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Many recent studies on a wide range of networks by means of high quality, high time-resolution measurements have indicated that traffic burstiness and correlations among inter-arrival intervals are present over many time scales, which can be modelled using the long-range dependent (LRD) process. A LRD process is characterised by a hyperbolically decaying correlation function. However, interconnection networks used in current multicomputers have been mainly designed and analysed under the assumption that traffic follows the traditional short-range dependent process (e.g., the Poisson arrival process). In an effort to reevaluate network performance, this paper presents a new analytical model for circuit-switched interconnection networks under LRD traffic. Simulation experiments reveal that the model exhibits a good degree of accuracy under various operating conditions.