Nonlinear Optimal Velocity Car Following Dynamics (II): Rate of Convergence In the Presence of Fast Perturbation

Traffic flow models have been the subject of extensive studies for decades. The interest in these models is both as the result of their important applications as well as their complex behavior which makes them theoretically challenging. In this paper, an optimal velocity dynamical model is considered and analyzed. We consider a dynamical model in the presence of perturbation and show that not only such a perturbed system converges to an averaged problem, but also we can show its order of convergence. Such understanding is important from different aspects, and in particular, it shows how well we can approximate a perturbed system with its associated averaged problem.