Performance Analysis of $f$ -Cast Crosstalk-Free Optical Banyan Networks

Banyan networks serve as a class of important switching network architecture, whose multicast capability is critical for future high-performance switches to support multicast-intensive applications. The available literature indicates that, in order to construct optical multicast banyan networks based on the directional coupler (DC) technology, a high-hardware cost is usually involved to ensure the nonblocking property. In this paper, we conduct blocking probability analysis for such networks to explore the inherent tradeoff between blocking probability and hardware cost. In particular, we focus on a class of DC-based optical networks built on the replicated banyan network (RBN) architecture, and develop a theoretical upper bound on blocking probability for such networks under the general f-cast traffic, which covers the unicast and multicast as special cases. This bound captures the overall blocking behavior of f-cast optical RBN networks and agrees with the conditions of strictly nonblocking f-cast optical RBN networks. The proposed bound is significant because it provides a fundamental guideline to achieve the desirable tradeoff between blocking probability and hardware cost. This paper shows that the hardware cost of an f-cast optical RBN network can be dramatically reduced if a small blocking probability is allowed.