Nonblocking Multirate 2-Stage Networks

A 2-stage network is the most compact multistage interconnection network (MIN) for interconnecting small switches to form a large one. For larger networks, the switches in each stage can be replaced with 2-stage networks to reduce crosspoint cost. The 2-stage network preserves only conditional nonblockingness, while a multirate 2-stage network preserves nonblockingness. Multirate MINs have been exploited in many prior works, but multirate 2-stage networks have not previously been studied. In this letter, we prove the necessary and sufficient conditions for strictly nonblocking, rearrangeable nonblocking, and re-packable nonblocking multirate 2-stage networks. The results can be directly applied to the architecture design of elastic optical networks which allocate a flexible use of the spectrum to each connection, as each space switch is replaced with a bandwidth-variable waveband-converting switch, which has full-range conversion capability.