Wide - sense Non - blocking Multirate and Multicast log 2 ( N ; m ; p ) Switching Networks

In this paper we are going to investigate the non-blocking operation of multirate log2(N; m; p) switching networks with multicast connections. The nonblocking operation of multi-log2N switching networks for point-to-point connections was firstly considered in [5, 6]. Conditions under which these switching networks are nonblocking for multicast connections were proposed by Tscha and Lea [7] and corrected by the same authors in [8]. They considered a wide-sense nonblocking switching networks and proposed a control algorithm based on the blocking window of a given size. Their results were later generalized by Danilewicz and Kabaciński to blocking windows of any size [9, 10, 11]. Multirate multi-log2N switching networks for point-to-point connections were considered by Lea in [14] and by Kabaciński and Żal in [15]. Frank K. Hwang and Bey-Chi Lin in [17] made an attempt to extended these connections to multicast log2(N; m; p) networks but encountered some difficulties which were commented by Danilewicz and Kabaciński in [18] where the correct results were given. In this paper we will extend these known results to multirate c switching networks with multicast connections and this is the continuation of results given in [16, 17] and [18]. The nonblocking operation at the connection level is considered.