COMPANION GRAPHICS AND EXPERIMENTS
Traffic CA Snapshots from the paper (in gif format, 806K compressed)
Traffic CA Experiments corresponding to the figures of the paper
(in mcl format for use with MCell, + custom palettes, 5K compressed)
MCell, a great 32-bit CA program for Windows, by Mirek Wójtowicz,
to run the above library of mcl Traffic CA experiments.