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Several analytical models of interconnection networks of multi-cluster systems under uniform traffic pattern have been proposed in the literature. However, there has been hardly any work reported yet that deals with other important non-uniform traffic patterns in parallel applications. In this paper we propose a new analytical model based on fat-tree interconnection networks in the presence of traffic pattern generated by matrix-transpose permutation, which is an important communication operation in parallel applications such as matrix computation problems. The model is validated through comprehensive simulations, which demonstrated that the proposed model exhibit a good degree of accuracy for various system organizations and under different working conditions.