Many multiplexing technologies have been proposed to meet the need for high network capacity. One can foresee that transmission systems with many multiplexing levels will be used in telecommunication networks in the future, and the need for switching connections to pass through multiplexed fiber links will rise accordingly. One Clos-like network with k multiplexing levels was proposed in an earlier work, and the work proved only the strictly nonblocking (SNB) conditions. In this paper, we propose a unifying method to prove not only the SNB condition, but also rearrangeable, repackable and wide-sense nonblocking conditions for the Clos-like network with k multiplexing levels. Note that the proposed new proof for the SNB condition is more compact than that given in the earlier work.

已经提出了许多复用技术来满足对高网络容量的需求。可以预见，将来在电信网络中将使用具有许多复用级别的传输系统，并且交换连接以通过复用光纤链路的需求也将随之增加。在较早的工作中提出了一个具有k个多路复用级别的Clos类网络，该工作仅证明了严格的无阻塞（SNB）条件。在本文中，我们提出了一种统一的方法，不仅可以证明具有k个多路复用级别的Clos类网络的SNB条件，而且可以证明其可重排，可重新包装和广义的无阻塞条件。请注意，针对SNB条件的拟议新证据比早期工作中给出的更为紧凑。