Near-collision dynamics in a noisy car-following model

Hossein Nick Zinat Matin; Richard B. Sowers

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arXiv · 2111.01832

Near-collision dynamics in a noisy car-following model

Hossein Nick Zinat Matin·Richard B. Sowers

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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.

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Hossein Nick Zinat Matin, Richard B. Sowers. 2021-11-02. Near-collision dynamics in a noisy car-following model. https://arxiv.org/abs/2111.01832

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