Structure and Instability of High-Density Equations for Traffic Flow

TL;DR

This paper derives fluid-dynamic equations for congested traffic from kinetic theory, revealing new instability phenomena and connecting traffic flow modeling with granular flow physics.

Contribution

It introduces a novel derivation of high-density traffic equations incorporating anisotropic interactions, extending previous models with new instability insights.

Findings

Identification of a new type of instability in high-density traffic models

Derivation of equations similar to dense gas dynamics

Relevance to granular flow behavior

Abstract

Similar to the treatment of dense gases, fluid-dynamic equations for the dynamics of congested vehicular traffic are derived from Enskog-like kinetic equations. These contain additional terms due to the anisotropic vehicle interactions. The calculations are carried out up to Navier-Stokes order. A linear instability analysis indicates an additional kind of instability compared to previous macroscopic traffic models. The relevance for describing granular flows is outlined.