Table of Contents
ISRN Probability and Statistics
Volume 2013, Article ID 246045, 10 pages
http://dx.doi.org/10.1155/2013/246045
Research Article

Computable Throughput and Metastability in a Cellular Automaton Model for Traffic Flow

Saint John Fisher College, 3690 East Avenue, Rochester, NY 14618, USA

Received 30 October 2013; Accepted 20 November 2013

Academic Editors: V. Patrangenaru and S. Sagitov

Copyright © 2013 Ryan Gantner. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A cellular automaton model for traffic flow is analyzed. For this model, it is shown that under ergodic initial configurations, the distribution of cars will converge in time to a mixture of free flow and solid blocks. Furthermore, the nature of the free flow and solid block distributions is fully described, thus allowing for a specific computation of throughput in terms of the parameters. The model is also shown to exhibit a hysteresis phenomenon, which is similar to what has been observed on actual highways.