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The paper presents a novel approach for dynamic bandwidth allocation in geostationary satellite networks. Each satellite gateway (SG) uses a local adaptive predictor to forecast the future input traffic flow along with a local predictive (receding-horizon) controller to generate a bandwidth request to the network control center (NCC). In turn, the NCC globally shares out the available bandwidth among the requesting SGs according to a suitable fair resource allocation policy. Simulation experiments demonstrate the effectiveness of the proposed approach in terms of efficient bandwidth usage and low packet delivery delays under different traffic load conditions.