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Detailed theoretical analysis of cross-gain (XG) wavelength conversion in quantum dot semiconductor optical amplifier (QD-SOA) is presented. The model takes into account the effect of the excited states, the wetting layer (WL) and the nonlinear optical gain of the dots. An analytical model of the small-signal XG conversion efficiency is also derived. The XG efficiency shows strong dependence on the escape and relaxation lifetimes between the ground and excited states. The model/analysis provides insight on the escape/relaxation lifetime of QD lasers which is very important for characterizing and understanding the performance characteristics of QD devices.