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Overall Blocking Behavior Analysis of General Banyan-Based Optical Switching Networks

机译：基于常规榕树的光交换网络的整体阻塞行为分析

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摘要

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.
机译：榕树网络因其良好的深度小特性和绝对的信号丢失均匀性而吸引人，可作为光交换架构。将光学榕树网络的水平扩展和垂直堆叠相结合是构建基于榕树的光交换网络的通用方案。所得到的水平扩展和垂直堆叠的光学榕树（HVOB）网络通常需要较高的硬件成本或较大的网络深度才能保证无阻塞性。阻塞行为分析是研究网络性能并在硬件成本，网络深度和阻塞概率之间找到合适折衷方案的有效方法。但是，很少有分析通用HVOB网络的阻塞行为的。在本文中，我们研究了一般HVOB网络的整体阻塞行为，其中，相对于平面（堆叠副本）和阶段数，开发了HVOB网络的阻塞概率上限。上限准确地描述了HVOB网络的总体阻塞行为，这一点已通过广泛的仿真研究验证，并且与网络的严格无阻塞条件相符。得出的上限很重要，因为它揭示了阻塞概率，网络深度和网络硬件成本之间的内在关系，因此可以在它们之间进行理想的权衡。特别是，我们的界限为网络开发人员提供了一种有效的工具，可用来估计HVOB网络的最大阻塞概率，其中可以应用各种路由策略，并在阻塞概率，硬件成本和网络深度方面保证性能。我们的上限模型预测了HVOB网络的一些明显的定性行为，并且得出了一个重要的结论，即在不引入显着高昂的硬件成本或成本的情况下，在HVOB网络中可以实现极低的阻塞概率（例如，小于0.001％）。网络深度大。

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