Performance modelling for vertically stacked optical banyan networks with extra stage

A combination of horizontal expansion and vertical stacking of optical banyan (HVOB) is the general scheme for building banyan-based optical switching networks. The HVOB networks usually require either higher hardware cost or larger depth to guarantee the nonblocking property. In this paper, we analyse the blocking probabilities of HVOB networks with one extra stage and develop their upper bound. The bound depicts accurately the overall blocking behaviours of HVOB networks and reveals the inherent relationships among blocking probability, network depth and network hardware cost and enables a desirable tradeoff to be made among them.