| Issue |
ESAIM: M2AN
Volume 59, Number 1, January-February 2025
|
|
|---|---|---|
| Page(s) | 487 - 518 | |
| DOI | https://doi.org/10.1051/m2an/2024082 | |
| Published online | 08 January 2025 | |
A nonlocal traffic flow model with stochastic velocity
University of Mannheim, Department of Mathematics, B6, 68159 Mannheim, Germany
* Corresponding author: goettlich@uni-mannheim.de
Received:
18
June
2024
Accepted:
27
November
2024
In this paper, we investigate a nonlocal traffic flow model based on a scalar conservation law, where a stochastic velocity function is assumed. In addition to the modeling, theoretical properties of the stochastic nonlocal model are provided, also addressing the question of well-posedness. A detailed numerical analysis offers insights how the stochasticity affects the evolution of densities. Finally, numerical examples illustrate the mean behavior of solutions and the influence of parameters for a large number of realizations.
Mathematics Subject Classification: 35L65 / 60H30 / 65M12 / 90B20
Key words: Nonlocal scalar conservation laws / traffic flow / stochastic velocities / numerical simulations
© 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.
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