A Unifying Approach to Determine the Blocking Probability for Four Models in the Multicast Three-stage Clos Network

Multicast communication is one of the most significant collective communication operations and is highly demanded in data communications and scalable parallel and distributed computing systems. In this paper, we consider the issue of supporting multicast in the far and wide used well-known three-stage Clos network C(N, n ,m; f(2)). We make use of Hwang's unifying approach and Pattavina and Tesei's method to determine the blocking probability for models 0, 1, 2 and 3 in the multicast three-stage Clos network. As the unifying approach's application, we also respectively give the blocking probability for each model. Compared to previous results the newly proposed unifying approach can more correctly and comprehensively describe the blocking behavior of the general Clos type network.