Intersection Modeling using a Convergent Scheme based on Hamilton-Jacobi Equation

This paper presents a convergent scheme for Hamilton-Jacobi (HJ) equations posed on a junction. The general aim of the approach is to develop a framework using similar tools to the variational principle in traffic theory to model intersections taking in account many incoming and outgoing roads. Then a time-explicit numerical scheme is proposed. It is based on the very classical Godunov scheme. The proposed model could be characterized as a pointwise model of intersection without any internal state. Moreover, our model respects the invariance principle. This scheme is applied to the cases of diverge junctions. The goal is to know how to manage the fluxes in order to maximize the flow through the junction.