A new stochastic cellular automaton model on traffic flow and its jamming phase transition

TL;DR

This paper introduces a comprehensive stochastic cellular automaton model for traffic flow that encompasses existing models and reveals metastable states and phase transitions through analytical and numerical analysis.

Contribution

It presents a new unified stochastic CA model for traffic flow, including well-known models as special cases, and analytically characterizes phase transitions and metastability.

Findings

Model includes Nagel-Schreckenberg, Quick-Start, and Slow-to-Start models.

Fundamental diagrams show metastable states near critical density.

Analytic phase transition curves match numerical results.

Abstract

A general stochastic traffic cellular automaton (CA) model, which includes slow-to-start effect and driver's perspective, is proposed in this paper. It is shown that this model includes well known traffic CA models such as Nagel-Schreckenberg model, Quick-Start model, and Slow-to-Start model as specific cases. Fundamental diagrams of this new model clearly show metastable states around the critical density even when stochastic effect is present. We also obtain analytic expressions of the phase transition curve in phase diagrams by using approximate flow-density relations at boundaries. These phase transition curves are in excellent agreement with numerical results.