Effects of link failures on the overall blocking behavior of banyan-based optical switches

Due to its nice properties of small depth and absolute signal loss uniformity, vertical stacking of optical banyan (VSOB) networks becomes an attractive optical switch architecture. It is expected that a VSOB switch will have a good fault-tolerant capability, because it consists of multiple banyan networks. To verify our expectation, in this paper we study the overall blocking behavior of a VSOB switch by establishing an upper bound on its blocking probability in presence of link failures. The upper bound accurately depicts the overall blocking behavior of a VSOB switch for a reasonable small link failure rate, as verified by extensive simulation results. Although our upper bound demonstrates that VSOB switches have a good fault-tolerance property, it reveals a surprising overall blocking behavior of a faulty VSOB switch that, not as we usually expected, the blocking probability of the switch may not always increase monotonously with the increase of link failure rate. Our upper bound is significant, because it provides switch designers a quantitative tool to determine the effects of link failure on the blocking behavior and to estimate the maximum blocking probability of a VSOB switch, in which different routing algorithms can be applied with a guaranteed performance in terms of blocking probability and hardware cost