Lower-bound on blocking probability of a class of crosstalk-free optical cross-connects (OXCs)

A combination of horizontal expansion and vertical stacking of optical Banyan (HVOB) is the general architecture for building Banyan-based optical cross-connects (OXCs), and the intrinsic crosstalk problem of optical signals is a major constraint in designing OXCs. In this paper, we analyze the blocking behavior of HVOB networks and develop the lower bound on blocking probability of a HVOB network that is free of first-order crosstalk in switching elements. The proposed lower-bound is significant because it provides network designers an effective tool to estimate the minimum blocking probability they can expect from a HVOB architecture regardless what kind of routing strategy to be adopted. Our lower bound can accurately depict the overall blocking behavior in terms of the minimum blocking probability in a HVOB network, as verified by extensive simulation based on a network simulator with both random routing and packing routing strategies. Surprisingly, the simulated and theoretical results show that our lower bound can be used to efficiently estimate the blocking. probability of HVOB networks applying packing strategy. Thus, our analytical model can guide network designers to find the tradeoff among the number of planes (stacked copies), the number of SEs, the number of stages and blocking probability in a HVOB network applying packing strategy.