Analytical Studies on a Modified Nagel-Schreckenberg Model with the Fukui-Ishibashi Acceleration Rule

TL;DR

This paper introduces a modified cellular automaton traffic model combining FI acceleration and NS stochastic delay, providing analytical solutions for traffic flow characteristics that align well with simulations.

Contribution

It presents an analytical approach to a modified Nagel-Schreckenberg model incorporating Fukui-Ishibashi acceleration rules, enhancing understanding of traffic flow dynamics.

Findings

Analytical fundamental diagrams for speed and flux derived.

Excellent agreement between theory and simulations.

Enhanced analytical understanding of the NS model.

Abstract

We propose and study a one-dimensional traffic flow cellular automaton model of high-speed vehicles with the Fukui-Ishibashi-type (FI) acceleration rule for all cars, and the Nagel-Schreckenberg-type (NS) stochastic delay mechanism. By using the car-oriented mean field theory, we obtain analytically the fundamental diagrams of the average speed and vehicle flux depending on the vehicle density and stochastic delay probability. Our theoretical results, which may contribute to the exact analytical theory of the NS model, are in excellent agreement with numerical simulations.