Stripe formation instability in crossing traffic flows

TL;DR

This paper analyzes the stripe formation instability in crossing traffic flows using coupled equations, revealing how randomness in traffic entry causes stripe patterns, with explicit formulas and comparisons to simpler models and numerical solutions.

Contribution

It provides an analytical framework for understanding the origin of stripe formation instability in crossing traffic flows, linking it to traffic density and randomness.

Findings

Instability arises from randomness in traffic entry.

Green function forms a Gaussian wave packet with stripe oscillations.

Explicit formulas relate traffic density to stripe characteristics.

Abstract

At the intersection of two unidirectional traffic flows a stripe formation instability is known to occur. In this paper we consider coupled time evolution equations for the densities of the two flows in their intersection area. We show analytically how the instability arises from the randomness of the traffic entering the area. The Green function of the linearized equations is shown to form a Gaussian wave packet whose oscillations correspond to the stripes. Explicit formulas are obtained for various characteristic quantities in terms of the traffic density and comparison is made with the much simpler calculation on a torus and with numerical solution of the evolution equations.