Cellular automaton models and traffic flow

TL;DR

This paper investigates a cellular automaton model for traffic flow, deriving the fundamental diagram using an improved mean-field approximation that accounts for correlations, with results aligning well with numerical data.

Contribution

It introduces a generalized cellular automaton model for traffic flow and provides an accurate analytical method for fundamental diagram calculation.

Findings

Exact results for maximum velocity 1

Excellent agreement with numerical data for higher velocities

Improved mean-field approximation captures short-range correlations

Abstract

A recently introduced cellular automaton model for the description of traffic flow is investigated. It generalises asymmetric exclusion models which have attracted a lot of interest in the past. We calculate the so-called fundamental diagram (flow vs.\ density) for parallel dynamics using an improved mean-field approximation which takes into account short-range correlations. For maximum velocity 1 we find that the simplest non-trivial of these approximations gives already the exact result. For higher velocities our results are in excellent agreement with numerical data.