In this paper, the effects of homogeneous and inhomogeneous broadenings on the response of quantumdot semiconductor optical amplifier (QD-SOAs) are investigated. For the first time, the state space model is used to simulate static and dynamic characteristics of the QD-SOA. It is found that with decreasing the homogeneous and inhomogeneous broadenings, the saturation power of the QD-SOA decreases and the optical gain and the ultrafast gain compression increase. Simulation results show that with decreasing the homogeneous broadening from 20 to 1 meV, the gain compression increases from 40% to 90%, the unsaturated optical gain becomes approximately tripled, and the saturation power becomes two times less. Also, simulations demonstrate that with decreasing the inhomogeneous broadening from 50 to 25 meV, the gain compression increases from less than 50% to more than 90%, the unsaturated optical gain becomes approximately 10-fold, and the saturation power becomes three times less. In addition, it is found that the homogeneous and inhomogeneous linewidths should be small for nonlinear applications. The homogeneous and inhomogeneous broadenings need to be large enough for linear applications.