Lagrangian second order traffic modeling and application to traffic control on nodes

This paper is concerned with the macroscopic modeling, simulation of traffic flow on junctions and application of traffic control on intersections. More precisely, we deal with a generic class of second order models, known in the literature as the GSOM family. While classical approaches focus on the Eulerian point-of-view, here we recast the model using its Lagrangian coordinates and we treat the junction as a specific discontinuity in Lagrangian framework. We propose a complete numerical methodology based on a finite difference scheme for solving such a model and we provide an application of traffic control on intersections and some numerical examples. Notice that in our scheme vehicles are discretized into packets of N particles. Hence, our scheme can be seen as a microscopic car-following model for the particular choice of N = 1.