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.