Nonblocking conditions for a multicast WSW architecture based on subtree scheme for elastic optical networks

Elastic optical networks (EONs) are a promising solution for future high-speed optical communication, and multicasting in EONs can efficiently support many emerging services. Different schemes, such as path, tree and subtree schemes, serve multicast services. In this paper, we consider a three-stage wavelength-space-wavelength (WSW) node architecture, which adopts wavelength switches in the first and last stages and space switches in the middle stage, and uses the path scheme to accommodate multicast requests, as proposed in an earlier work for elastic optical networks. We also enhance the WSW architecture to serve multicast requests in a more spectrum-efficient way, namely, using the subtree scheme, by making each switch support multicast capacity, and we term the resulting architecture M-WSW. To the best of our knowledge, this is the first study of the WSW architecture using the subtree scheme to support multicast capacity. We prove the sufficient and necessary conditions, in terms of the number of middle switches, of the M-WSW architecture for being strictly nonblocking (SNB) and wide-sense nonblocking (WSNB) under the two routing algorithms proposed in this paper. Our results show that the number of middle switches required for the architecture to be WSNB under each of the two proposed routing algorithms is much less than the number of middle switches required for SNB, especially when the SNB results meet the boundary condition.