On 1-rate wide-sense nonblocking for 3-stage Clos networks

This paper considers the multirate environment in which each network link has a unity capacity and each call is associated with a rate w, 1 greater than or equal to w > 0. The multirate environment is reduced to the I-rate environment if all rates are identical. Circuit switching is a special case of 1-rate in which the constant rate is w=1. We establish some general relations between wide-sense nonblocking in circuit switching and I-rate wide-sense nonblocking for the 3-stage Clos network. We also give necessary and sufficient conditions for a 3-stage Clos network with two input switches and two output switches to be wide-sense nonblocking, and give a necessary condition when there are three input switches and three output switches. We conjecture that I-rate wide-sense nonblocking implies circuit switching wide-sense nonblocking and give some partial evidence.