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

Abstract

This paper considers the nonblocking conditions for a multirate log ( , 0, ) 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 ⌊( −1)/2⌋ 0 ≥ 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 0 , 1 , and . In the continuous bandwidth model for + > 1, the results given in this paper are also the same as those by Hwang et al. (2005); however, for + ≤ 1, it was proved that a smaller number of vertically stacked log switching networks are needed.

Strict‐Sense Nonblocking Conditions for the log2⁡N − 1 Multirate Switching Fabric for the Discrete Bandwidth Model

“…It should also be noted that the cost of a whole switching fabric is the cost of one plane multiplied by the number of such planes plus additional passive optical elements (optical splitters at the input side and optical combiners at the output side of the switching network) used to connect these planes to inputs and outputs of the switching fabric (as it can be seen in Figure 1). A detailed description of one plane's cost of the multiplane banyan switching fabric is given in [56] and the cost of one plane of a multiplane log 2 − 1 switching fabric is given in [1]. Therefore, taking into account the number of planes given in Theorem 1, the exact cost of a multiplane log 2 − 1 switching fabric can be calculated.…”