Homogenization of second order discrete model 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 models from microscopic models. At the microscopic scales, we consider a Bando model, of the type following the leader, i.e. the acceleration of each vehicle depends on the distance to the vehicle in front of it. We take into account the possibility that each driver can have different characteristics such as sensibility to other drivers or optimal velocities. After rescaling, we prove that the solution of this system of ODEs converges to the solution of a macroscopic homogenized Hamilton-Jacobi equation which can be seen as a LWR (Lighthill-Whitham-Richards) model.

Mots clés: homogenization; macroscopic model; microscopic model; viscosity solution; Traffic flow; viscosity solution.

Domaines: Equations aux dérivées partielles [math.AP]

Nicolas Forcadel, Wilfredo Salazar, Mamdouh Zaydan. Homogenization of second order discrete model and application to traffic flow. Differential and integral equations, 2015, 28 (11-12), pp.1039-1068. ⟨10.3934/dcds.2017060⟩. ⟨hal-00966729⟩