Lower bounds for wide-sense non-blocking clos network

Abstract

The 3–stage Clos network is generally considered the most basic multistage interconnecting network(MIN). The nonblocking property of such network has been extensively studied in the past. However there are only a few lower bound results regarding wide–sense nonblocking. We show that in the classical circuit switching environment, for large r to guarantee wide–sense nonblocking, 2n − 1 center switches are necessary where r is the number of input switches and n is the number of inlets of each input switch. For the multirate environment, we show that for large enough r any 3–stage Clos network needs at least 3n−2 center switches to guarantee wide–sense nonblocking. Our proof works for even 2–rate environment.