It has become increasingly important to test diverse Satellite Systems (Low Earth Orbit and Geosynchronous Satellites) under realistic traffic loads. None of the currently used techniques are able to achieve good results. Formal techniques can be applied to only over simplified models and statistical techniques relying on simulation often fail. Our approach relies on integrating the Genetic Algorithm (GA) with the simulator of the system under verification. We applied our approach to quantitative verification of the Satellite Transport Protocol (TCP Reno and TCP Vegas) successfully. Our simulation results are better than those achieved by traditional statistical methods.