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In the relevant literature, fuzzy relational inequalities with addition-min composition have been proposed to model the data transmission mechanism in a BitTorrent-like peer-to-peer file-sharing system. In this paper, we present a two-phase approach to find an optimal solution to data transmission that minimizes an associated function while its components are controlled to result in reduced network congestion. Numerical examples are given to illustrate the procedures of the two-phase approach.