  We prove existence and uniqueness of solutions to a transport equation
modelling vehicular traffic in which the velocity field depends non-locally on
the downstream traffic density via a discontinuous anisotropic kernel. The
result is obtained recasting the problem in the space of probability measures
equipped with the $\infty$-Wasserstein distance. We also show convergence of
solutions of a finite dimensional system, which provide a particle method to
approximate the solutions to the original problem.
