A junction condition by specified homogenization of a discrete model with a 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

In this paper, we focus on deriving traffic flow macroscopic models from microscopic models containing a local perturbation. At the microscopic scale, we consider a first order model of the form "follow the leader" i.e. the velocity of each vehicle depends on the distance to the vehicle in front of it. We consider a local perturbation located at the origin that slows down the vehicles. At the macroscopic scale, we obtain an explicit Hamilton-Jacobi equation left and right of the origin and a junction condition at the origin (in the sense of [18]). As it turns out, the macroscopic model is equivalent to a LWR model, with a flux limiting condition at the junction. Finally, we also present qualitative properties concerning the flux limiter at the junction.

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

Domaines: Equations aux dérivées partielles [math.AP]

Nicolas Forcadel, Wilfredo Salazar, Mamdouh Zaydan. A junction condition by specified homogenization of a discrete model with a local perturbation and application to traffic flow. 2016. ⟨hal-01097085v2⟩