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arXiv · 1912.04416

Structural Properties of the Stability of Jamitons

Rabie A. Ramadan·Rodolfo Ruben Rosales·Benjamin Seibold
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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.

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Rabie A. Ramadan, Rodolfo Ruben Rosales, Benjamin Seibold. 2019-12-09. Structural Properties of the Stability of Jamitons. https://doi.org/10.1007/978-3-030-66560-9_3

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