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

Nicolas Forcadel (1) , Wilfredo Salazar (1) , Mamdouh Zaydan (1)

1 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie

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 ho-mogenized Hamilton-Jacobi equation with a flux limiting condition at junction which can be seen as a LWR (Lighthill-Whitham-Richards) model.

Mots clés: traffic flow; Hamilton-Jacobi equations; Slepčev formulation; integro-differential operators; specified homogenization; microscopic models; macroscopic models; viscosity solutions

Domaines: Equations aux dérivées partielles [math.AP]

Nicolas Forcadel, Wilfredo Salazar, Mamdouh Zaydan. Homogenization of second order discrete model with local perturbation and application to traffic flow. Discrete and Continuous Dynamical Systems - Series A, 2017, 37 (3), pp.1437-1487. ⟨10.3934/dcds.2017060⟩. ⟨hal-01311363⟩