Mean-field theory for the Nagel-Schreckenberg model with overtaking strategy

TL;DR

This paper applies mean-field theory to analyze a modified Nagel-Schreckenberg traffic model with overtaking, revealing how overtaking influences flow and the role of braking probability in phase transitions.

Contribution

It provides a theoretical mean-field analysis of the NSOS model, especially for the case with overtaking, offering insights into traffic flow dynamics and phase transition mechanisms.

Findings

Traffic flow increases with overtaking at high densities.

Braking probability p dominates the transition density influence.

Exact solutions obtained for the case v_max=1.

Abstract

Based on the Nagel-Schreckenberg (NS) model with periodic boundary conditions, a modified model considered overtaking strategy (NSOS) has been proposed \cite{su2016occurrence,su2016the}. In this paper, we focus on the theoretical analysis of traffic flow for NSOS model by using mean-field method. In the special case of $v_{max}=1$ where vehicles can not overtake preceding ones, the features of stationary state can be obtained exactly. However, in the case of $v_{max}>1$ where overtaking happens, some approximative methods have to be took into account. The main results are that we find the reason why traffic flow is increased in the regime where densities exceed the maximum flow density, and the influence of traffic flow on the transition density is dominated by the braking probability $p$.