  We analyze the steady-state flow as a function of the initial density for a
class of deterministic cellular automata rules (``traffic rules'') with
periodic boundary conditions [H. Fuks and N. Boccara, Int. J. Mod. Phys. C 9, 1
(1998)]. We are able to predict from simple considerations the observed,
unexpected cutoff of the average flow at unity. We also present an efficient
algorithm for determining the exact final flow from a given finite initial
state. We analyze the behavior of this algorithm in the infinite limit to
obtain for R_m,k an exact polynomial equation maximally of 2(m+k)th degree in
the flow and density.
