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The reliability of a multi-state network is defined as the probability that the network can successfully send d (demand) units of data from the source to the sink. To predict the value of maximum demand (dmax) that could be accommodated by a network, a cut-set based approach is presented in this study. The presented approach is simple and easy to implement. The proposed method was applied to many examples studied in literature to illustrate its efficiency. The results show that the reliability value at maximum demand (max d R) is less than any Rd.