  The aim of this work is to introduce a two-dimensional macroscopic traffic
model for multiple populations of vehicles. Starting from the paper [20], where
a two-dimensional model for a single class of vehicles is proposed, we extend
the dynamics to a multi-class model leading to a coupled system of conservation
laws in two space dimensions. Besides the study of the Riemann problems we also
present a Lax-Friedrichs type discretization scheme recovering the theoretical
results by means of numerical tests. We calibrate the multi-class model with
real data and compare the fitted model to the real trajectories. Finally, we
test the ability of the model to simulate the overtaking of vehicles.
