  We present a formal kinetic derivation of a second order macroscopic traffic
model from a stochastic particle model. The macroscopic model is given by a
system of hyperbolic partial differential equations (PDEs) with a discontinuous
flux function, in which the traffic density and the headway are the averaged
quantities. A numerical study illustrates the performance of the second order
model compared to the particle approach. We also analyse numerically uncertain
traffic accidents by considering statistical measures of the solution to the
PDEs.
