Structural Properties of the Stability of Jamitons

TL;DR

This paper investigates the stability of jamitons, nonlinear traffic waves, using computational methods and stability analysis to determine which jamitons can form and persist in traffic flow models.

Contribution

It introduces a novel procedure for characterizing jamiton stability and highlights the importance of shock perturbations and sonic points in their stability analysis.

Findings

Certain jamitons are shown to be dynamically stable.

Stability depends on proper treatment of shock perturbations.

The study identifies conditions under which jamitons form and persist.

Abstract

It is known that inhomogeneous second-order macroscopic traffic models can reproduce the phantom traffic jam phenomenon: whenever the sub-characteristic condition is violated, uniform traffic flow is unstable, and small perturbations grow into nonlinear traveling waves, called jamitons. In contrast, what is essentially unstudied is the question: which jamiton solutions are dynamically stable? To understand which stop-and-go traffic waves can arise through the dynamics of the model, this question is critical. This paper first presents a computational study demonstrating which types of jamitons do arise dynamically, and which do not. Then, a procedure is presented that characterizes the stability of jamitons. The study reveals that a critical component of this analysis is the proper treatment of the perturbations to the shocks, and of the neighborhood of the sonic points.