Corpus ID: 233481804

Network models for nonlocal traffic flow

@article{Friedrich2021NetworkMF,
  title={Network models for nonlocal traffic flow},
  author={Jan Friedrich and Simone G{\"o}ttlich and Maximilian Osztfalk},
  journal={ArXiv},
  year={2021},
  volume={abs/2105.00834}
}
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. 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… Expand

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References

SHOWING 1-10 OF 52 REFERENCES
On kinematic waves II. A theory of traffic flow on long crowded roads
  • M. Lighthill, G. Whitham
  • Engineering, Computer Science
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1955
TLDR
The theory of kinematic waves is applied to the problem of estimating how a ‘hump’, or region of increased concentration, will move along a crowded main road, and is applicable principally to traffic behaviour over a long stretch of road. Expand
Models for vehicular traffic on networks
A non-local traffic flow model for 1-to-1 junctions
We present a model for a class of non-local conservation laws arising in traffic flow modelling at road junctions. Instead of a single velocity function for the whole road, we consider two differentExpand
Speed limit and ramp meter control for traffic flow networks
TLDR
In this work, a method to manage variable speed limits combined with coordinated ramp metering within the framework of the Lighthill–Whitham–Richards (LWR) network model is introduced and the switch of speeds at certain fixed points in time is explained. Expand
A non-local macroscopic model for traffic flow
In this work, we propose a non-local Hamilton–Jacobi model for traffic flow and we prove the existence and uniqueness of the solution of this model. This model is justified as the limit of a rescaledExpand
An explicit finite volume algorithm for vanishing viscosity solutions on a network
<p style='text-indent:20px;'>In [Andreianov, Coclite, Donadello, Discrete Contin. Dyn. Syst. A, 2017], a finite volume scheme was introduced for computing vanishing viscosity solutions on aExpand
Nonlocal approaches for multilane traffic models
TLDR
A multilane traffic model based on balance laws, where the nonlocal source term is used to describe the lane changing rate, and together with the $L^1$-contractivity property, it is proved existence and uniqueness of weak solutions. Expand
Tonnoir, A non-local macroscopic model for traffic flow
  • ESAIM Math. Model. Numer. Anal.,
  • 2021
A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels
We deal with the problem of approximating a scalar conservation law by a conservation law with nonlocal flux. As convolution kernel in the nonlocal flux, we consider an exponential-type approximationExpand
An explicit finite volume algorithm for vanishing viscosity solutions on a network, preprint, (2020)
  • 2020
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