A unifying approach to determine the necessary and sufficient conditions for nonblocking multicast 3-stage Clos networks

The 3-stage Clos network is the most-studied switching network. However, exact conditions on the strictly nonblocking multicast three-stage Clos network under various models are difficult to get, due to the messy detail and because each case employs a different argument. Hwang and Liaw (2000) made the latest attempt and pointed out errors in previous attempts. However, they made errors, too. In this paper, we propose a unifying approach to study those models systematically (which also applies to some wide-sense nonblocking (WSNB) networks). We also propose a new routing algorithm, and use the unifying approach to derive a necessary and sufficient condition for WSNB.