A non-local traffic flow model for 1-to-1 junctions with buffer

F. A. Chiarello; J. Friedrich; S. Göttlich; F. A. Chiarello; J. Friedrich; S. Göttlich

doi:10.3934/nhm.2024018

Networks and Heterogeneous Media

2024, Volume 19, Issue 1: 405-429. doi: 10.3934/nhm.2024018

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A non-local traffic flow model for 1-to-1 junctions with buffer

1.
DISIM, University of L'Aquila, Via Vetoio Ed. Coppito 1, 67100 L'Aquila, Italy
2.
IGPM, RWTH Aachen University, Templergraben 55, 52064 Aachen, Germany
3.
Department of Mathematics, University of Mannheim, B6, 28-29, 68159 Mannheim, Germany

Received: 18 July 2023 Revised: 31 January 2024 Accepted: 02 April 2024 Published: 08 April 2024

In this paper, we introduce a non-local PDE-ODE traffic model devoted to the description of a 1-to-1 junction with buffer. We present an existence result in the free flow case as well as a numerical method to approximate weak solutions in the general case. In addition, we show a maximum principle, which is uniform in the non-local interaction range. Further, we exploit the limit models as the support of the kernel tends to zero and to infinity. We compare them with other already existing models for traffic and production flow and presented numerical examples.
- scalar conservation laws,
- anisotropic non-local flux,
- coupled PDE-ODE model,
- traffic flow
Citation: F. A. Chiarello, J. Friedrich, S. Göttlich. A non-local traffic flow model for 1-to-1 junctions with buffer[J]. Networks and Heterogeneous Media, 2024, 19(1): 405-429. doi: 10.3934/nhm.2024018

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Abstract

In this paper, we introduce a non-local PDE-ODE traffic model devoted to the description of a 1-to-1 junction with buffer. We present an existence result in the free flow case as well as a numerical method to approximate weak solutions in the general case. In addition, we show a maximum principle, which is uniform in the non-local interaction range. Further, we exploit the limit models as the support of the kernel tends to zero and to infinity. We compare them with other already existing models for traffic and production flow and presented numerical examples.

References

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