Shared p-cycles design for dual link failure restorability in optical WDM networks

THE JOURNAL OF CHINA UNIVERSITIES OF POSTS AND TELECOMMUNICATIONS Volume 14, Issue 3, September 2007

XIE Zheng-cheng, XING Jun-wei, WU Li, JI Yue-feng

Shared pcycles design for dual link failure restorability in optical WDM networks CLC number TN915.01

Document A

Abstract Pre-configured cycles (p-cycles) can attain high capacity efficiency and fast protection switching times in wavelength division multiplexing (WDM) networks. This article proposes the weighted straddling link algorithm (WSLA) for generating a subset of all cycles that can guarantee 100% restorability in case of dual link failure, and give an integer linear programming (ILP) formulation that solves the shared p-cycles design problem minimizing the total spare capacities. Numerical result shows that our method can achieve 100% dual link failure restorability with acceptable spare capacity. The larger standard deviation of demand set and the larger node degree network, the better the shared p-cycles scheme performs. Keywords dual link failure, p-cycles, WDM

1 lntroductlon At present, optical network employing wavelength division multiplexing can provide huge bandwidth for satisfying the ever-increasing demand for bandwidth, and the research of survivability of high speed optical network based on WDM technology is poured down subsequently. Most research to date in survivable optical network design and operation focuses on single link failure. However, the occurrence of dual link failure is not uncommon in a network topology [ 1,2]. So far, there are two classes of solutions for dual link failure restorability. One is the spare capacity reconfiguration to design the network for surviving to single link failure, then enhance the survivability to dual link failure without adding any extra capacity or only a little capacity [3]. The other is to achieve 100% restorability to dual link failure by providing two backup capacity for each link, then optimize the model to minimize the total spare capacity. Both for single link failure and dual link failure restorability, shared backup path protection (SBPP) is comparatively an optimal solution using the least total spare capacity. However, Received date: 2006-09- 14 XIE Zheng-cheng (K),XING Jun-wei, WU Li, JI Yue-feng Key Laboratory of Optical Communications and Lightwave Technologies, Beijing University of Posts and Telecommunications. Beijing 100876,China E-mail: zhch.xie8gmail.com

Article ID

1005-8885 (2007) 03-0074-05

it has the fatal fault that transmission integrity can not be assured. Fortunately, the p-cycles scheme presented by Grover in 1998 [4]can solve the question completely. Its protection structures are fully pre-cross-connected, so the optical protection paths can be pre-engineered and tested, and be in a known working condition prior to their use [ 5 ] . In previous works, p-cycles scheme has been used to dual link failure restorability. Multi-failure survivability scheme (MFS) is present in Ref. [3]. It designs to recover from single link failure by using normal p-cycles first, and add additional p-cycles(AP) to survive from the second link failure. It can achieve high probability to survive multiple failures without adding any extra capacity, but it can not achieve 100% restorability for dual link failure. In Ref. [6], some initial analyses of dual failures restorability with static p-cycles have been done, and it proved that we can improve the dual link failure restorability by modifying the selection of p-cycles. Strategies with static p-cycles to enhance the dual link failure restorability based on the concepts of failure spreading and limiting the maximum number of protection relationships of any p-cycle is proposed in Ref. [7]. A static p-cycles protection deployment rule for dual span failures is proposed in Ref. [8]. In this article, we design networks to achieve 100% restorability for dual link failure by using shared p-cycles. WSLA is proposed to generate the p-cycles set which is applicable to shared p-cycles design. And an ILP formulation is given to solve the shared p-cycles design problem minimizing the total spare capacities. The essence of the shared p-cycles design is that it allows multiple p-cycles that have a common span to share the spare capacity on that span, so as to reduce the total spare capacity reserved for protection. Compared to independent p-cycles design, shared p-cycles design can reduce the total spare capacity remarkably. In Ref. [9], the concept of shared p-cycles is described in detail. The rest of the article is organized as follows. In Sect. 2, we provide an algorithm for generating a subset of all cycles that can guarantee 100% restorability in case of dual link failure given enough spare capacities. In Sect. 3, we give an ILP formulation that solves the shared p-cycle design problem

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XIE Zheng-cheng, et al.: Shared p-cycles design for dual link failure restorability in optical WDM networks

minimizing the total spare capacities. In Sect. 4, we present some simulation results on two networks and evaluate the efficiency performance of the shared p-cycles design scheme for dual link failure. Finally, a conclusion is given in Sect. 5.

2 The welghted straddling llnk algortthm One of the most attractive particularities of p-cycles is to provide two restoration paths for their straddling edges. Therefore, we can design networks survivable to dual link failure by selecting felicitous p-cycles set, where each edge straddles on at least one p-cycle or is part of at least two link-disjoint p-cycles. In Ref. [lo], Zhang Han-xi proposed the straddling link algorithm (SLA), which generates p-cycles having at least one edge straddling on. However, the SLA aims for survivability to single link failure, so we propose the WSLA to apply to dual link failure restorability. Although their names are similar, they have distinct difference in generating p-cycles. Before we introduce our WSLA in detail, two considerations are presented. 1) In order to make the network to survive dual link failure, the candidate cycles must be able to protect all spans in the network. That is, each span must be an on-cycle span of at least two link-disjoint candidate p-cycles or a straddling span of at least one candidate p-cycle. 2) Since we would like to minimize the spare capacity by a shared p-cycles ILP, the more candidate p-cycles share the spans, the better. Then we give the description of some variables used in the WSLA. 1) The weight of span W E (1,3,5] : “1” denotes that the edge

I5

between node 2 and node 3 by Dijkstra algorithm and join them to a p-cycle(P1). Then the w and s of all spans interrelated to PI are reset (Fig. l(b)). And the spans whose w value equal to 1 are preferred to be included by the next p-cycle. It is also supposed that p-cycle P2 straddling on s5.6 is secondly generated in WSLA process, then the w and s of all spans interrelated to P2 are reset (Fig. 1(c)).

(a) A three-connected network whose all spans are set initial weight value

(b) P-cycle P1 straddled on the span of node 2 and node 3 is

found, and the w of spans on P1 are reset

prefers to be used, “3” is the initial value, “5” denotes that the edge prefers to be not used. 2) The symbol of spans€ (0,1,2) : the number denotes how many backup paths the span has, and the default value is 0. When the WSLA complete, s of each span is 2. Statements: 1) When we refer to find the shortest path between the end nodes of one span, the span itself is excluded. 2) The WSLA is to be used in three-connected networks or more than three-connected networks, it can find two link-disjoint shortest paths between the end nodes of any span by Dijkstra a algorithm. To interpret the WSLA more intuitionally, we take a simple three-connected network for example. First, we define that sij denotes the span between node i and node j . Fig. l(a) shows the network topology, the initial values of w and s of all the network spans. We assume that the first p-cycle should be straddling on ~ 2 . 3 .We can get two link-disjoint shortest paths

(c) P-cycle P2 straddled on the span of node 5 and node 6 is found, and the w of spans on P2 are reset

Fig. 1 A simple example

In the following, the WSLA is explained in detail. Step 1 Set w and s of all spans default value. Step 2 Check s of span i. If s does not equal to 0, go to Step 7; else go to Step 3. Step 3 If it can find two link-disjoint shortest paths between the end nodes of span i, then join them to a p-cycle, and sets of i 2, go to Step 5; else, go to Step 4. Step 4 Find one shortest paths between the end nodes of the span, combine the span itself and the shortest path to a p-cycle. Step 5 For each span j on the new p-cycle, if s is 0, set s of

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1 and set w 1, go to Step 7; if s is 1, go to Step 6. Step 6 Select out the existing p-cycles via span j . If one of them is link-disjoint to the new p-cycle besides span j , sets 2 and set w 5. Step 7 If s of all spans do not equal to 0, go to Step 8; else loop Step 2. Step 8 Check s of span i. If s equals to 1, go to Step 9; else go to Step 11. Step 9 Set w and s of all spans to default value. Step 10 Find two link-disjoint shortest paths between the end nodes of span i, then joint them to a p-cycle. Step 11 Checks of span i. If s of all spans equal to 2, algorithm is complete; else go to Step 8.

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ILp formulatlon for shared pcycles deslgn

We model a WDM network as a graph G(V, E ) where V denotes the set of nodes and E denotes the set of edges. A unit of capacity on an edge is defined as one wavelength channel. We assume that an edge j contains 1, fibers of K wavelength channels each, so the capacity of edge j is c,= l,K. In this article, we discuss the bi-directional p-cycles, so each edge consists of at least a pair of fibers which transmits date in opposite directions. In the counter directional fibers, the capacity may not be equal. A bi-directional p-cycle can provide one restoration path for every on-cycle edge, and two restoration paths for any straddling edges. Let P denote the set of all candidate bi-directional p-cycles for a given network. The set of all candidate p-cycles are pre-determined by the algorithms present in Sect. 2. In the following, we describe several variables and parameters involved in the ILP model. W, is the number of working units which should be protected on edge j . s, is the number of spare units required on edge j to configure p-cycles. n, is the number of backup units of p-cycle i , and it is the max value of all the w, which are protected by p-cycle i. ySr indicates the relationship between the failed edge and p-cycle i;

y , , = 1 if r is protected by p-cycle i , otherwise Y , , = ~ 0. p : , indicates the relationship among the failed edge r, the other edge j , and the p-cycle i ; p,:, = 1 if r is protected by p-cycle i while j is an on-cycle edge to p-cycle i, otherwise p : , = 0. x , ~ indicates the protective capacity of p-cycle i to the working capacity on edge j ; xlJ = 2 if edge j is straddling on p-cycle i, xlJ = 1 if edge j is on p-cycle i, otherwise xEJ= 0. We assume that the network is a virtual wavelength path (VWP) network where all nodes can convert a wavelength on any input fiber to any other wavelength on any output fiber. The objective of shared p-cycles design is to minimize the total cost of spare resources. So, the ILP for dual link failure

restoration based shared p-cycles design can be formulated as follows: Objective: Minimizext,s,

(1)

I‘ E

wi +s,
VjeE

(6)

Constraints in Eq. ( 2 ) and Eq. ( 3 ) determine the required spare units on j to recovery from failed edge rl and r2. Constraints in Eq. (4)ensure that all pairs of failed edges share the spare units on the edge j . Constraints in Eq. (5) guarantee that all the working units can be protected twice. And constraint in Eq. (6) shows the capacity restriction on an edge. All the variables in Eqs. (1)-(6) are non-negative except the ti. Note that Eqs. (2) and (5) are newly introduced in this article. Eq. (6) has been discussed in many literatures. In the wavelength path(WP) network, the nodes are not capable of wavelength conversion, so we need to consider the wavelength continuity constraint on the lightpaths. Fortunately, we can take individual wavelengths on every edge in to account, and can consider a WP network to be K independent networks which have distinct wavelength. For our ILP, Eqs. (2) and (6) are still valid for every wavelength. JXq. (1) needs to be modified to minimize the total cost over all individual wavelengths.

4

Numerical results

To estimate the efficiency of the shared p-cycles design for dual link failure restorability, we select two networks as the test cases. Their properties are shown in Table 1. The WSLA is programmed by C language, and the ILP is resolved using software M 6.5. The two networks are both three-connected, therefore it is topologically feasible for the dual link failure to survive if adequate spare capacity is present. We assume that all nodes perform full wavelength conversion, each span has two fibers for bi-directional transmission, and the number of wavelength per fiber is 128. The cost for every wavelength channel on every edge is identical, so the cost of all edges is also uniform. Table 1 The properties of two tested networks Network Number of nodes Number of spans Average of nodal degree

COST 239 11 26 4.1

Network #2 11 20 3.6

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XIE Zheng-cheng, et al.: Shared p-cycles design for dual link failure restorability in optical WDM networks

We consider full mesh of demands for each test network, i.e. the demands exist among all the pairs of end nodes. The light path number of each demand is randomly chosen from 20 to 30, and all the light paths are assumed to bi-directional. In order to balance the traffic load on each edge and minimize the number of working wavelengths on each edge, we route the demands according to shortest path routing algorithm with metrics reciprocal to the free capacity of the edge. Ten demand sets are taken into account in each test network, and their standard deviations, which describe the balance degree of the working capacity o n each edge, vary from 0 to 3.5. And the standard deviation can be calculated by Eq. (7) and Eq. (8). According to Fig. 2, we can draw a conclusion that larger the standard deviation of demand set, the more capacity cost. In p-cycles design, the spare capacity of each p-cycle is determined by the maximum of the working capacity protected by it, so the more balanced the working capacity of a p-cycle, the smaller spare capacity is required. - 1 "

x =-Ex, n

where n is the number of the demand in a demand set, and Xi is the numbers of the working capacity of demand i. 6 2.70

2.65

2301

<, 0

scheme. Also, Fig. 3 tell us that our method performs better in the COST 239 than in network #2, which is different from the former in degree of nodes. So, the larger the degree of nodes, the better are the shared p-cycles design. 0.485

.

r

2 0 480 P e,

0475 V 0

5 0470 E

2 0465 -2

2 0 460

d '0

5

+COST 239 -+Network #2

0 455

% 0 450

A .-

0

05 10 15 2 0 25 30 The standard deviation of demand set

3.5

Fig. 3 Performance of shared p-cycles design and independent

p-cycles design

b Concluslonr

(7)

,=I

3

77

05 10 1 5 20 2 5 30 The standard deviation of demand set

I

35

Fig. 2 Relative spare capacity cost required in two test

networks for 100%dual link failure restorability For the COST 239, the relative spare capacity cost is similar to the result in Ref. [8]. As for the network #2, the relative spare capacity is more than COST 239. So, we know that we can gain 100% dual link failure restorability in larger node degree network using less spare capacity. We compared the performance of the shared p-cycles design with the independent p-cycles design, the former distinctly outperformed the latter. And the result profits from the ILP given in Sect. 3. Especially, Eq. (4) is the soul of the ILP. Figure 3 shows that spare capacity required in shared p-cycles design is only 4 5 4 9 % of that required in independent p-cycles design. Therefore, it is necessary to use the shared

P-cycles are well known for high capacity efficiency and fast protection switching time. One of the most important merits of p-cycle is that it can provide two restoration paths for its straddling edges, which is incapable for ring protection. In this article, we use p-cycles to protect from dual link failure completely. First, we propose WSLA for generating a p-cycles set that can guarantee 100% restorability in case of dual link failure. Then an ILP formulation is given to solve the shared p-cycles design problem minimizing the total spare capacities. We selected the pan-European COST 239 and other networks with 11 nodes and 20 spans as the test network. Numerical result shows that our method can achieve 100% dual link failure restorability with acceptable spare capacity. The larger the standard deviation of demand set and the larger node degree network, the better our shared p-cycles scheme performs. Acknowledgements This work is supported by the National Science Fund for Distinguished Young Scholars (60325l04), the National Natural Science Foundation of China (60572021), the SRFDP of MOE (20040013001).

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Biographies: XIE Zheng-cheng, Ph. D. Candidate in Beijing University of Posts and Telcommunications, interested in survivability of intelligent optical networks.

self-planning network restoration. Proceedings of IEEE International Conference on Communications: Vol I, Jun 7-1 I , 1998, Atlanta, GA, USA. Piscataway, NJ, USA: IEEE, 1998: 537-543

5. Kodian A, Grover W D. Failure-independent path-protection p-cycles: efficient and simple fully preconnected optical-path protection. Journal of Lightwave Technology, 2005, 23( 10): 3241-3259 6. Schupke D A. Multiple failure survivability in WDM networks with p-cycles, Proceedings of the 2003 IEEE International Symposium on Circuits and Systems: Vol 3, May 25-28 2003, Bangkok, Thailand. Piscataway, NJ, USA: IEEE, 2003: 866-869 7. Schupke D A, Grover W D, Clouqueur M. Strategies for enhanced dual failure restorability with static or reconfigurable p-cycle networks. Proceedings of IEEE International Conference on Communications: Vol 3, Jun 20-24 2004, Paris, France. Piscataway, NJ, USA: IEEE, 2004: 1628-1633 8. Hou Lin, Zhou Yu, Gu Wan-yi. A static p-cycles protection deployment rule for dual span failures. Journal of Beijing University of Posts and Telecommunications, 2006, 29(4): 57-60 (in Chinese) 9. Zhong Wen-de, Zhang Zhen-rong. Design of survivable WDM networks with shared-p-cycle. Optical Fiber Communication Conference: Vol 1, Feb 23-25 2004, Washington, DC, USA. Piscataway, NJ, USA: IEEE, 2004: 554-556 10. Zhang Han-xi, Yang 0. Finding protection cycles in DWDM

XING Jun-wei, M. S. Candidate in Beijing University of Posts and Telcommunications, interested in survivability of intelligent optical networks.

WU Li, M. S. Candidate in Beijing University of Posts and Telcommunications, interested in survivability of intelligent optical networks

JI Yue-feng, Beijing University of Posts and Telcommunications, professor, advisor, interested in optical fiber communication.