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An interactive satellite network consists of a hub, a geostationary Earth orbit (GEO) satellite, and a group of terminals. Terminals in need of capacity send a capacity request (CR) message to the hub and the hub then makes a capacity-allocation schedule according to the CR and broadcasts that schedule to the terminals. Thus, it takes the round-trip time plus the scheduling time for a terminal to receive a response from the hub. Due to such intrinsic delay between capacity request and capacity allocation, it is difficult to promptly transmit user data via interactive channels of GEO satellites. The preferred solution to this problem is to have a prediction-based resource-allocation policy and to have as short a period of scheduling time as possible. As a solution to use such policies, we mathematically formulate a resource-allocation problem as a nonlinear integer programming problem considering uncertain future traffic conditions and we develop a real-time heuristic solution algorithm. Computational complexity analysis and extensive simulation results demonstrate the excellent performance of the proposed method on computational efficiency and heuristic solution quality.