K-ary N-cube Networks Research Articles

Performance analysis of mesh interconnection networks with deterministic routing

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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The impact of pipelined channels on k-ary n-cube networks

In a pipelined-channel interconnection network, multiple bits may be simultaneously in flight on a single wire. This allows the cycle time of the network to be independent of the wire lengths, significantly affecting the network design trade-offs. This paper investigates the design and performance of pipelined channel k-ary n-cube networks, with particular emphasis on the choice of dimensionality and radix. Networks are investigated under the constant link width, constant node size and constant bisection constraints. We find that the optimal dimensionality of pipelined-channel networks is higher than that of nonpipelined-channel networks, with the difference being greater under looser wiring constraints. Their radix should remain roughly constant as network size is grown, decreasing slightly for some unidirectional tori and increasing slightly for some bidirectional meshes. Pipelined-channel networks are shown to provide lower latency and higher bandwidth than their nonpipelined-channel counterparts, especially for high-dimensional networks. The paper also investigates the effects of switching overhead and message lengths, indicating where results agree with and differ from previous results obtained for nonpipelined-channel networks.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Performance analysis of k-ary n-cube interconnection networks

VLSI communication networks are wire-limited, i.e. the cost of a network is not a function of the number of switches required, but rather a function of the wiring density required to construct the network. Communication networks of varying dimensions are analyzed under the assumption of constant wire bisection. Expressions for the latency, average case throughput, and hot-spot throughput of k-ary n-cube networks with constant bisection that agree closely with experimental measurements are derived. It is shown that low-dimensional networks (e.g. tori) have lower latency and higher hot-spot throughput than high-dimensional networks (e.g. binary n-cubes) with the same bisection width. >