We present modelling results investigating the carrier dynamics of an SOA composed of an inhomogeneous array of quantum dots designed to produce broad gain amplification when optically pumped. We use a set of rate equations that describe the QDs inhomogeneity and include an energy dependent occupation factor within each inhomogeneously broadened level and numerically solve them with the propagation equation to investigate the amplification of optical signals in the waveguide. By treating the carrier filling according to the quasi-equilibrium distribution, we are able to investigate the effect of band-filling (BFE) on the gain and refractive index. The linewidth enhancement factor (α) is computed and analysed with respect to optical signal intensity as well as electrical current density.