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The paper introduces and analyzes the bandwidth allocation process over space communication systems, corrupted by rain fading, in presence of quality of service (QoS) constraints. To reach the aim, the work proposes two schemes both aimed at assigning the bandwidth, among earth stations, so to approach the ideal situation as close as possible and at guaranteeing a fixed performance for each traffic flow traversing the space network. The mathematical framework of the paper is the multi-objective programming (MOP) theory and the reference allocation scheme considered is called "minimum distance" algorithm. The performance evaluation is carried out analytically by varying the fading level of the channel and considering TCP traffic sources.