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-log 2 switching networks with multicast connections in this paper. We prove that such networks are wide-sense nonblocking if they are design by vertically stacking at least 2 1 + 2 2 1 planes of a log 2 networks together, where 1 2 and defines the size of a blocking window = 2 . For = 2 and even, and for 2 the number of planes must be at least 2 1 + 1 and 2 + ( 1) 2 1 2 1 + 1, respectively. In the case of strict-sense nonblocking switching networks, the number of planes is at least 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 = 2 considered in [1]. 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. Minimum number of planes for such operation in general is still open issue.