Primal meets dual: A generalized theory of logical topology survivability in IP-over-WDM optical networks

K. Thulasiraman, Muhammad S. Javed, G. Xue
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引用次数: 26

Abstract

The survivable logical topology mapping (SLTM) problem in an IP-over-WDM optical network is to map each link (u, v) in the logical topology (at the IP layer) into a lightpath between the nodes u and v in the physical topology (at the optical layer) such that failure of a physical link does not cause the logical topology to become disconnected. It is assumed that both the physical and logical topologies are 2-edge connected. For this problem Kurant and Thiran presented an algorithmic framework called SMART that involves successively contracting circuits in the logical topology and mapping the logical links in the circuits into edge disjoint lightpaths in the physical topology. In a recent work we presented a dual framework involving cutsets and showed that both these frameworks possess the same algorithmic structure. Algorithms CIRCUIT-SMART, CUTSET-SMART, CUTSET-SMART-SIMPLIFIED and INCIDENCE-SMART were also presented in. Effectiveness of both these frameworks as well as their robustness in providing survivability against multiple failures depends on the lengths of the cutset cover and circuit cover sequences on which they are based. To improve their effectiveness and robustness, in this paper we first introduce the concept of generalized cutset cover and generalized circuit cover sequences. We present an algorithm to get a generalized cutset (circuit) cover sequence from any given cutset (circuit) cover sequence. We then present GENCUTSET-SMART and GEN-CUTSET-SMART-SIMPLIFIED algorithms that remove some of the shortcomings of the dual framework of. We prove that there is a one-to-one correspondence between the set of generalized circuit cover sequences and the set of generalized cutset cover sequences. We then show that for each execution of GEN-CIRCUIT-SMART there exists an execution of GEN-CUTSET-SMART-SIMPLIFIED such that the groups of edges that they map into edge disjoint lightpaths are exactly the same. In other words, the distinction between the primal and dual methods disappears when they use generalized sequences. Preliminary simulation results confirm our expectation that GEN-CUTSET-SMART-SIMPLIFIED will perform better than CIRCUIT-SMART and CUTSET-SMART-SIMPLIFIED (when started with a circuit or a cutset sequence) in terms of number of additional protection edges to be added.
原始满足对偶:IP-over-WDM光网络中逻辑拓扑生存性的广义理论
IP-over- wdm光网络中的生存性逻辑拓扑映射(SLTM)问题是将逻辑拓扑(IP层)中的每条链路(u, v)映射到物理拓扑(光层)中节点u和v之间的光路中,以使物理链路的故障不会导致逻辑拓扑断开。假设物理拓扑和逻辑拓扑都是2边连接的。对于这个问题,Kurant和Thiran提出了一个名为SMART的算法框架,该框架涉及在逻辑拓扑中连续收缩电路,并将电路中的逻辑链接映射到物理拓扑中的边缘不相交光路。在最近的一项工作中,我们提出了一个涉及切割集的双重框架,并表明这两个框架具有相同的算法结构。文中还介绍了CIRCUIT-SMART、cut - set - smart、cut - set - smart - simplified和INCIDENCE-SMART算法。这两种框架的有效性以及它们在提供抗多次故障的生存能力方面的鲁棒性取决于它们所基于的切割集覆盖和电路覆盖序列的长度。为了提高它们的有效性和鲁棒性,本文首先引入了广义割集覆盖和广义电路覆盖序列的概念。提出了一种从任意给定的割集(电路)覆盖序列中得到广义割集(电路)覆盖序列的算法。然后,我们提出了GENCUTSET-SMART和gen - cutset - smart简化算法,这些算法消除了双框架的一些缺点。证明了广义电路覆盖序列集与广义割集覆盖序列集之间存在一一对应关系。然后我们证明,对于GEN-CIRCUIT-SMART的每次执行,都存在gen - cut - set - smart - simplified的执行,使得它们映射到边缘不相交光路的边缘组完全相同。换句话说,当使用广义序列时,原始方法和对偶方法之间的区别就消失了。初步的仿真结果证实了我们的预期,即GEN-CUTSET-SMART-SIMPLIFIED在要添加的额外保护边数量方面,将比circuit - smart和cutset - smart - simplified(当从电路或切割集序列开始时)表现更好。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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