To compensate for the loss of carrier density along the active region of quantum-dot semiconductor optical amplifiers (QD-SOAs), tapered structure of the waveguide is introduced. In this paper, a method for theoretically modeling of such devices is proposed, and according to that model different shapes of tapered waveguides are studied. This study is pivoted around the optical gain and cross-gain modulation (XGM) of the QDSOA under investigation to show how altering the shape of the waveguide affects the main characteristics of the device. For doing so, the rate equation model has been employed and solved through finite difference method and MATLAB ODE. Through this, as long as monotonically increasing profiles for the width of the waveguide are used, the shape of the waveguide has a negligible effect on the gain which mainly depends on the width ratio of the waveguide output to its input. However, this carrier compensation has adverse effect on the XGM, where its efficiency rely on how the pump signal can effectively reduce carrier density and upset the gain.