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We have developed a new hybrid model for an heterogeneous traffic flow, based on a coupling of the Lighthill — Whitham and Richards  (LWR) macroscopic model and the kinetic model. On the highways of a road network, we consider the macroscopic description of the traffic flow and switch to the kinetic model to compute the mass flux through a junction. This new model reproduces the capacity drop phenomenon at a merge junction, for instance, without imposing any priority rule. We present some numerical simulations in which we compare the results of the hybrid model with those given by the fully macroscopic model. Furthermore, we illustrate the consequences of the velocity distribution on the flow through a merging junction.

A Macro-kinetic Hybrid Model for Traffic Flow on Road Networks