C. Yu, X. Jiang, and S. Horiguchi (Japan)
Optical switching networks, banyan networks, blocking probability, horizontal expansion and vertical stacking.
A combination of horizontal expansion and vertical stacking of optical banyan network is the general scheme for constructing banyan-based nonblocking optical switching networks. The resulting networks, namely horizontally expanded and vertically stacked optical banyan (HVOB) networks, preserve the attractive properties of banyan network structures (such as absolutely loss uniformity and small depth), but usually require a high hardware cost. Analysis of blocking probability of a HVOB network is an effective way to studying network performance and finding graceful tradeoffs among hardware cost, network depth and blocking probability, but little is known on analyzing the blocking probabilities of general HVOB networks that do not meet the nonblocking condition (i.e., with fewer stacked copies than required by nonblocking condition). As the first important step toward the blocking probability analysis of general HVOB networks, we analyze in this paper the blocking probabilities of HVOB networks with one extra stage and develop their upper bound with respect to the number of planes in the networks. The bound depicts accurately the overall blocking behaviors of HVOB networks as confirmed by extensive simulation results and it agrees with the conditions of strictly nonblocking HVOB networks. The proposed bound is significant because it reveals the inherent relationships among blocking probability, network depth and network hardware cost and enables a desirable tradeoff to be made among them. In particular, our bound provides network developers an effective tool to estimate the maximum blocking probabilities of HVOB networks in which different routing strategies may be applied. An important conclusion draw from our work is that the hardware cost of a HVOB network can be reduced dramatically if a negligible small blocking probability is allowed.
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