Microscopic Derivation of a Traffic Flow Model with a Bifurcation

Abstract

The goal of the paper is a rigorous derivation of a macroscopic traffic flow model with a bifurcation or a local perturbation from a microscopic one. The microscopic model is a simple follow-the-leader with random parameters. The random parameters are used as a statistical description of the road taken by a vehicle and its law of motion. The limit model is a deterministic and scalar Hamilton–Jacobi on a network with a flux limiter, the flux-limiter describing how much the bifurcation or the local perturbation slows down the vehicles. The proof of the existence of this flux limiter—the first one in the context of stochastic homogenization—relies on a concentration inequality and on a delicate derivation of a superadditive inequality.