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Performance modelling of generalized processor sharing (GPS) systems in the presence of self-similar traffic has attracted significant research efforts. To simplify the interdependent relationships between traffic flows in GPS systems, most existing studies have been confined to the unrealistic scenarios where only two traffic flows are taken into account. This paper develops an analytical model for investigating both queue length distributions and loss probabilities of GPS systems subject to multi-class self-similar traffic. To this end, we present an efficient approach to decompose the complicated system based on the notion of feasible ordering of GPS systems and the empty buffer approximation. Through extensive comparisons between analytical and simulation results, we investigate the correctness of the decomposition approach and validate the accuracy of the analytical performance results.