Equilibrium Properties of the Cellular Automata Models for Traffic Flow in a Single Lane

Abstract

In the last thirty years, the application of cellular automata as models of physical systems has attracted much attention, particularly for studying and simulating behaviour of fluid systems and traffic flow. In this work we present a theoretical analysis of the equilibrium properties of the cellular automata models for multi-speed traffic flow in a single lane highway. We hope our studies may advance some steps in the line of establishing a quite well formulated physical theory for these models. Our interest in this problem comes from the believe that general theoretical results about the traffic cellular automata may help very much to improve the speed of the associated computer models that scientists and engineers use for traffic flow simulations; but on another hand, it is much close related to the need of having, in a near future, a simple, but efficient tool for estimating the distribution in space and time of the pollutant emission rates coming from vehicular traffic in urban settlements, in such a way we can use the simulation results as the emissions input for the air pollution dispersion models we use to asses air quality in big urban places like Mexico city.