The Strict‐Sense Nonblocking Multirate log_d(N, 0, p) Switching Network

Abstract

This paper considers the nonblocking conditions for a multirate log d ( N , 0, p ) switching network at the connection level. The necessary and sufficient conditions for the discrete bandwidth model, as well as sufficient and, in particular cases, also necessary conditions for the continuous bandwidth model, were given. The results given for d ⌊( n − 1)/2⌋ f 0 ≥ f 1 + 1 in the discrete bandwidth model are the same as those proposed by Hwang et al. (2005); however, in this paper, these results were extended to other values of f 0 , f 1 , and d . In the continuous bandwidth model for B + b > 1, the results given in this paper are also the same as those by Hwang et al. (2005); however, for B + b ≤ 1, it was proved that a smaller number of vertically stacked log d N switching networks are needed.