We investigate the dynamic and static gain characteristics of quantum-dot semiconductor optical amplifiers (QD-SOAs) operating at 1.55 mu m based upon the experimental measurements performed on an InAs/InGaAsP/InP QD-SOA and simple modeling tools. A two-level rate equation model proved to be sufficient to explain the experimental gain dynamics as a function of current. The simple model allowed the derivation of the saturation power of QD-SOAs in the static regime. We show that the saturation power of QD-SOAs, in contrast to bulk and quantum well amplifiers, is enhanced by a factor of roughly two that depends on the material and device parameters. Our modeling tools are based on the experimentally obtained quantities and facilitates the analysis of different devices' designs and the identification of the parameters that play a key role in the fast QD-SOA gain recovery and its high saturation output power, namely, a fast capture time of carriers into the dot and a large energy difference between wetting layer and quantum dot states. (C) 2013 Elsevier B.V. All rights reserved.