Semi-rearrangeably nonblocking operation of Clos networks in the multirate environment

We study the semi-rearrangeably nonblocking (SRN) operation of asymmetrical three-stage Clos (1953) switching networks in the multirate environment. We develop a basic algorithm that balances the established connections among middle-stage switches by performing a small number of rearrangements per disconnection. For this algorithm, we first derive general conditions under which rearranging from a single middle-stage switch is sufficient to achieve SRN operation. In the most general case, however, a sequence of rearrangements from several middle-stage switches may be required for SRN operation. An algorithm to achieve this sequence of rearrangements is presented and its correctness is proved. The minimum resource requirements to achieve SRN operation, in terms of the number of middle-stage switches, are derived for various cases