Eddie Wilson
Car-Following Models as Dynamical Systems and the Mechanisms
for Macroscopic Pattern Formation
I will use a general linear analysis of car-following models
to identify and explain the `dynamic upscaling' effect, where small
wavelength perturbations to traffic flow magnify into large wavelength
structures. (Within very broad bounds, almost all car-following models
can be shown to have this property in the correct way.) I will
then show how this outlook is modified by nonlinear effects
and how
stop-and-go waves may still be found when uniform flow is linearly
stable. If time permits, I will describe some recent results with
Tony Humphries in which we solve for and classify travelling wave
solutions of car-following models in terms of a single
advance/delay
differential equation.
Talk