Nonblocking multicast Clos networks

This paper studies the necessary and sufficient nonblocking conditions for multicast Clos network or v(m, n1, r1, n2, r2) network, wherein there are r1/r2 switch modules at first/third stage, n1 input/n2 output ports on each first/third stage switch module, and m central stage modules. We prove that given constant n1, n2, if r1 ≥ L = n2 ((m over n2−1)−1)+1, r2 ≥ n1ⁿ²(L over n2), m ≥ n1n2 is a necessary and sufficient nonblocking condition. Analogy to point-to-point Clos network, this result is independent of r1,r2 and improves on the current best sufficient condition at the given region. We also present a wide-sense nonblocking routing algorithm for satisfying each input multicast call.