Photon Netw Commun (2012) 23:123–129 DOI 10.1007/s11107-011-0342-y
Knight’s tour-based fast fault localization mechanism in mesh optical communication networks Ruyan Wang · Dapeng Wu · Yang Li · Xiong Yu · Zhao Hui · Keping Long
Received: 23 July 2011 / Accepted: 17 November 2011 / Published online: 29 November 2011 © Springer Science+Business Media, LLC 2011
Abstract Based on the knight’s tour theory, a novel link failure localization mechanism is proposed in the paper. Firstly, degree aware node splitting method is introduced. Then, the nodes and links of the network are mapped on the squares and steps of the corresponding chessboard. Subsequently, the probing signals are sent periodically to detect the network status in real-time manner. Once the link failure is detected, according to returned fault information, the link failure is located by searching the static mapping table. In the case of achieving failure localization of any link failure, the localization time and cover length of links are analysis. Numerical results show that the link failure can be located effectively and rapidly by the proposed strategy with less network resources utilized. Keywords Optical network · Knight’s tour · Node splitting · Fault localization
1 Introduction Optical networks have gained tremendous development due to their ability to support very high data rates. By using the dense wavelength division multiplexing (DWDM) technology, hundreds of wavelengths can be carried by the unique fiber. Due to the high speed nature of optical network, large amounts of data will loss due to the link failure. To R. Wang · D. Wu (B) · Y. Li · X. Yu · Z. Hui Optical Internet and Optical Signal Processing Research Lab, Chongqing University of Posts and Telecommunications, Chongqing, China e-mail:
[email protected] K. Long University of Science & Technology Beijing, Beijing, China
minimize data loss, it is critical to detect and locate the failed link immediately [1]. Fault detection and localization are essential for fault protection and restoration. Moreover, the link failure detection and localization can be implemented at different protocol layers. In general, using upper layer protocols require much longer detection period than the optical/physical layer scheme. So, it is desired that these faults can be uniquely identified and corrected at physical layer before they are even noticed at higher layers. Therefore, some monitoring techniques are used to solve the link failures problem, such as wideband and wavelength optical power monitoring, optical spectrum analysis, eye-diagram, optical pilot [1–7] and others. Previous work on fault detection and localization in optical network has been researched. In [3], based on the method of monitoring cycles (m-cycles), a fault detection scheme for the all-optical networks (AONs) is proposed. Independent wavelengths are employed as supervisory channels in this scheme. For each monitoring cycle, a node is designated to monitor the performance of this cycle, and a link failure is located by decoding the alarm signals that are generated by the monitors on a set of m-cycles passing through the failed link. Since the network is decomposed into cycles, faults can be located on the cycle. But the failed link within that cycle cannot be identified by this kind of localization method. An integer linear program (ILP)-based approach is introduced in [1] and [4], where both cyclic and acyclic monitoring structures are jointly considered to achieve link failure localization, which is called monitoring trail (m-trail) algorithm. It is shown that the m-trail outperforms the m-cycle at the same simulation scenarios. In order to minimize the sum of monitoring cost and bandwidth overhead, based on random code assignment and swapping, a simple algorithm for m-trail design is introduced in Ref. [4], and a general
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optical monitoring structure is provided, which includes the m-cycle, loop trails and open trails. Furthermore, the optimal m-trail architecture is constructed in the paper, which always achieves the localization of link failure with less monitoring resources. Additionally, the scheme of utilizing monitoring cycles (MCs) and monitoring paths (MPs) is presented in [5]. Any link failure can be located by the combination of MCs and MPs, which are required to pass through one or more monitoring locations. The limited perimeter vector matching (LVM) mechanism is introduced in [6]. Firstly, a smaller perimeter area around the shortest affected path is determined. Furthermore, by exchanging the information of fault vectors, the failed link within limited perimeter is located. In [7], a multi-failure localization protocol is presented on the basis of LVM mechanism. To handle multi-link failures, each failure in a small perimeter area is separated by the proposed protocol, so the failures can be located in a distributed manner, respectively. Most of the proposed monitoring techniques above are based on the establishment of dedicated monitoring cycles or paths; thus, a large number of monitors and other network resources are utilized to achieve the fault localization; moreover, the higher computational complexity and the more memory cells are demanded. In order to address the above mentioned deficiencies, the link failure localization mechanism based on the method of knight’s tour is proposed in the paper. The failed links can be located rapidly and accurately by the proposed scheme with less network resources consumed. The remainder of the paper is organized as follows. The model of the link failure localization is introduced in Sect. 2. The proposed fault localization scheme based on knight’s tour is presented in Sect. 3. The performances of proposed scheme are evaluated through numerical results in Sect. 4. The conclusion of this paper is presented in Sect. 5.
2 Model of failure localization Generally, the network topology can be described by undirected graph G(V, E), in which the nodes and links of the network are represented by the vertexes and edges of the graph, respectively. Subsequently, by constructing the adjacency matrix, the connection between the nodes and links is illustrated clearly. The specific connection between the objective vertexes can be characterized by the graph. If the squares on the chessboard are represented by vertexes of the graph and the relationships between the squares are expressed by the links, so the chessboard can be seen as a special undirected graph. Therefore, by a certain method, the connectivity between the nodes and links of the network can be reflected on the chessboard without changing the original attributes of the network topology. Based on the knight’s
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Fig. 1 Path of knight’s tour on the 4 × 6 chessboard
tour theory, the connectivity between the nodes and links is mapped on the squares and the legal horse steps, respectively. Consequently, using the method of the knight’s tour theory, the network state is monitored in real manner. Thus, the problem of the link failure localization can be solved effectively. The knight’s tour theory is illustrated as follow: For the chessboard with specified size and dimension, to find a sequence of legal knight moves such that the knight traverses every square once and only once. Generally, the knight’s tour theory can be solved by graph theory. Considering the square of chessboard as the vertex of graph, and regarding the knight’s step as the edge of graph, the problem of fault localization can be solved. Based on the knight’s tour theory, a path or circle that traversing every vertex once of a graph can be found [8]. The m × n chessboard is considered as a matrix of m rows and n columns. If the knight’s position is a(i, j), according to the knight’s tour theory, a(i ± 2, j ± 1) or a(i ± 1, j ± 2) is considered as the next legal position. Specially, the legal steps of the knight are a1 = i + j ± 3 or a1 = i + j ± 1[9], while a0 = i + j. Based on the constraint of knight step, a sequence path on the m × n chessboard can be labeled. One path of the knight traversing a 4 × 6 chessboard is shown by the Fig. 1. After traversing the entire chessboard, the knight starts from “S” and returns to the adjacent square of the chessboard “D” in the figure. According to the knight’s tour theory, the connectivity relationship of the nodes and links can be reflected on the chessboard. Therefore, after the fault localization model is established by the chessboard, the link failure of the network can be located by the scheme of the fault monitoring and localization. The detail model and scheme of the fault localization are introduced in the next section.
3 Fault localization scheme based on knight’s tour In order to locate the link failure in optical network efficiently and rapidly, the degree aware node splitting mechanism based on knight’s tour algorithm is introduced in the paper, where all the nodes and links in the network are mapped on the corresponding m × n chessboard. Furthermore, after the failed
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link information returned by the probing signals, by searching static mapping table, the link failure is exactly located by source node. This link failure localization scheme will be divided into two processes, the degree aware node splitting scheme and the fault localizing method, respectively. 3.1 Degrees aware node splitting mechanism The network with N nodes and L links can be denoted as an undirected graph G(V, E), so the relationships between the vertexes and edges can be shown clearly by the theorems as follow. Theorem 1 For any graph G, v∈V d(v) = 2m Proof Considering the graph G with m edges, there are two nodes for each link, so the total degree of the graph is 2 m, so the conclusion can be drawn that v∈V d(v) = 2m. Theorem 2 For any graph G, the number of vertices with odd degree must be even. Proof Let V1 and V2 are the corresponding set of nodes with odd degrees and even degrees of the G. Based on the Theo rem 1, theconclusion can be drawn that v∈V1 d(v)+ v∈V2 d(v) = v∈V d(v) = 2m. For the V2 is the node set with even degrees, so the sum of v∈V2 d(v) must be even; on the other hand, for the value of 2m is even, so the sum of v∈V1 d(v) is even also. As a result, the value of the V1 must be even. The main aim of this mechanism is to reconstruct the logical topology; furthermore, the reconstructed logical topology of the network can be mapped on the chessboard, where each node and link in the network corresponds to the square and the legal knight’s step logically. But the original properties of the network remain unchanged. Thus, the degree aware node splitting mechanism is proposed according to the relationship between the network and chessboard. The steps of degree aware node splitting mechanism are shown by Fig. 2. According to the Theorem 2, the numbers of nodes, which the value of node degrees is odd, must be even. Firstly, the two nodes with odd degrees are chosen as the source and destination nodes. Secondly, some virtual links will be added into logical network topology. For the case of single hop distance between two nodes, a virtual link will be added between the nodes with odd degrees. Otherwise, the shortest path between the two nodes with odd degrees is searched, and the virtual link is added between the node and its adjacency node within the path. Thirdly, the node is split into several copies according to the network connectivity, and the number of copies is the half-value of node degrees. Moreover, this execution begins from the node with maximal value of degrees. When there are several nodes have the same degrees, the node with low serial number is selected
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Target network
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Number of odd degree =2?
Yes The two odd degree nodes are regarded as source and destination node
Adding virtual link between odd degrees node
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Number of odd degrees = 0 ?
Node degrees self-sensing splitting: the number of the
node copies is the half value of the node degrees nodeNum: the value of the nodes total after nodes copies
Path: connect the nodes with existent link between source and destination nodes
There are several paths?
Yes
No Find a path from source to destination traversing all the nodes and links
exchange some nodes of the cycle with other link
Only one path: write as equence of nodes of the found path
Fig. 2 Flowchart of the degree aware node splitting mechanism
firstly. The process will continue until all the nodes in the network have been split. The parameter of nodeN um denotes the number of the nodes copies. Furthermore, a path from source node to destination node will be found which consists all the links in the network. Lastly, the serial number is assigned for the each node and link in the path. Generally, by the degree aware node splitting mechanism, the unique path covers all the nodes and links of the network can be found for any target network. 3.2 Fast fault localization method By the proposed node splitting mechanism, the target network topology is reconstructed logically. As a result, the
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1 Create the adjacency matrix of the network adjnet[ N ][ N ] 2 Initialize empty arrays degree[] , node[][] , path[] , kt _ path[] 3 for i from 1 to N 4
set count
