  We present a review of two methods used to model recent LCLS experimental
results for the 3C/3D line intensity ratio of Fe XVII (Bernitt et al. 2012),
the time-dependent collisional-radiative method and the density-matrix
approach. These are described and applied to a two-level atomic system excited
by an X-ray free electron laser. A range of pulse parameters is explored and
the effects on the predicted Fe XVII 3C and 3D line intensity ratio are
calculated. In order to investigate the behavior of the predicted line
intensity ratio, a particular pair of A-values for the 3C and 3D transitions
was chosen (2.22 $\times$ 10$^{13}$ s$^{-1}$ and 6.02 $\times$ 10$^{12}$
s$^{-1}$ for the 3C and 3D, respectively), but our conclusions are independent
of the precise values. We also reaffirm the conclusions from Oreshkina et
al.(2014, 2015): the non-linear effects in the density matrix are important and
the reduction in the Fe XVII 3C/3D line intensity ratio is sensitive to the
laser pulse parameters, namely pulse duration, pulse intensity, and laser
bandwidth. It is also shown that for both models the lowering of the 3C/3D line
intensity ratio below the expected time-independent oscillator strength ratio
has a significant contribution due to the emission from the plasma after the
laser pulse has left the plasma volume. Laser intensities above $\sim 1\times
10^{12}$ W/cm$^{2}$ are required for a reduction in the 3C/3D line intensity
ratio below the expected time independent oscillator strength ratio.
