| Issue |
ESAIM: M2AN
Volume 58, Number 4, July-August 2024
|
|
|---|---|---|
| Page(s) | 1523 - 1539 | |
| DOI | https://doi.org/10.1051/m2an/2024054 | |
| Published online | 27 August 2024 | |
The continuum limit of non-local follow-the-leader models
1
Department of Mathematical Sciences, NTNU Norwegian University of Science and Technology, 7491 Trondheim, Norway
2
Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway
* Corresponding author: helge.holden@ntnu.no
Received:
26
January
2024
Accepted:
1
July
2024
We study a generalized Follow-the-Leader model where the driver considers the position of an arbitrary but finite number of vehicles ahead, as well as the position of the vehicle directly behind the driver. It is proved that this model converges to the classical Lighthill–Whitham–Richards model for traffic flow when traffic becomes dense. This also underscores the robustness of the Lighthill–Whitham–Richards model.
Mathematics Subject Classification: 35L02 / 35Q35 / 82B21
Key words: Follow-the-Leader model / Lighthill–Whitham–Richards model / traffic flow / continuum limit
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.