Strict-sense nonblocking networks with k degrees of freedom

In this paper we extended the well known conditions for strict-sense nonblocking operation of the three-stage Clos switching network to the case in which k multiplexing levels (called later in this paper as k degrees of freedom) are used on input, output, and interstage links. Up till now only the cases with one multiplexing level were considered in the literature—time-division or wavelength-division. Current research shows that transmission systems with many multiplexing levels will be used in the future to increase available transmission speed in telecommunication networks. There will be also a need for switching connecting paths going through such multiplexed links in large capacity optical cross-connect systems, routers, or data center networks. In this paper we proved the strict-sense nonblocking conditions for the three-stage Clos network with k degrees of freedom. We also analyzed the cost of switching fabrics of selected capacities and with three degrees of freedom in terms of the required number of elements.