On a discrete optimal velocity model and its continuous and ultradiscrete relatives

TL;DR

This paper introduces a discrete traffic flow model with discrete time, deriving its continuum and ultradiscrete limits, revealing phase transitions, and connecting to existing models like Fukui-Ishibashi.

Contribution

It presents a novel discrete traffic model with continuum and ultradiscrete limits, linking it to established traffic flow models and analyzing phase transitions.

Findings

Phase transition from free flow to jam observed

Ultradiscrete model includes Fukui-Ishibashi model as a special case

Both models exhibit fundamental diagram phase transition

Abstract

We propose a discrete traffic flow model with discrete time. Continuum limit of this model is equivalent to the optimal velocity model. It has also an ultradiscrete limit and a piecewise-linear type of traffic flow model is obtained. Both models show phase transition from free flow to jam in a fundamental diagram. Moreover, the ultradiscrete model includes the Fukui-Ishibashi model in a special case.