Ultra-discrete Optimal Velocity Model: a Cellular-Automaton Model for Traffic Flow and Linear Instability of High-Flux Traffic

TL;DR

This paper introduces an ultra-discrete cellular automaton model for traffic flow based on the optimal velocity model, capturing high-flux traffic instability and solitonic properties.

Contribution

It develops a novel ultra-discrete cellular automaton model derived from the optimal velocity model, linking soliton theory with traffic flow simulation.

Findings

Reproduces high-flux traffic instability

Captures both absolute and convective instability

Inherits solitonic properties from soliton equations

Abstract

In this paper, we propose the ultra-discrete optimal velocity model, a cellular-automaton model for traffic flow, by applying the ultra-discrete method for the optimal velocity model. The optimal velocity model, defined by a differential equation, is one of the most important models; in particular, it successfully reproduces the instability of high-flux traffic. It is often pointed out that there is a close relation between the optimal velocity model and the mKdV equation, a soliton equation. Meanwhile, the ultra-discrete method enables one to reduce soliton equations to cellular automata which inherit the solitonic nature, such as an infinite number of conservation laws, and soliton solutions. We find that the theory of soliton equations is available for generic differential equations, and the simulation results reveal that the model obtained reproduces both absolutely unstable and convectively unstable flows as well as the optimal velocity model.