Since satellite communication systems are both bandwidth and power limited, it is important to maximize the utility of satellite resources. To achieve this goal, on-board packet switching is expected to be more efficient than its circuit-switched counterpart in supporting cell based ATM traffic. For congestion control, a TLB (tunable leaky bucket) scheme is implemented at the ground station to adjust the traffic flow according the predicted congestion status of downlink queue. Congestion in downlink queues is declared when the queue length exceeds a certain threshold. The performance of this broadband satellite communication system is evaluated using a matrix analytic queueing model. Heterogeneous traffic sources are assumed as MMPPs (Markov modulated Poisson process). Numerical results on congestion probability are given.