  We extend the existing analytical model of reionization by Furlanetto et al.
(2004) to include the biasing of reionization sources and additional absorption
by Lyman Limit systems. Our model is, by construction, consistent with the
observed evolution of the galaxy luminosity function at z<8 and with the
observed evolution of Ly-{\alpha} forest at z<6. We also find that, for a wide
range of values for the relative escape fraction that we consider reasonable,
and which are consistent with the observational constraints on the relative
escape fraction from lower redshifts, our reionization model is consistent with
the WMAP constraint on the Thompson optical depth and with the SPT and EDGES
constraints on the duration of reionization. We, therefore, conclude that it is
possible to develop physically realistic models of reionization that are
consistent with all existing observational constraints.
