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 constraint of crosstalk-free, the hardware cost will be high for a strictly nonblocking banyan-type optical MIN built on the vertical stacking scheme. In this paper, 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 blocking probabilities under the constraint of crosstalk-free. These bounds reveal the inherent relationship between the blocking probability and network cost in term 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.