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

Abstract

Wide-sense nonblocking (WSNB) log ₂ (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 log ₂ (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 log _d (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.