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Homogenization of second order discrete model and application to traffic flow. (English) Zbl 1357.49113

Summary: The goal of this paper is to derive 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.

MSC:

49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
90B20 Traffic problems in operations research
35F21 Hamilton-Jacobi equations
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