Modeling the blocking probabilities of crosstalk-free optical MINs with vertical stacking

Vertical stacking is a novel technique for creating nonblocking optical multistage interconnection networks (MINs). Available results indicate that under the crosstalk-free constraint, the hardware cost will be high for a strictly nonblocking banyan-type optical MIN built on the vertical stacking scheme. We study the blocking behaviors of this class of optical MINs from the probabilistic viewpoint, and establish an upper-bound and a lower-bound on the blocking probabilities under the crosstalk-free constraint. These bounds reveal the inherent relationship between the blocking probability and network cost in terms of the number of vertically stacked planes, and show quantitatively with a predictable quality of service (nonblocking probability) guarantee the trade-offs between blocking probability and hardware cost.