The Riemann solver for traffic flow at an intersection with buffer of vanishing size

Alberto Bressan; Anders Nordli; Alberto Bressan; Anders Nordli

doi:10.3934/nhm.2017007

Networks and Heterogeneous Media

2017, Volume 12, Issue 2: 173-189. doi: 10.3934/nhm.2017007

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The Riemann solver for traffic flow at an intersection with buffer of vanishing size

Alberto Bressan ^{1
,},
Anders Nordli ^{2
,}

1.
Department of Mathematics, Penn State University, University Park, Pa. 16802, USA
2.
Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway

Received: 01 December 2015 Revised: 01 March 2016
Primary: 35L65, 90B20; Secondary: 35R02

The paper examines the model of traffic flow at an intersection introduced in [2], containing a buffer with limited size. As the size of the buffer approaches zero, it is proved that the solution of the Riemann problem with buffer converges to a self-similar solution described by a specific Limit Riemann Solver (LRS). Remarkably, this new Riemann Solver depends Lipschitz continuously on all parameters.
- Hyperbolic conservation laws,
- continuum traffic models,
- Riemann problem,
- Riemann solver
Citation: Alberto Bressan, Anders Nordli. The Riemann solver for traffic flow at an intersection with buffer of vanishing size[J]. Networks and Heterogeneous Media, 2017, 12(2): 173-189. doi: 10.3934/nhm.2017007

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Abstract

The paper examines the model of traffic flow at an intersection introduced in [2], containing a buffer with limited size. As the size of the buffer approaches zero, it is proved that the solution of the Riemann problem with buffer converges to a self-similar solution described by a specific Limit Riemann Solver (LRS). Remarkably, this new Riemann Solver depends Lipschitz continuously on all parameters.

References

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