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The k-ary n-cube which has an n-dimensional grid structure with k nodes in each dimension has been a popular topology for interconnection networks. Analytical models for k-ary n-cubes have been widely reported under the assumptions that the message destinations are uniformly distributed over all network nodes and the message arrivals follow a non-bursty Poisson process. Recent studies have convincingly demonstrated that the traffic pattern in interconnection networks reveals the bursty nature in the both spatial domain (i.e., non-uniform distribution of message destinations) and temporal domain (i.e., bursty message arrival process). With the aim of capturing the characteristics of the realistic traffic pattern and obtaining a comprehensive understanding of the performance behaviour of interconnection networks, this paper presents a new analytical model for k-ary n-cubes in the presence of spatio-temporal bursty traffic. The accuracy of the model is validated through extensive simulation experiments of an actual system.