Phantom traffic jams, jamitons, and the sub-characteristic condition

Rodolfo Rosales
Massachusetts Institute of Technology

The sub-characteristic condition (SCC) was introduced by Whitham in the 1950's to characterize the stability of steady state solutions in hyperbolic systems with relaxation terms. For systems like this, an important question is: what is the behavior of the system in the zero relaxation limit? Is it the lower order system that naively arises via a regular expansion in the small relaxation parameter, or is it something else? In the context of continuum models for traffic flow, this translates into when a 2nd order model is well approximated by its corresponding 1st order model. Much analysis has been done on this question, and the rough answer is that this happens when the SCC is satisfied [or an appropriate generalization when shocks are involved].

However, what happens when the SCC condition is not satisfied? This is the regime in which phantom traffic jams occur. We argue that, for generic 2nd models of traffic flow, in this regime the solutions are dominated by jamitons.

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