Supplement to “Asymmetrical Space-Conversion Space SCS1 Strict-Sense and Wide-Sense Nonblocking Switching Fabrics for Continuous Multislot Connections” - the SCS2 Switching Fabrics Case

Recently, Danilewicz has proposed strict-sense and wide-sense nonblocking structures of asymmetrical space-conversion-space (S-C-S) switching fabrics. One of the two possible architectures, called the SCS1 switching fabric, was previously considered. In this paper, the second architecture, called the SCS2 switching fabric, is presented. Similarly to the previous study, this paper considers a more general case in which conversion in the middle-stage switches can be made for one of the different domains (frequency, time, etc.). Moreover, m-slot connections are a basis for the presented theory. For the S-C-S switching fabrics discussed in this paper, we derive and prove strict-sense nonblocking conditions for asymmetrical SCS2 switching fabrics when m-slot connections are set up in which m
_min
≤ m ≤ m
_max
. In addition, wide-sense nonblocking conditions for SCS2 switching fabrics with functional decomposition of center-stage switches are presented. This paper is a supplementary study to the previous paper devoted to the SCS1 switching fabrics. Motivation, state-of-the-art, and many definitions and assumptions are the same as for the SCS1 and SCS2 solutions, so for these the reader is referred to the previous paper.