  We study a Follow-the-Leader (FtL) ODE model for traffic flow with rough road
condition, and analyze stationary traveling wave profiles where the solutions
of the FtL model trace along, near the jump in the road condition. We derive a
discontinuous delay differential equation (DDDE) for these profiles. For
various cases, we obtain results on existence, uniqueness and local stability
of the profiles. The results here offer an alternative approximation, possibly
more realistic than the classical vanishing viscosity approach, to the
conservation law with discontinuous flux for traffic flow.
