Overall Blocking Behavior Analysis of General Banyan-Based Optical Switching Networks
Overall Blocking Behavior Analysis of General Banyan-Based Optical Switching Networks
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DOI：
10.1109/tpds.2006.126
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发表时间：
2006-09
影响因子：
5.3
通讯作者：
Chen Yu;Xiaohong Jiang;S. Horiguchi;M. Guo
中科院分区：
文献类型：
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作者：
Chen Yu;Xiaohong Jiang;S. Horiguchi;M. Guo
榕树网络具有深度小、信号损耗绝对均匀等优点，在光开关结构中具有很大的应用前景。将光榕树网络的水平扩展和垂直堆叠相结合是构建榕树光交换网络的一般方案。由此产生的水平扩展和垂直堆叠的光学榕树（HVOB）网络通常需要很高的硬件成本或大的网络深度来保证非阻塞性。阻塞行为分析是研究网络性能和在硬件成本、网络深度和阻塞概率之间找到一个合理的折衷的有效方法，然而，对于一般HVOB网络的阻塞行为分析还很少。在本文中，我们研究了一般HVOB网络的整体阻塞行为，其中HVOB网络的阻塞概率的上界相对于平面（堆叠副本）的数量和阶段的数量。上界准确地描述了HVOB网络的整体阻塞行为，通过广泛的模拟研究验证，它同意严格的非阻塞条件的网络。推导出的上限是显着的，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，使一个理想的权衡可以在它们之间。特别是，我们的界限网络开发人员提供了一个有效的工具来估计的最大阻塞概率的HVOB网络，其中不同的路由策略，可以应用于有保证的性能方面的阻塞概率，硬件成本和网络深度。我们的上限模型预测了HVOB网络的一些不明显的定性行为，并得出了一个重要的结论，即很低的阻塞概率（例如，小于0.001%），而不会引入明显较高的硬件成本或较大的网络深度
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