Self-sustained nonlinear waves in traffic flow

TL;DR

This paper introduces 'jamitons', nonlinear traveling wave solutions in traffic flow that resemble detonation waves, demonstrating their existence, stability, and relevance to real traffic congestion phenomena.

Contribution

The study provides a theoretical framework for jamitons, establishing existence criteria, analyzing their properties, and demonstrating their relevance through numerical simulations and applications.

Findings

Jamitons are attracting solutions under certain road conditions.

Numerical simulations show convergence towards jamiton-dominated states.

Jamitons feature sharp density increases over short road segments.

Abstract

In analogy to gas-dynamical detonation waves, which consist of a shock with an attached exothermic reaction zone, we consider herein nonlinear traveling wave solutions, termed "jamitons," to the hyperbolic ("inviscid") continuum traffic equations. Generic existence criteria are examined in the context of the Lax entropy conditions. Our analysis naturally precludes traveling wave solutions for which the shocks travel downstream more rapidly than individual vehicles. Consistent with recent experimental observations from a periodic roadway (Sugiyama et al., New Journal of Physics, 10, 2008), our numerical calculations show that, under appropriate road conditions, jamitons are attracting solutions, with the time evolution of the system converging towards a jamiton-dominated configuration. Jamitons are characterized by a sharp increase in density over a relatively compact section of the roadway. Applications of our analysis to traffic modeling and control are examined by way of a detailed example.