On the well-posedness of the “Bando-follow the leader” car following model and a time-delayed version

Gong X, Keimer A (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Networks and Heterogeneous Media American Institute of Mathematical Sciences (AIMS)

Book Volume: 18

Pages Range: 775-798

Journal Issue: 2

DOI: 10.3934/nhm.2023033

Abstract

In this contribution we study the “Bando-follow the leader” car-following model, a second order ordinary differential equation, for its well-posedness. Under suitable conditions, we provide existence and uniqueness results, and also bounds on the higher derivatives, i.e., velocity and acceleration. We then extend the result to the “reaction” delay case where the delay is instantiated in reacting on the leading vehicle’s position and velocity. We prove that the solution of the delayed model converges to the undelayed when the delay converges to zero and present some numerical examples underlying the idea that it is worth looking in more details into delay as it might explain problems in traffic flow like “phantom shocks” and “stop and go” waves.

Involved external institutions

Arizona State University (ASU) US United States (USA) (US) University of California, Berkeley US United States (USA) (US)

How to cite

APA:

Gong, X., & Keimer, A. (2023). On the well-posedness of the “Bando-follow the leader” car following model and a time-delayed version. Networks and Heterogeneous Media, 18(2), 775-798. https://dx.doi.org/10.3934/nhm.2023033

MLA:

Gong, Xiaoqian, and Alexander Keimer. "On the well-posedness of the “Bando-follow the leader” car following model and a time-delayed version." Networks and Heterogeneous Media 18.2 (2023): 775-798.

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