Nonlocal reaction traffic flow model with on-off ramps

Felisia Angela Chiarello; Harold Deivi Contreras; Luis Miguel Villada; Felisia Angela Chiarello; Harold Deivi Contreras; Luis Miguel Villada

doi:10.3934/nhm.2022003

Networks and Heterogeneous Media

2022, Volume 17, Issue 2: 203-226. doi: 10.3934/nhm.2022003

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Nonlocal reaction traffic flow model with on-off ramps

1.
Department of Mathematical Sciences "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
2.
GIMNAP-Departamento de Matemáticas, Universidad del Bío-Bío, Concepción, Chile
3.
GIMNAP-Departamento de Matemáticas, Universidad del Bío-Bío, Concepción, Chile, and CI²MA, Universidad de Concepción, Casilla 160-C, Concepción, Chile

Received: 01 August 2021 Revised: 01 December 2021 Published: 18 February 2022
Primary: 65M08; Secondary: 35L45, 90B20

We present a non-local version of a scalar balance law modeling traffic flow with on-ramps and off-ramps. The source term is used to describe the inflow and output flow over the on-ramp and off-ramps respectively. We approximate the problem using an upwind-type numerical scheme and we provide $ \mathbf{L^{\infty}} $ and $ \mathbf{BV} $ estimates for the sequence of approximate solutions. Together with a discrete entropy inequality, we also show the well-posedness of the considered class of scalar balance laws. Some numerical simulations illustrate the behaviour of solutions in sample cases.
- Lighthill-Whitham-Richards traffic model,
- nonlocal conservation laws,
- ramps,
- upwind scheme,
- well-posedness
Citation: Felisia Angela Chiarello, Harold Deivi Contreras, Luis Miguel Villada. Nonlocal reaction traffic flow model with on-off ramps[J]. Networks and Heterogeneous Media, 2022, 17(2): 203-226. doi: 10.3934/nhm.2022003

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Abstract

We present a non-local version of a scalar balance law modeling traffic flow with on-ramps and off-ramps. The source term is used to describe the inflow and output flow over the on-ramp and off-ramps respectively. We approximate the problem using an upwind-type numerical scheme and we provide $ \mathbf{L^{\infty}} $ and $ \mathbf{BV} $ estimates for the sequence of approximate solutions. Together with a discrete entropy inequality, we also show the well-posedness of the considered class of scalar balance laws. Some numerical simulations illustrate the behaviour of solutions in sample cases.

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