Double laser pulses of duration - 75 ps and short laser pulses ∼ 1 ps superimposed on longer duration background pulses have been shown to efficiently pump lasing in Ne-like and Ni-like ions. For the 75 ps pumping, X-ray laser output without travelling wave pumping is shown to be well-described by a model of ASE output. With 1 ps pumping, the X-ray laser output with different velocity travelling wave pumping is well-fitted with an extension to the ASE model allowing for travelling wave excitation of the gain along the plasma line. The model is used to investigate the production of short (< 1 ps) x-ray laser pulses and the effects of non-ideal travelling wave velocities on the X-ray laser output. Resonance line spectra of emission perpendicular to the plasma line are measured and simulated. It is shown that an accurate opacity model for the more intense Ne-like ions is needed to correctly simulate the spectra.