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 ((_n2-1^m)-1)+1, r₂ ≥ n₁ⁿ²(_n2^L), 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.