James Greenberg

Traffic congestion - An instability in a hyperbolic system

In this talk I will analyze a class of second order trafficc 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 uni- formly 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 increas- ing functions of a
Lagrange mass index. These smooth portions are separated by shock waves that travel at computable negative velocity.