  We consider two scalar conservation laws with non-local flux functions,
describing traffic flow on roads with rough conditions. In the first model, the
velocity of the car depends on an averaged downstream density, while in the
second model one considers an averaged downstream velocity. The road condition
is piecewise constant with a jump at $x=0$. We study stationary traveling wave
profiles cross $x=0$, for all possible cases. We show that, depending on the
case, there could exit infinitely many profiles, a unique profile, or no
profiles at all. Furthermore, some of the profiles are time asymptotic
solutions for the Cauchy problem of the conservation laws under mild assumption
on the initial data, while other profiles are unstable.
