Discrete stochastic models for traffic flow

TL;DR

This paper analyzes a probabilistic cellular automaton model for single-lane traffic flow on a ring, combining simulations and improved mean-field approximations to understand equilibrium properties and fundamental diagrams.

Contribution

It introduces an enhanced mean-field approximation that accurately predicts traffic flow, extending previous models to higher velocities with excellent agreement to simulations.

Findings

Exact results for maximum velocity 1

Good agreement between analytical and numerical results for higher velocities

Improved approximation captures short-range correlations effectively

Abstract

We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties and calculate the so-called fundamental diagrams (flow vs.\ density) for parallel dynamics. This is done numerically by computer simulations of the model and by means of an improved mean-field approximation which takes into account short-range correlations. For cars with maximum velocity 1 the simplest non-trivial approximation gives the exact result. For higher velocities the analytical results, obtained by iterated application of the approximation scheme, are in excellent agreement with the numerical simulations.