Wide-sense nonblocking multicast logd (N, m, p) switching networks under the window algorithm

The generalized multiplane wide-sense nonblocking switching network for multicast connections is presented in this paper. This switching network is based on the well-known baseline network. Up to now, wide-sense nonblocking operations for multicast connections have been considered for the following switching networks which are based on the baseline network: multiplane switching networks composed of 2 × 2 switching elements (called log₂ (N, 0, p) networks), multiplane switching networks composed of 2 x 2 switching elements and with m extra stages (called log₂ (N, m, p) networks), and multiplane generalized switching networks composed of d x d switching elements (called log_d (N, 0, p) networks). The control algorithm under which these networks are wide-sense nonblocking for multicast connections is called the window algorithm. In this paper, multiplane switching networks composed of dxd switching elements with m extra stages (called log_d (N, m, p) networks) are considered and in this way the last link in the studies of wide-sense nonblocking multicast multiplane switching networks under blocking window algorithms is presented. In this article, the path-searching algorithm is adopted for the general case d ¿ 2 and the wide-sense nonblocking conditions for switching networks for different sizes of the blocking window and for different numbers of extra stages are derived. The cost of different multiplane switching networks is compared in terms of the number of planes and the number of crosspoints.