Wide-sense and strict-sense nonblocking operation of multicast multi-log2 n switching networks

Multicast connections are used in broad-band switching networks as well as in parallel processing. We consider wide-sense and strict-sense nonblocking conditions for multi-log₂ N switching networks with multicast connections. We prove that such networks are wide-sense nonblocking if they are designed by vertically stacking at least t · 2^n-t-1 + 2 ^n-2t-1 planes of a log₂ N networks together, where 1 ⩽ t ⩽ [n/2] and t defines the size of a blocking window K = 2^t. For t = [n/2] and n even, and for [n/2] ⩽ t ⩽ n the number of planes must be at least t · 2^n-t-1 + 1 and 2^t + (n - t - 1) · 2^n-t-1 - 2^2t-n-1 + 1, respectively. In the case of strict-sense nonblocking switching networks, the number of planes is at least N/2. The results obtained in this paper show that in many cases number of planes in wide-sense nonblocking switching networks is less than those for t = [n/2] considered by Tscha and Lee (see ibid., vol.47, p.1425-31, Sept. 1999). The number of planes given in the paper is the minimum number of planes needed for wide-sense nonblocking operation provided that Algorithm 1 is used for setting up connections. The minimum number of planes for such operation in general is still open issue