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This paper introduces a buffer occupancy-based admission control mechanism aimed to counter link congestion while fairly sharing the bandwidth in converged IP and broadcasting networks. The proposed connection admission control (CAC) scheme favors fairness and downlink bandwidth sharing between different served satellite terminals (sub-networks) in presence of congestion events. Our CAC is intended to overcome major obstacles such as: instantaneous link capacity (available bandwidth) assessing, high computational complexity in flows characterization, and use of traffic descriptors with new flows. This makes the scheme more suitable for DVB-S2 environments where the link capacity may vary as consequence of physical layer adaptive coding/modulation during noisy periods. Simulations results show that the proposed system can avoid uplink and downlink congestion and share fairly the bandwidth between satellite terminals. Further, our CAC minimize the probability of congestion events while still achieving high resources utilization.