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<p><b>Abstract</b>—A stochastic analysis of multidimensional networks with unidirectional or bidirectional links between nodes is presented. The analysis allows the development of an accurate model for examining the performance and cost trade-offs of different network configurations. The model is validated through simulation and does not rely on the simplifying assumptions of previous models. In addition, the model is valid for the hypercube network. Two new performance-based design constraints are introduced: constant maximum throughput and constant unity queue. These new constraints are fundamentally different than previous constraints, which are based on some characterization of hardware implementation costs. Both of the new constraints allow performance and cost comparisons of different network configurations to be made on the basis of an equal ability to handle a range of traffic load. Results under the new constraints clearly show that a low dimensional network, while offering the lowest message latency, must be significantly more expensive than a comparable high dimensional network and, in some cases, may be impractical to implement. In addition, the constraints demonstrate that performance is highly dependent on offered load.</p>
Interconnection networks, multidimensional network, $k$-ary $n$-cube, direct-connected, queue waiting time, message latency, performance analysis, maximum throughput, unity queue waiting time.
James R. Anderson, Seth Abraham, "Performance-Based Constraints for Multidimensional Networks", IEEE Transactions on Parallel & Distributed Systems, vol. 11, no. , pp. 21-35, January 2000, doi:10.1109/71.824636
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