NEAR-COLLISION DYNAMICS IN A NOISY CAR-FOLLOWING MODEL

Hossein Nick Zinat Matin, Richard B. Sowers

Research output: Contribution to journalArticlepeer-review

Abstract

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

Original languageEnglish (US)
Pages (from-to)2080-2110
Number of pages31
JournalSIAM Journal on Applied Mathematics
Volume82
Issue number6
DOIs
StatePublished - 2022

Keywords

  • Brownian perturbations
  • asymptotics
  • car-following dynamics
  • differential equations

ASJC Scopus subject areas

  • Applied Mathematics

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