Blocking probability of vertically stacked optical banyan networks under random routing

Vertical stacking of optical banyan networks is an attractive scheme for building nonblocking (crosstalk-free) optical switching networks. The resulting networks, namely vertically stacked optical banyan (VSOB) networks, preserve all the good properties of banyan networks, but increase hardware cost significantly. In this paper, we study the blocking probabilities of VSOB networks under random routing strategy, and develop a model to compute the blocking probabilities with respect to the number of planes in the networks. Our model calculates the blocking probabilities stage by stage recursively, and it depicts accurately the blocking behaviors of VSOB networks under random routing. The proposed model is significant because it reveals the inherent relationships between blocking probability and network hardware cost in terms of the number of planes, and provides network developers a quantitative guidance to find a desirable tradeoff between blocking probability and hardware cost. An important conclusion drawn from our work that has practical applications is that the hardware cost of a VSOB network can be reduced dramatically if a predictable and almost negligible non-zero blocking probability is allowed.