| Issue |
ESAIM: M2AN
Volume 59, Number 4, July-August 2025
|
|
|---|---|---|
| Page(s) | 2021 - 2054 | |
| DOI | https://doi.org/10.1051/m2an/2025051 | |
| Published online | 17 July 2025 | |
A microscopic derivation of a traffic flow model on a junction with two entry lines
CEREMADE, UMR CNRS 7534, Université Paris Dauphine-PSL, Place de Lattre de Tassigny, 75775 Paris Cedex 16, France
* Corresponding author: cardaliaguet@ceremade.dauphine.fr
Received:
2
September
2024
Accepted:
16
June
2025
We derive a conservation law on a network made of two incoming branches and a single outgoing one from a discrete traffic flow model. The continuous model is obtained from the discrete one by letting the number of vehicles tend to infinity and after scaling. In the discrete model, the vehicles solve a follow-the-leader model on each branch. The priority rule at the junction is given by a time-periodic traffic light (with – for technical reasons – a period tending to infinity with the scaling). The conservation law at the limit is L1-contractive and described in terms of a germ depending on the flux and on the average amount of time the traffic light is “green” on a branch.
Mathematics Subject Classification: 35L65 / 35R02 / 76A30 / 35B27
Key words: Homogeneization / traffic flow / junction condition / scalar conservation law
© The authors. Published by EDP Sciences, SMAI 2025
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.