Deterministic Models for Traffic Jams

TL;DR

This paper investigates deterministic one-dimensional traffic models, revealing phase transitions in discrete cases and self-organized criticality in continuous cases, enhancing understanding of traffic flow dynamics.

Contribution

Introduces a unified analysis of deterministic traffic models, highlighting phase transitions and criticality depending on variable discretization.

Findings

Discrete models exhibit high and low density phases with a clear transition.

Continuous models demonstrate self-organized criticality influenced by the slowest vehicle.

The study provides insights into traffic flow behavior under different modeling assumptions.

Abstract

We study several deterministic one-dimensional traffic models. For integer positions and velocities we find the typical high and low density phases separated by a simple transition. If positions and velocities are continuous variables the model shows self-organized criticality driven by the slowest car.