Four-level rate equation model is used to describe the carrier dynamics in quantum dot (QD) semiconductor optical amplifiers (SOAs) which takes into account the effect of QD continuum state. A phenomenological description is used to model the intradot carrier scattering between discrete quantum dot states and the continuum state. Analytical results are presented for the small-signal response of wavelength conversion based on the four-wave mixing and cross gain modulation in these advanced amplifiers.