Wide-sense Nonblocking for 3-stage Clos Networks
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Let C,(n,m,r) denote the symmetric 3-stage Clos network with r n × m crossbars in the first and third stage, and m r × r crossbars in the second stage. A network is wide-sense nonblocking if it is nonblocking under a given routing algorithm. Packing is a routing algorithm much heralded in the folklore, and was shown to save n/2 center switches for r = 2. We prove the surprising result that packing does not save anything for r ≥ 3. We also show that C (n,m,r) is not wide-sense nonblocking (under any algorithm) for r ≥ 3 if m < [7n/4]. We also extend some results to asymmetric 3-stage Clos networks
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