Wide-Sense Nonblocking ${\rm log}_{d}(N, 0, p)$ Multicast Switching Networks

Abstract

Wide-sense nonblocking (WSNB) log2(N, 0, p) switching networks under the fixed-size blocking window algorithm have been proposed by Tscha and Lee. We have generalized this approach to the variable-size blocking window algorithm and shown that the minimum number of planes depends on the window size and the number of stages. We have also generalized this concept to log2(N, m, p) switching networks. Later, Hwang and Lin have proved that for m > 2, the number of required planes for WSNB operation under the blocking window algorithm is always greater than for m les 2, and determined the optimal window size and optimal m. In this paper, we further generalized these results to logd(N, 0, p) switching networks. In the paper, we prove that the minimum number of planes for any d is reached also for different sizes of blocking window depending on d and n.