Nonblocking conditions for (f1,f2)-cast Clos networks under balanced traffic

Cost efficient design of nonblocking multicast Clos switching networks has been a challenging issue due to the high cost involved in such networks. This paper focuses on the study of wide-sense nonblocking and strictly nonblocking Clos networks under the (f1,f2)-cast traffic, where the minimum fanout and the maximum fanout of each connection request are restricted to the values of f1 and f2, respectively. The (f1,f2)-cast is general in the sense it covers the unicast and multicast as special cases. Our study addresses the specific case in which the (f1,f2)-cast traffic loads evenly the input stage switches based on f1. We conduct analysis on the sufficient conditions for wide-sense nonblocking as well as the necessary and sufficient conditions for strictly nonblocking in such networks. Our results indicate that under (f1,f2)-cast traffic, the number of middle stage switches required in the special Clos networks can be reduced. It is expected that this study can provide a fundamental guideline to the cost efficient design of nonblocking multicast Clos networks for different applications, including, e.g., optical switching fabrics for data center environments.