@article{c2462a19416a49b0a995359fc1c3379f,
title = "NEAR-COLLISION DYNAMICS IN A NOISY CAR-FOLLOWING MODEL",
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.",
keywords = "asymptotics, Brownian perturbations, car-following dynamics, differential equations",
author = "Matin, {Hossein Nick Zinat} and Sowers, {Richard B.}",
note = "Funding Information: \ast Received by the editors October 20, 2021; accepted for publication (in revised form) August 22, 2022; published electronically December 16, 2022. https://doi.org/10.1137/21M1454055 Funding: This material is based upon work supported by the National Science Foundation under grant CMMI 1727785. Part of this research was performed while the author was visiting the Institute for Pure and Applied mathematics (IPAM), which is supported by the National Science Foundation (grant DMS-1925919). This research was also supported by the Campus Research Board of the University of Illinois at Urbana-Champaign. This work is based on the Ph.D. thesis of H. N. Z. Matin at the University of Illinois at Urbana-Champaign. Funding Information: This material is based upon work supported by the National Science Foundation under grant CMMI 1727785. Part of this research was performed while the author was visiting the Institute for Pure and Applied mathematics (IPAM), which is supported by the National Science Foundation (grant DMS-1925919). This research was also supported by the Campus Research Board of the University of Illinois at Urbana-Champaign. This work is based on the Ph.D. thesis of H. N. Z. Matin at the University of Illinois at Urbana-Champaign. Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics Publications. All rights reserved.",
year = "2022",
doi = "10.1137/21M1454055",
language = "English (US)",
volume = "82",
pages = "2080--2110",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "6",
}