  We extend the classical LWR traffic model allowing different maximal speeds
to different vehicles. Then, we add a uniform bound on the traffic speed. The
result, presented in this paper, is a new macro- scopic model displaying 2
phases, based on a non-smooth 2x2 system of conservation laws. This model is
compared with other models of the same type in the current literature, as well
as with a kinetic one. Moreover, we establish a rigorous connection between a
microscopic Follow-The-Leader model based on ordinary differential equations
and this macroscopic continuum model.
