Traffic congestion - An instability in a hyperbolic system
by J. M. Greenberg  

Vol. 2 No. 2 (2007) P.123~P.138

ABSTRACT

In this paper we analyze a class of second order tracffic models and show these models support stable oscillatory traveling waves typical of the waves observed on a congested roadway. The basic model has trivial or constant solutions where cars are uniformly spaced and travel at a constant equilibrium velocity that is determined by the car spacing. The stable traveling waves arise because there is an interval of car spacing for which the constant solutions are unstable. These waves consist of a smooth part where both the velocity and spacing between successive cars are increasing functions of a Lagrange mass index. These smooth portions are separated by shock waves that travel at computable negative velocity.

KEYWORDS
Trac modeling and congestion, follow-the-leader model

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35, 65

MILESTONES

Received: 2004-07-16
Revised :
Accepted:

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