Non-local multi-class traffic flow models

Felisia Angela Chiarello; Paola Goatin; Felisia Angela Chiarello; Paola Goatin

doi:10.3934/nhm.2019015

Networks and Heterogeneous Media

2019, Volume 14, Issue 2: 371-387. doi: 10.3934/nhm.2019015

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Non-local multi-class traffic flow models

Felisia Angela Chiarello ,
Paola Goatin ^,

Inria Sophia Antipolis - Méditerranée, Université Côte d'Azur, Inria, CNRS, LJAD, 2004 route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex, France

Received: 01 August 2018 Revised: 01 October 2018
Primary: 35L65, 90B20; Secondary: 65M08

We prove the existence for small times of weak solutions for a class of non-local systems in one space dimension, arising in traffic modeling. We approximate the problem by a Godunov type numerical scheme and we provide uniform ${{\mathbf{L}}^\infty } $ and BV estimates for the sequence of approximate solutions, locally in time. We finally present some numerical simulations illustrating the behavior of different classes of vehicles and we analyze two cost functionals measuring the dependence of congestion on traffic composition.
- System of conservation laws,
- non-local flux,
- macroscopic traffic flow models,
- finite volume schemes,
- multi-class model
Citation: Felisia Angela Chiarello, Paola Goatin. Non-local multi-class traffic flow models[J]. Networks and Heterogeneous Media, 2019, 14(2): 371-387. doi: 10.3934/nhm.2019015

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Abstract

We prove the existence for small times of weak solutions for a class of non-local systems in one space dimension, arising in traffic modeling. We approximate the problem by a Godunov type numerical scheme and we provide uniform ${{\mathbf{L}}^\infty } $ and BV estimates for the sequence of approximate solutions, locally in time. We finally present some numerical simulations illustrating the behavior of different classes of vehicles and we analyze two cost functionals measuring the dependence of congestion on traffic composition.

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