Performance of Unbuffered Shuffle-Exchange Networks

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Abstract
The throughput of unbuffered shuffle-exchange networks (also known as delta networks) is related to the arrival rate by a quadratic recurrence relation. Lower and upper bounds on the solution of this recurrence relation are derived in this paper. Two approaches for improving the throughput of unbuffered delta networks are investigated. The first approach combines multiple delta subnetworks of size N × N each, in parallel, to obtain a network of size N × N. Three policies used to distribute the incoming packets between the subnetworks are discussed and the relative effect of each on the throughput is compared. The second approach replaces each link of the simple delta networks by K parallel links (K equals 2,4,...,). The throughput of such networks is analyzed and one possible implementation for crossbar switches that could be used in these networks is discussed. The throughput of such networks with four parallel links is almost equal to the throughput of crossbars.