| Issue |
ESAIM: M2AN
Volume 56, Number 1, January-February 2022
|
|
|---|---|---|
| Page(s) | 213 - 235 | |
| DOI | https://doi.org/10.1051/m2an/2022002 | |
| Published online | 07 February 2022 | |
Network models for nonlocal traffic flow
University of Mannheim, Department of Mathematics, 68131 Mannheim, Germany
* Corresponding author: goettlich@uni-mannheim.de
Received:
30
April
2021
Accepted:
3
January
2022
We present a network formulation for a traffic flow model with nonlocal velocity in the flux function. The modeling framework includes suitable coupling conditions at intersections to either ensure maximum flux or distribution parameters. In particular, we focus on 1-to-1, 2-to-1 and 1-to-2 junctions. Based on an upwind type numerical scheme, we prove the maximum principle and the existence of weak solutions on networks. We also investigate the limiting behavior of the proposed models when the nonlocal influence tends to infinity. Numerical examples show the difference between the proposed coupling conditions and a comparison to the Lighthill-Whitham-Richards network model.
Mathematics Subject Classification: 35L65 / 65M12 / 90B20
Key words: Nonlocal scalar conservation laws / traffic flow networks / coupling conditions / upwind scheme
© The authors. Published by EDP Sciences, SMAI 2022
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