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This paper develops detailed analytical performance models for k-ary n-cube networks with single-hit or infinite buffers, wormhole routing, and the nonadaptive deadlock-free routing scheme proposed by Dally and Seitz (1987). In contrast to previous performance studies 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 for arbitrary source-destination probability distributions; and explicitly models the virtual channels used in the deadlock-free routing algorithm. The models are used to examine several performance issues for 2-D networks with shared-memory traffic. These results should prove useful for engineering high-performance systems based on low-dimensional k-ary n-cube networks.< >