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This paper develops detailed analytical performance models for k-ary n-cube networkswith single-hit or infinite buffers, wormhole routing, and the nonadaptive deadlock-freerouting scheme proposed by Dally and Seitz (1987). In contrast to previous performancestudies of such networks, the system is modeled as a closed queueing network that:includes the effects of blocking and pipelining of messages in the network; allows forarbitrary source-destination probability distributions; and explicitly models the virtualchannels used in the deadlock-free routing algorithm. The models are used to examineseveral performance issues for 2-D networks with shared-memory traffic. These resultsshould prove useful for engineering high-performance systems based on low-dimensional k-ary n-cube networks.