Stability and homogenization of the optimal velocity model

Abstract

Local and collective stability analysis give the conditions for that the stationary solutions of car-following models are uniform. Recent homogenization methods allow to obtain sufficient conditions for that the system converges with no collision to the uniform solution. These conditions are calculated and illustrated by numerical experiments with the linear optimal velocity model. As expected, the homogenization condition is more restrictive than the condition for the collective stability. More precisely, the homogenization condition corresponds to the overdamped case of the local stability.