An improved car-oriented mean-field theory for stochastic traffic flow models

2026/08/05 by Yasar Efe Dai, Andreas Schadschneider, Michael Schreckenberg
Physics and Astronomy · #cond-mat.stat-mech #nlin.CG #physics.soc-ph

paper · pdf

arxiv created 2026/08/05 · arxiv updated 2026/08/07

Abstract

We propose an improved mean-field analysis of cellular automata models of single-lane vehicular traffic. By combining aspects of the Car-Oriented-Mean-Field (COMF) theory and the 2-site cluster method, which have been previously successfully applied to similar models, we aim to capture both short- and long-range correlations more accurately. In contrast to classical mean-field theories, the improved method is well suited for models with inhomogeneous stationary states and able to capture the essential properties of phase separation, e.g. in models with slow-to-start rules. The improved accuracy and new physical insights are illustrated through an application to the VDR model with v_max=1.

Citations

• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• Nonequilibrium Dynamics in Low Dimensional Systems
• Statistical Physics of Vehicular Traffic and Some Related Systems
• Boundary Induced Phase Transitions in Driven Lattice Gases with Metastable States
• The Nagel-Schreckenberg model revisited
• Metastable States in Cellular Automata for Traffic Flow
• Garden of Eden states in traffic models
• Traffic flow models with ‘slow‐to‐start’ rules
• Car-oriented mean-field theory for traffic flow models
• Cellular automata models of traffic flow along a highway containing a junction
• Emergent Traffic Jams
• Discrete stochastic models for traffic flow
• 1/f NOISE IN A TRAFFIC MODEL