Hybrid approaches to the solutions of the “Lighthill–Whitham–Richards” model

This paper presents a hybrid “Lighthill–Whitham–Richards” (LWR) model combining both macroscopic and microscopic traffic descriptions. Simple interfaces are defined to translate the boundary conditions when changing the traffic description. They are located in discrete points in space and are based on a generalisation of demand and supply concepts. Simulation results show that the proposed interfaces ensure an accurate wave propagation along two links differently described. Furthermore, the demand and supply formulation of the hybrid model makes it fully compatible with major LWR extensions developed over the past few years (intersections modeling, multi-lanes representation, etc.). Finally, we prove that Newell’s optimal velocity car-following model can be derived from the Godunov scheme applied to the LWR model in Lagrangian coordinates. This proposes a microscopic resolution of the LWR model that is fully compatible with the usual macroscopic representation. This microscopic resolution is included in the hybrid model.