Car-oriented mean-field theory for traffic flow models

TL;DR

This paper introduces a novel mean-field analytical approach for single-lane traffic cellular automaton models that accounts for inter-car distances, successfully reproducing exact and simulation results.

Contribution

It proposes a new analytical framework based on inter-car distances instead of site occupation, capturing longer-range correlations in traffic models.

Findings

Exact solution for v_max=1 model

Good agreement with simulations for v_max=2

Enhanced understanding of traffic flow dynamics

Abstract

We present a new analytical description of the cellular automaton model for single-lane traffic. In contrast to previous approaches we do not use the occupation number of sites as dynamical variable but rather the distance between consecutive cars. Therefore certain longer-ranged correlations are taken into account and even a mean-field approach yields non-trivial results. In fact for the model with $v_{max}=1$ the exact solution is reproduced. For $v_{max}=2$ the fundamental diagram shows a good agreement with results from simulations.