Homogenization of second order discrete model with local perturbation and application to traffic flow

Nicolas Forcadel; Wilfredo Salazar; Mamdouh Zaydan

doi:10.3934/dcds.2017060

Article Contents

2017, Volume 37, Issue 3: 1437-1487. Doi: 10.3934/dcds.2017060

This issue Previous Article Multiple periodic solutions of Hamiltonian systems confined in a box Next Article Qualitative description of the particle trajectories for the N-solitons solution of the Korteweg-de Vries equation

Homogenization of second order discrete model with local perturbation and application to traffic flow

Normandie Univ, INSA de Rouen Normandie, LMI (EA 3226 -FR CNRS 3335), 76000 Rouen, France, 685 Avenue de l'Université, 76801 St Etienne du Rouvray cedex, France

* Corresponding author: N. Forcadel
* Corresponding author: N. Forcadel

Received: April 30, 2016

Revised: October 31, 2016

Published: May 2017

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Abstract

The goal of this paper is to derive a traffic flow macroscopic model from a second order microscopic model with a local perturbation. At the microscopic scale, we consider a Bando model of the type following the leader, i.e the acceleration of each vehicle depends on the distance of the vehicle in front of it. We consider also a local perturbation like an accident at the roadside that slows down the vehicles. After rescaling, we prove that the "cumulative distribution functions" of the vehicles converges towards the solution of a macroscopic homogenized Hamilton-Jacobi equation with a flux limiting condition at junction which can be seen as a LWR (Lighthill-Whitham-Richards) model.

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Mathematics Subject Classification: 35D40, 90B20, 35B27, 35F20, 45K05.

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