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The use of adaptively-routed wormhole switched k-ary n-cubes has been motivated by the high path diversity provided by the rich topology of this family of interconnection networks. Due to its insensitivity to message destination, adaptive wormhole switching has been an attractive design alternative not only in networks suggested for contemporary multicomputers but also in the new Network-on-Chip and System-on-Chip architectures. Although analytical performance models for wormhole switched networks have been widely reported in the literature over the past two decades, the majority of these models have unrealistically assumed negligible buffering capacity at each switching element of the network. This paper proposes the first analytical model to assess the performance of adaptively-routed wormhole-switched k-ary n-cubes with finite size buffers. The new model can also accounts for the use of any number of virtual channels in order to further improve system performance. The model is validated by means of an event-driven simulator and experiments show close agreement between model predictions and simulator results.