Near-collision dynamics in a noisy car-following model

TL;DR

This paper analyzes how small stochastic noise affects near-collision behavior in a car-following model, showing collisions are impossible without noise and unlikely with small noise over large timescales.

Contribution

It provides a detailed boundary-layer analysis of near-collision dynamics under stochastic perturbations in a car-following model, highlighting the impact of noise on collision likelihood.

Findings

Collision is impossible in the noise-free model.

Small noise makes collision asymptotically unlikely over large times.

Large time intervals scale with the inverse square of noise strength.

Abstract

We consider a small stochastic perturbation of an optimal velocity car-following model. We give a detailed analysis of behavior near the collision singularity. We show that collision is impossible in a simplified model without noise, and then we show that collision is asymptotically unlikely over large time intervals in presence of small noise, with large time interval scaling like a square of the reciprocal of the strength of the noise. Our calculations depend on careful boundary-layer analyses.