Lower-Bound on Blocking Probability of General Banyan-based Photonic Switches with Zero First-Order Switching-Element-Crosstalk

The horizontally expanded and vertically stacked photonic banyan (HVPB) is a general architecture for building banyan-based photonic switches. Blocking behavior analysis is an effective approach to studying network performance and finding a graceful compromise among hardware cost, network depth, and blocking probability. In this paper, we analyze the blocking probability of a HVPB network under the constraint of zero first-order switching-element-crosstalk and develop its lower bound with respect to the number of planes (stacked copies) and number stages in the network. Extensive simulation on a network simulator with both random routing and packing strategy has shown that the blocking probabilities of both strategies are nicely bounded by our lower bound, and the blocking probability of packing strategy actually matches the lower-bound. 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 HVPB architecture regardless what kind of routing strategy to be adopted. In particular, the proposed bound can be used to efficiently estimate the blocking probability of HVPB networks adopting packing routing strategy, in which the inherent relationship and tradeoff among blocking probability, network hardware cost in terms of the number of planes, and network depth can be explored.