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<p><b>Abstract</b>—Banyan networks are attractive for serving as the optical switch architectures due to their nice properties of small depth and absolutely signal loss uniformity. Combining the horizontal expansion and vertical stacking of optical banyan networks is a general scheme for constructing banyan-based optical switching networks. The resulting horizontally expanded and vertically stacked optical banyan (HVOB) networks usually take either a high hardware cost or a large network depth to guarantee the nonblocking property. Blocking behavior analysis is an effective approach to studying network performance and finding a graceful compromise among hardware cost, network depth, and blocking probability; however, little has been done to analyze the blocking behavior of general HVOB networks. In this paper, we study the overall blocking behavior of general HVOB networks, where an upper bound on the blocking probability of a HVOB network is developed with respect to the number of planes (stacked copies) and the number of stages. The upper bound accurately depicts the overall blocking behavior of a HVOB network as verified by an extensive simulation study, and it agrees with the strictly nonblocking condition of the network. The derived upper bound is significant because it reveals the inherent relationship among blocking probability, network depth, and network hardware cost, so that a desirable tradeoff can be made among them. In particular, our bound gives network developers an effective tool to estimate the maximum blocking probability of a HVOB network, in which different routing strategies can be applied with a guaranteed performance in terms of blocking probability, hardware cost and network depth. Our upper bound model predicts some unobvious qualitative behaviors of HVOB networks, and it draws an important conclusion that a very low blocking probability (e.g., less than 0.001 percent) can be achieved in a HVOB network without introducing either a significantly high hardware cost or a large network depth. </p>
Optical switching networks, banyan networks, blocking probability, horizontal expansion, vertical stacking.

X. Jiang, C. Yu, S. Horiguchi and M. Guo, "Overall Blocking Behavior Analysis of General Banyan-Based Optical Switching Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 17, no. , pp. 1037-1047, 2006.
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