Upper-bound for blocking probabilities of a class of optical MINs under crosstalk-free constraint

Available results indicate that under the crosstalk-free constraint, the hardware cost will be high for a strictly nonblocking optical multistage interconnection network (MIN) based on a vertical stacking scheme. In this paper, the blocking behaviors of this class of optical MINs are studied from the probabilistic view, and an upper bound probabilistic model is developed to describe the blocking behaviors of these switching systems under the crosstalk-free constraint. The simulation results based on a random request generator and a "conservative" routing strategy show that the probabilistic model is very accurate in describing the upper bound for blocking probabilities of these optical MINs. We further demonstrate through the analytical model that even the upper bound model is considered, the hardware of a optical MIN can still be reduced dramatically while a very low blocking probability is guaranteed.