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.

弹性光网络 (EON) 是未来高速光通信的一种很有前途的解决方案，EON 中的多播可以有效地支持许多新兴服务。不同的方案，例如路径、树和子树方案，服务于多播服务。在本文中，我们考虑了一种三级波长-空间-波长（WSW）节点架构，它在第一和末级采用波长开关，在中间阶段采用空间开关，并使用路径方案来容纳组播请求，如在弹性光网络的早期工作中提出。我们还增强了 WSW 架构，以更高效的频谱方式服务多播请求，即使用子树方案，通过使每个交换机支持多播容量，我们将最终架构称为 M-WSW。据我们所知，这是使用子树方案支持多播容量的 WSW 架构的第一次研究。我们证明了在本文提出的两种路由算法下，M-WSW 架构在中间交换机数量方面是严格无阻塞（SNB）和广义无阻塞（WSNB）的充分必要条件。我们的结果表明，在两种提议的路由算法下，架构成为 WSNB 所需的中间交换机数量远少于 SNB 所需的中间交换机数量，尤其是当 SNB 结果满足边界条件时。在本文提出的两种路由算法下，M-WSW架构的严格无阻塞（SNB）和广义无阻塞（WSNB）。我们的结果表明，在两种提议的路由算法下，架构成为 WSNB 所需的中间交换机数量远少于 SNB 所需的中间交换机数量，尤其是当 SNB 结果满足边界条件时。在本文提出的两种路由算法下，M-WSW架构的严格无阻塞（SNB）和广义无阻塞（WSNB）。我们的结果表明，在两种提议的路由算法下，架构成为 WSNB 所需的中间交换机数量远少于 SNB 所需的中间交换机数量，尤其是当 SNB 结果满足边界条件时。