A novel shared-path protection algorithm with correlated risk against multiple failures in flexible bandwidth optical networks

Optical Fiber Technology 18 (2012) 532–540

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A novel shared-path protection algorithm with correlated risk against multiple failures in flexible bandwidth optical networks Jie Zhang, Chunhui Lv ⇑, Yongli Zhao, Bowen Chen, Xin Li, Shanguo Huang, Wanyi Gu State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, 100876, China

a r t i c l e

i n f o

Article history: Received 17 June 2012 Revised 25 August 2012 Available online 13 October 2012 Keywords: Flexible bandwidth optical networks Survivability Multiple failures Correlated risk protection

a b s t r a c t In this paper, to decrease the traffic loss caused by multiple link failures, we consider the correlated risk among different connection requests when both the primary and backup paths are routed and assigned spectrum. Therefore, a novel shared-path protection algorithm is developed, named shared-path protection algorithm with correlated risk (SPP_CR), in flexible bandwidth optical networks. Based on the correlated risk, the routing can be diverse and the sharing in backup spectral resource will be restricted by SPP_CR algorithm, then the dropped traffic caused by simultaneous multiple failures between primary and backup path can be efficiently decreased. Simulation results show that, SPP_CR algorithm (i) achieves the higher successful service ratio (SSR) than traditional shared-path protection (SPP), shared-path protection with dynamic load balancing (SPP_DLB) and dedicated path protection (DPP); (ii) makes a better tradeoff in blocking probability, protection ratio (PR), average frequency slots consumed (AFSC) and redundancy ratio (RR) than SPP, SPP_DLB and DPP algorithms. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction Compared with traditional WDM networks, flexible bandwidth optical networks can provide appropriate bandwidth resource based on traffic demand. Authors in [1] proposed and demonstrated a novel SLICE network architecture, in which the necessary spectral resources can be allocated according to the traffic demands. For bandwidth allocation problem, Jinno et al. [2] have proposed the distance-based adaptive spectrum allocation scheme. Christodoulopoulos et al. [3] have also proposed a dynamic and elastic bandwidth allocation scheme in flexible OFDM-based optical networks, introducing the routing, modulation level and spectrum allocation (RMLSA). To overcome the recovery spectral insufficiency and to ensure a highly survivable traffic, a novel restoration scheme named bandwidth squeezed restoration (BSR) scheme [4], has been proposed by the manner of best-effort recovery. However, BSR does not provide high quality of transmission (QoT) to recovery traffic. Compared to the conventional survivable fixed grid networks, authors in [5] proposed an efficient survivable FWDM network design algorithm, which enables it to achieve a better efficiency in terms of spectral utilization, power consumption, and cost. However, they did not consider the shared-spectrum protection in this survivable FWDM algorithm. Compared with traditional backup sharing in WDM networks, the bandwidth allocation problem is more complex and challenging to share backup

⇑ Corresponding author. E-mail address: [email protected] (C. Lv). 1068-5200/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.yofte.2012.09.002

resources in flexible bandwidth optical networks. Authors in [6] proposed and evaluated shared-path protection strategies in OFDM-based optical networks, and showed that aggressive backup sharing can significantly improve capacity efficiency. For efficient restoration of traffic under multi-link failures, authors in [7] considered the shared-path protection of dynamic load balancing and investigated the network performance of multi-link failure restoration in spectrum-elastic optical path networks. However, the performance of this scheme has not yet sufficiently investigated since they did not consider the correlated risk of backup spectral sharing among different traffic. In high-capacity flexible bandwidth optical networks, multiple failures (especially including nodes’ or links’ failures) will result in huge traffic loss without effective survivable scheme. Considering the recovery time of failures and to improve capacity efficiency, we only focus on shared protection in this paper since restoration takes too long time to efficiently recovery failure traffic. To cope with single failure problem in WDM mesh networks, authors in [8] systematically summarized the protection schemes for survivability including dedicated-path protection (DPP), shared-path protection (DPP) and shared-link protection. Authors in [9] mainly focus on shared-path protection and investigated the problem of dynamic survivable lightpath provisioning strategies in WDM mesh networks. Considering the delay tolerance of shared-path protection, Cavdar et al. [10] investigated dynamic scheduling of connection requests by using different scheduling strategies for SPP, in which different dynamic scheduling algorithms are developed and compared by giving priority to connections according to their arrival rates, delay tolerances and holding times. These

J. Zhang et al. / Optical Fiber Technology 18 (2012) 532–540

papers cited above only consider the resources efficiency and recovery time for failure traffic whereas the multiple traffic correlated risk do not adopt efficiently protection measures to lessen the risk among different traffic. For shared risk link group (SRLG) problem, many papers have been investigated and proposed different kinds of models to solve it. Authors in [11] investigated the impact of SRLG failures on shared-path protection and evaluated different policies for backup re-provisioning. Ref. [12] proposed a disjoint path selection scheme for generalized multi-protocol label switching (GMPLS) networks, treating the number of SRLG members related to a link as part of the link cost when the k-shortest path (KSP) algorithm is executed. As an alternative to KSP, an innovative trap avoidance heuristic that requires much less running time than KSP (and ILP) was proposed [13] and yet could effectively avoid almost all the avoidable traps as an ILP-based approach. The authors also extent a algorithm for the scheme of protection with multiple segments (PROMISE) to provide efficient SRLG protection [14], achieving a higher bandwidth efficiency and lower request blocking probability. To solve the problem about finding an SRLG-disjoint backup path within reasonable computational complexity, authors in [15] presented a best effort SRLG failure protection, which chooses the backup path sharing and the least number of SRLGs with the working path. With some realistic constraints incorporated into the static provisioning problem, three classes of SRLG-diverse path protection schemes: dedicated, shared and unprotected, were considered and analyzed [16], respectively. Considering partial SRLGdisjoint protection based on differentiated reliability constraints [17], a novel survivable routing algorithm in WDM optical mesh networks has been proposed. For reliable collective communication problem with SRLGs, Zhu et al. [18] proposed integer linear program (ILP) model to solve this problem, and proved that the maximum reliable collective communication problem is NP-hard, providing a greedy approximation algorithm. However, these papers cited above did not consider the correlated risk among different connection requests in the case of multiple failures. The potential correlated risk occurs if and only if one connection request uses the same nodes or links with other connection requests together between the primary path and backup path (or several connection requests use the same spectrum resources of backup path), which differs from the concept of SRLG [11–22]. To lessen the potential correlated risk, we can disperse the routing of primary and backup paths and weaken the competition of backup resources sharing in the same backup path. So, the purpose of this paper is to decrease the correlated risk, by which we can reduce the loss caused by multiple failures and improve the efficiency of resource utilization at the same time. The rest of this paper is organized as follows: Section 2 states the network model and problem description. Section 3 describes the shared-path protection approach with correlated risk in detail. Section 4 presents the heuristic algorithms and analyzes its time complexity, Section 5 gives the simulation results and analysis, and Section 6 is the final conclusion. 2. Network model and problem statement 2.1. Network model For flexible bandwidth optical networks, each optical node is equipped with bandwidth-variable optical cross-connects (BVOXCs) and flexible transponders. The network topology is defined as G(N, L, S), where N, L and S are the set of nodes, fiber links and frequency slots respectively. |N|, |L|, and |S| represent the numbers of nodes, links, and the frequency slots, respectively. For each dynamic connection request arrival with random bandwidth requirement, source node and destination node, both primary path and

533

link-disjoint backup path are routed, and then the frequency slots will be assigned based on correlated risk value with other existed connection requests in the network, which need to satisfy both spectral continuity constraint and spectral consecutiveness constraint. In addition, some requisite notations and their definitions are listed Table 1. 2.2. Correlated risk We put forward the correlated risk among different connection requests (CRs) and consider the risk value when routing and assigning backup resource for dynamic traffic arrival. Assuming the traffic will be dropped once failing in both primary and backup paths, in our work, if (i) no more than one connection request will drop for arbitrary double-link failures at the same time and (ii) no connection requests share backup spectrum path, then correlated risk does not exist in a network. In other words, the correlated between two given connection requests exists if and only if both the primary and backup paths of one connection request share nodes (including links) with another connection request, or several connection requests share backup path, which is illustrated in Fig. 1. Fig. 1a has the best traffic distribution to endure multiple failures without the correlated risk. The connection request (CR) will not drop until both primary and backup paths fail, and arbitrary double link-failures can only break a connection request at most. However, CR1 and CR2 share links on both primary and backup paths in Fig. 1b, and share backup resource in Fig. 1c. Fig. 1d performs the worst case whereas it consumes much less resources. Because of the network capacity constraint, it is impossible to avoid the correlated risk for all CRs and the distribution in Fig. 1b and c is partly acceptable to some extent. We expect to reduce the traffic loss caused by multiple failures through decreasing the correlated risk among different traffic. So considering a connection request with single source–destination pair, our objective is to find a pair of primary and backup paths from source s to destination d making a tradeoff in correlated risk and resource utilization efficiency. We will develop an algorithm named shared-path protection with correlated risk (SPP_CR), in which we first compute the primary path and the correlated risk Table 1 Notations and definitions. Symbol

Meaning

Ni Li,j Ci,j CRk

The ith node (0 6 i 6 |N|1) The link between node i and j The initial cost of a link Li,j The kth connection request The number of frequency slot requirement for CRk The set of connection requests whose primary path traverse Li,j The set of connection requests whose backup path traverse Li,j The set of connection requests whose primary or backup path traverse Ni The dynamic cost on link Li,j for computing CRk’s primary path The dynamic cost on link Li,j for computing CRk’s backup path The primary and backup paths for CRk (a set of links) respectively The number of shared links by PPm  PPku and PPm  BPk respectively The number of shared nodes by PPm  PPk and PPm  BPk (excluding source and destination node) respectively The duration time that traffic m and k coexist The average holding time of traffic The factor of shared link risk, shared node risk The correlated primary-primary paths risk value between PPm and PPk The correlated primary-backup paths risk value between PPm and BPk The total correlated risk value on link Li,j for CRk The total correlated risk value on node Ni for CRk Link and node failure probability respectively

xk LPSi,j LBSi,j NSSi DCPijk DCBijk PPk, BPk SLPmk, SLBmk SNPmk, SNBmk STmk

s ql, qn CPRmk CBRmk CLRijk CNRik LFP, NFP

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2

1

3

4

2

1

5

6

Backup Path for CR1

6

4

Primary Path for CR2

7

Backup Path for CR2

Backup Path shared by CR1 and CR2 3

2

4

1

5

6

5

(b) The correlated risk by shared links

3

2

1

4

7

(a) With no correlated risk Primary Path for CR1

3

5

6

7

(c) The correlated risk by shared backup path

7

(d) The correlated risk by shared links and backup path

Fig. 1. Illustration of the correlated risk among different CRs.

with other online paths, then on the basis of correlated risk value, route and assign spectral resource for backup path. 2.3. Correlated risk parameters For further describe clearly the correlated risk problems, we will first introduce several important correlated risk parameters. Firstly, we define the correlated primary-primary paths risk value between PPm and PPk (CPRmk), and the correlated primary-backup paths risk value between PPm and BPk (CBRmk) as Eqs. (1) and (2), which will be used in routing and assigning spectrum for backup path, as follows:

CPRmk ¼ g  ðSLP mk  ql þ SNP mk  qn Þ  ST mk =s

ð1Þ

CBRmk ¼ g  ðSLBmk  ql þ SNBmk  qn Þ  ST mk =s

ð2Þ

where g is an adjustable parameter depending on specific topology and demand, and ql and qn should be constrained by ql + qn = 1 an ql:qn = LFP:NFP. The values of CPRmk and CBRmk virtually represent the correlated risk degree for two given paths within different traffic, which is proportional to the numbers of shared links and nodes between PPm  PPk and PBm  BPk, respectively. Besides, we assume that the normalized coexistence time factor 1/s also plays an important role. Secondly, considering the total correlated risk on single node or link, we define the correlated link risk value on link Li,j for CRk (CLRijk) and the correlated node risk value on Ni for CRk (CNRik), which mainly describe risk degree of the link and node for a coming traffic. The CLRijm and CNRim are written as follows:

CLRijm ¼ ql 

1

CNRim ¼ qn 

X

ST mk

s CRk 2fLPSij ;LBSij g 1 X

s CRk 2NSSi

ST mk

ð3Þ

ð4Þ

where STmk denotes duration time that CRm and CRk coexist. We take into account the potential risks of links and nodes in a network since one node’s or several links’ failure will result in multi-link failures. Finally, to decrease the competition of backup resources after multiple failures happen, we define the maximum shared times (MST) of backup spectrum resources to restrict the resource competition. 3. Shared-path protection with correlated risk For efficiently degrease the correlated risk for shared-path protection between primary and backup paths and to weaken the competition of backup resources sharing at the same time, how to route and assign spectrum for backup path become a great challenge based on the correlated risk. 3.1. Diverse routing with correlated risk Once the primary path for a CRk is set up successfully (compute the shortest path by Dijkstra algorithm), we can compute its correlated risk values for all primary and backup paths with current online traffic by CPRmk and CBRmk. Considering the influence of other paths traversing link Li,j, the dynamic link cost Li,j can be adjusted for a new CRk arrival as follows:

0 DCBijk ¼ C ij @1 þ

X CRm 2LBSij

CPRmk þ

X

1 CBRmk A

ð5Þ

CRm 2LPSij

where DCBijk denotes the dynamic cost to compute backup path on link Li,j for a new arrival CRk, which includes basic cost and the correlated risk costs between CPRmk and CBRmk. Eq. (5) elaborates that: (i) the present CRm on primary and backup paths will effect the computing paths for a new coming CRk, i.e., considering the effect of correlated risk between each present CRm online and the new

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(a)

(b)

Fig. 2. Illustration of routing for backup path in traditional SPP (a) and SPP_CR (b).

coming traffic CRk while selecting paths for CRk, the more nodes or links shared by PPk and PPm (BPm), the larger dynamic cost the links on BPm(PPm) have; (ii) the additional link cost will generated by the sum of all the effects of CRm2LBSij and CRm2LBSij. After the cost of all Li,j have been adjusted, the Dijkstra algorithm will be applied to compute the backup path for a new coming traffic CRk. For example, considering the traffic correlated risk in a 9-node network in Fig. 2, we will dispose with three connection requests (CR1 from node A to node D, CR2 from A to B and CR3 from C to D), which dynamically arrive one by one with the order of time. Firstly the primary and shared backup paths can be computed by Dijkstra algorithm, by which we can obtain A–B–C–D and A– H–I–D for CR1, A–B and A–H–B for CR2, C–D and C–I–D for CR3, respectively. Whereas in SPP_CR algorithm, to minimize correlated risk between CRs, we can adjust link cost by formula (5) on the corresponding backup links of CR1, in which we consider both the correlated primary-primary paths risk value CPRmk and the correlated primary-backup paths risk value CBRmk. For CR2, the cost of link A– H, H–I and I–D is adjusted and set to higher values, then the cost of a path A–E–F–C–B may have the least cost and this path is selected as backup path, which shows in Fig. 2b. By the same method, CR3 can be also established and its primary and backup paths are C–D and C–F–G–D, respectively. We can see that, in Fig. 2a, once links between A–B and H–I (or C–D and I–D) simultaneously fail, both CR1 and CR3 (or CR2 and CR3) will drop. However, considering

the correlated risk, no more than one CR will be dropped when any two links fail simultaneously in this network. Therefore, we can adopt the method of considering the correlated risk to efficiently decrease the failure traffic dropped by best effort. However, this example above describes a best case. With the traffic load increasing, some connection requests shared links on primary path also have to share some links on backup path for the network-scale and resources-capacity constraints. For this kind of CRs, considering the primary paths of different connection requests may have the correlated risk, the sharing times of spectrum resources should be restricted and it can be described as follow. 3.2. Spectrum allocation with correlated risk We define TS as a threshold value of the correlated risk, which determines that the CRm cannot share backup path with CRk if their CPRmk smaller than TS. S(i, j, u) denotes the uth frequency slot on Li,j, SN(i, j, u) represents the sharing time of traffics’ backup spectral resources on Li,j and ASSij is the set of available slot for the allocation of backup spectrum on Li,j, where available frequency slots means the slots not occupied by primary path. The set of available frequency slots for BPk (ASSk) is acquired:

ASSk ¼ fnjðn 2 ASSij ; Lij 2 BP k Þ;

PP for CR3

backup slot for CR1

E

PP for CR2

1

2

3

4

5

C

6

1 2 3 4 5 6

H backup slot shared by CR1 and CR3

D

1 2 3 4 5 6

B 1 2 3 4 5 6

A

backup slot for CR2

G

PP for CR1

0 6 n 6 jSj  1; n 2 Ng

1

2

3

4

5

6

I backup slot for CR3

vacant slot

Fig. 3. Illustration of spectrum assignment for backup path in SPP_CR.

ð6Þ

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by CPRmk and CBRmk. Simultaneously, a critical threshold value of correlated risk also need to be considered when allocating the spectral resources in backup path for each dynamic CRk = (s, d, x, ta, th) arrival, where s and d are the source and destination node respectively, x is the number of frequency slots demandbased bandwidth, ta and th denote arrival and holding time respectively. The traditional shared-path protection (SPP), shared-path protection with dynamical load balancing (SPP_DLB) and dedicated-path protection (DPP) are also investigated to compare with our proposed SPP_CR algorithm. Here, we mainly describe our proposed SPP_CR algorithm and SPP_DLB algorithm, which are described in Algorithms 1 and 2, respectively, as follows:

For traditional shared-path protection, ASSk is used to pick out continuous frequency slots which satisfy the xk. While for SPP_CR algorithm, the set of available frequency slots should be modulated by considering the correlated risk:

ASS0k ¼ fnjn 2 ASSk ; ðn R ASSk ; SRP mk > TS; BP m \ BPk –;Þg

ð7Þ

To decrease the competition of backup resources after multiple failures happen, we need to consider the MST for each CR. Therefore, the set of available frequency slots should be:

ASS00k ¼ fnjðn R ASS0k ; ½SNði; j; nÞ < MST; li;j 2 BPk g

ð8Þ

There are three given connection requests, Fig. 3 describes how to allocate the spectrum resources for backup path. Firstly, connection request 1 (CR1) comes into the network which consumes 3 frequency slots, corresponding to the primary path A–B–C and backup path A–H–I–C, respectively. The frequency slots for the serial numbers 1, 2 and 3 are assigned to this CR by fist fit (FF). Secondly, CR2 chooses the path B–C–D as its primary path, which requires three frequency slots and simultaneously gets the backup path B–H–I–D by considering the correlated risk among different traffic. For traditional shared-path protection, on the link H-I, the frequency slots for the serial numbers 1, 2 and 3 could be shared to enhance the resource utilization ratio. The B–C link failure, nevertheless, will lead to the competition for the shared frequency slots 1, 2 and 3 on link H–I. In this case, one of CRs will drop. However, considering the competition mechanism of shared spectral resources among different CRs, the CRs which share the correlated risk on primary path cannot share backup frequency slots on backup path when the correlated risk value exceeds a critical threshold. So the frequency slots for the serial numbers 4, 5 and 6 can be used for the backup spectrum sharing for CR2. Finally, for CR3 (two slots), whose bandwidth requirement needs two frequency slots, the primary path (A–E–G–D) isolates with primary and backup paths for other CRs, which means that they do not have correlated risk among these CRs in this network. Therefore, its frequency slots in backup path can be used for spectral resources sharing with other CRs. To make full use of backup frequency slots, we choose the path A–H–I–D and frequency slots for the serial numbers 1 and 2 are used as the backup spectrum for new CR. Therefore, no CRs will drop in case of any link failure.

Algorithm 1. Shared-Path Protection Algorithm with Correlated Risk (SPP_CR). Input: Connection request CRk = (s, d, x, ta, th), topology G(N, L, S). Output: Primary and backup paths with allocated working and backup frequency slots for CRk. Step 1: Compute a primary path by Dijkstra algorithm from source s to destination d; if no path can be found, return null. Step 2: Calculate the set of available frequency slots. If there exist continuous frequency slots based on traffic bandwidth requirement in the set, pick the subset out by first fit (FF), and then employ these as the working spectrum; otherwise, return null. Step 3: For each link Li,j2L, adjust the cost DCPijk by formula (5). Step 4: Run Dijkstra algorithm to compute shared backup path for source s to destination d based on the costadjusted topology; if no path can be found, return null. Step 5: Compute the set ASS00k by formula (8); if there exist continuous frequency slots based on traffic bandwidth requirement in ASS00k , pick the subset out by FF, and then use these as the backup spectrum; otherwise, return null. Step 6: Return primary and backup paths with allocated working and shared backup frequency slots.

In SPP_DLB, we consider dynamical load balancing in path computation, i.e., light-load links are preferred when computing both the primary and backup paths for a CR; on the other hand, we adopt two different link-cost functions to update the link cost since the patterns of reserved spectrum resources for primary path and backup path are different. Therefore, for a link Li,j, the link-cost function for primary path computation is defined as follows:

4. Heuristic algorithm By considering the correlated risk between primary and backup paths and the competition of backup spectral resources sharing, we can calculate the correlated risk values for all primary and backup paths with online traffic and dynamically adjusting each link cost

3 11

8

0

1 7 0

10 4

9

13 2

6

3

4

2

12

5

8

5

6

9

1 7

10

(a)

(b) Fig. 4. Test networks NSFNET (a) and COST239 (b).

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( DW i;j ¼

if FSi;j ¼ 0

1 d FSi;j

C I;J

ð9Þ

if FSi;j > 0

where d is a tunable parameter and d > 1. As clearly shown in Eq. (1), if the link has no free frequency slots, the link cost is set to infinite. Otherwise, the more free frequency slots one link has, the less link cost will be set. Similarly, the link-cost function for shared backup path computation is defined as follows:

( BW i;j ¼

if FSi;j ¼ 0 and BSi;j ¼ 0

1 d FSi;j þbBSi;j

C i;j

ð10Þ

otherwise

where d and b are tunable parameters and d > 1 and b > 1. This linkcost function is adopted during shared backup path computation. Next, SPP_DLB can be described as follows: Algorithm 2. Shared Backup Path Protection with Dynamic Load Balancing (SPP_DLB). Input: Connection request CRk = (s, d, x, ta, th), topology G(N, L, S). Output: Primary and backup paths with allocated working and backup frequency slots for CRk. Step 1: For each link Li;j 2 L, adjust the cost DWi,j by formula (9). Step 2: Compute a primary path by Dijkstra algorithm from source s to destination d; if no path can be found, return null. Step 3: Calculate the set of available frequency slots. If there exist continuous frequency slots based on traffic bandwidth requirement in the set, pick the subset out by first fit (FF), and then employ these as the working spectrum; otherwise, return null. Step 4: For each link Li;j 2 L, adjust the cost BWi,j by formula (10). Step 5: Run Step 2 to compute shared backup path from source s to destination d. Step 6: Run Step 3 to allocate the backup spectrum resources. Step 7: Return primary and backup paths with allocated working and shared backup frequency slots.

For Algorithm 1, the time complexity of steps 1 and 2 is O(|L|log|N|) + O(|S|log|N|) for shared-path protection algorithm with correlated risk. We suppose there exists a (traffic load, k=l) traffics in the network and all of them have the correlated risk with the

0.35

0.20 0.15 0.10 0.05 0.00 50

60

70

80

5.1. Simulation environment and parameters We adopt NSFNET (14 nodes, 21 links) and COST239 (11 nodes, 26 links) as shown in Fig. 4 to evaluate the performance between our proposed SPP_CR algorithm and the traditional protection algorithms in survivable flexible bandwidth optical networks, where each link is bidirectional. CRs are uniformly distributed between all source–destination pairs. The traffic arrival obeys Poisson distribution with k and the traffic holding time obeys a negative exponential distribution with departure rate l. Thus, the traffic load equals a = k/l. It is assumed that the available spectrum width of each link is 2500 GHz, and each frequency slot is 25 GHz. The traffic bandwidth demand is uniformly distributed within the range of [2,7] frequency slots for each CR, and the assigned and reserved frequency slots must satisfy both spectral continuity and spectral consecutiveness constraints between primary and linkdisjoint shared backup paths. The link cost denotes the link length. To obtain the best performance, we tried amount of times in simulation and eventually set g = 0.25 for Eqs. (1) and (2) and d = 1, b = 7 for Eqs. (9) and (10). At the same time, the maximum shared times of backup frequency slots (MST) is 3. The computer in our simulation is configured with Intel Xeon 2.27 GHz CPU and 1.5 G RAM under the operation of Red Hat. Here, we setup a failure generator as well as the connection request generator to generate random multiple failures. When the network traffic is running, failure events randomly happen as well as the connection request events and will be dealt with dynamically. And for each failure event, the failure models include (i) multiple frequency slots and multiple traffic are interrupted simultaneously by only single link failure per time; (ii) a single link failure takes place before one existed failure link completely recovered; (iii) multiple links fail simultaneously while nodes are reliable; (iv) single node failure causes different multi-link failures. In simulation, the rate of link failure probability over node failure

Blocking Probability

Blocking Probability

0.25

5. Simulation and analysis

(a)

SPP_CR(TS=0) SPP_CR(TS=0.25) SPP_DLB SPP DPP

0.30

new primary path in step 3, then the amount of operations in the worst case is O(|S|log|N|). Similar with steps 1 and 2, the complexity of steps 4 and 5 is also O(|L|log|N|) + O(|S|log|N|). In total, the maximum time complexity of SPP_CR algorithm is O((2|L| + 2|S| + a)log|N|). For Algorithm 2, we can easily compute the complexity for SPP_DLB is O((2|L| + 2|S|)log|N|). Compared with SPP_DLB algorithm, the time complexity of SPP_CR algorithm is larger but has the same order of magnitude, because a is generally proportional to |S| and |L|.

90

100

Traffic Load (Erlang)

110

120

0.26 0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00

SPP_CR(TS=0) SPP_CR(TS=0.25) SPP_DLB SPP DPP

(b)

110 120 130 140 150 160 170 180 190 200 210 220 230

Traffic Load (Erlang)

Fig. 5. Blocking probability (BP) in different schemes for NSFNET (a) and COST239 (b).

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probability is set to LFP:NFP = 4:1, therefore, according to mentioned principle in Section 2.3, we set ql and qn of Eqs. (1) and (2) to 0.8 and 0.2 respectively. Four different protection algorithms are simulated: (1) the shared-path protection algorithm with correlated risk (SPP_CR) with TS = 0 and TS = 0.25; (2) traditional shared-path protection algorithm (SPP); (3) SPP algorithm with dynamic load balancing (SPP_DLB), (4) traditional dedicated-path protection algorithm (DPP). To evaluate the different network performances in this paper, the metrics are adopted by blocking probability (BP), successful service ratio (SSR), protection ratio (PR), average frequency slots consumed (AFSC) and redundancy ratio (RR). These statistical average values are obtained when the traffic flow becomes steady. BP is the ratio of the number of connection requests rejected by the network over the number of all CRs arriving at the network. The successful service ratio (SSR), which means the ratio of the number of connection requests not blocked at arrival and no dropping through the whole holding time over total number of arriving connection requests. When the SSR is bigger than the algorithm’s combination property will be better and the revenue will also be larger. TRR is the ratio of the amount of successfully recovery traffic over the amount of traffic affected by the failures. A bigger TRR means a better survivability. AFSC is calculated by the total frequency slots consumed between primary and backup paths over the total network capacity, which can exactly reveal the resource utilization efficiency. RR is defined as the total backup frequency slots consumed over the total primary frequency slots consumed.

Therefore, for smaller value RR, the better spectrum efficiency is obtained. 5.2. Results and analysis As shown in Fig. 5, we can find that (1) SPP_DLB algorithm achieves the best performance of blocking probability while DPP algorithm is the worst; (2) SPP_CR algorithm obtains smaller blocking probability than DPP algorithm but larger than SPP and SPP_DLB algorithms. There are several reasons for these. Firstly, SPP_DLB considers the load balancing in primary and backup path computation, helping some links avoid to be more over-loaded than others. Secondly, DPP algorithm consumes much more frequency slots than other schemes because its spectral resources in backup path are dedicated. Thirdly, considering the correlated risk with other traffics, the primary and backup paths for SPP_CR algorithm may not choose the shortest path by Dijkstra algorithm and will limit the resource sharing. Besides, the condition for sharing will be more rigorous with smaller TS value. Therefore, for the performance of resource utilization efficiency reflected by blocking probability, SPP_CR algorithm makes a tradeoff between DPP and SPP_DLB algorithm. In Fig. 6, it can be seen clearly that (1) SPP_CR algorithm with TS = 0 and TS = 0.25 achieves the highest successful service ratio (SSR); (2) the SSR of DPP algorithm fast drops as traffic load increases, so it becomes the worst algorithm after 75 and 180 Erlangs, respectively; (3) the SSR of SPP_DLB algorithm outper-

(a)

0.85

0.80

0.75 SPP_CR(TS=0) SPP_CR(TS=0.25) SPP_DLB SPP DPP

0.70

(b)

0.94

Successful Service Ratio

Successful Service Ratio

0.90

0.65

0.92 0.90 0.88 0.86 0.84

SPP_CR(TS=0) SPP_CR(TS=0.25) SPP_DLB SPP DPP

0.82 0.80 0.78

50

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110 120 130 140 150 160 170 180 190 200 210 220 230

Traffic Load (Erlang)

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Fig. 6. Successful service ratio (SSR) in different schemes for NSFNET (a) and COST239 (b).

0.95

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1.00

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Protection Ratio

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0.85 0.80 0.75 0.70 0.65

0.55

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0.45 50

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0.50 110 120 130 140 150 160 170 180 190 200 210 220 230

Traffic Load (Erlang)

Fig. 7. Protection ratio (PR) in different schemes for NSFNET (a) and COST239 (b).

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30

(a)

SPP_CR(TS=0.25) SPP DPP

average consumed slots

average consumed slots

28

20 SPP_CR(TS=0) SPP_DLB

26 24 22 20 18 16

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16 14 12 10

14 12 50

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8 110 120 130 140 150 160 170 180 190 200 210 220 230

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Traffic Load (Erlang)

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Fig. 8. Average frequency slots consumed (AFSC) in different schemes for NSFNET(a) and COST239(b).

2.2 2.0

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SPP_CR(TS=0) SPP_DLB

Redundency Ratio

Redundency Ratio

1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 50

60

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1.9 1.8 SPP_CR(TS=0) SPP_CR(TS=0.25) 1.7 SPP_DLB SPP DPP 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 110 120 130 140 150 160 170 180 190 200 210 220 230

(b)

SPP_CR(TS=0.25) SPP DPP

120

Traffic Load (Erlang)

Traffic Load (Erlang)

Fig. 9. Redundancy ratio (RR) in different schemes for NSFNET (a) and COST239 (b).

forms that of SPP algorithm, both of which are little sensitive with traffic load increasing and fairly stable; (4) the SSR of SPP_CR algorithm become smaller with TS increasing. The reasons for these are that, (1) SPP_CR algorithm has the least traffic loss caused by multiple failures, and consumes receptive spectral resources; (2) the resource utilization of DPP algorithm is lower than that of other algorithms and it will lead to reject a lot traffic on heavy traffic load; (3) SPP_DLB algorithm considers the load balancing to hold more arrived traffic than SPP algorithm. Fig. 7 presents the protection ratio for five schemes and reveals that, in both test networks NSFNET (a) and COST239 (b), DPP has the best protection ability over all shared-path protection because of its exclusive backup resource. However, SPP_CR is just inferior to DPP and has a great advantage over SPP and DLBSPP especially when TS takes small value, because SPP_CR limits the sharing to reduce the correlated risk among traffics while the SPP and SPP_DLB do not consider any restriction of sharing for connection request and maximize the resource sharing. Besides, the smaller TS means less correlated risk, and means less completion for backup resource. Because SPP and SPP_DLB share backup resource as much as possible, their protection ratios are the lowest. Therefore, for the performance of Successful service ratio (SSR), SPP_CR algorithm makes a tradeoff between DPP and SPP_DLB algorithm. Figs. 8 and 9 show the resource utilization efficiency in the view of average frequency slots consumed (AFSC) and redundancy ratio (RR), respectively. We can conclude that: (1) the DPP algorithm consumes much more backup resource than all the shared-path

protection; (2) the consumed backup frequency slots of SPP_CR algorithms with TS = 0 and TS = 0.25 are much more than that of SPP and SPP_DLB algorithms. The bigger TS value is, the less resource will be consumed. These results are entirely consistent to the blocking probability and protection ratio results. Besides, the AFSCs decrease with the growth of traffic load, because connection requests with long paths are easy rejected and heavy traffic load means more traffic share backup resource for shared-path protection. With results from Figs. 5–9, it is concluded that as TS grows, the resource utilization efficiency of SPP_CR improves but the protection ability decreases. The reason is that TS affects the restriction to resource sharing and bigger TS value will allow more resource sharing, meanwhile bring more correlated risk. In the limit cases, if TS takes infinite value, SPP_CR will turn into traditional SPP; while if TS takes zero, SPP_CR will become DPP. Therefore, to maximize the total revenue, the best TS value can be found by a large number of simulations for specific network. What is more, due to better connectivity of COST239 network, the traffics get shorter backup path and consume less resource than NSFNET network. 6. Conclusion In this paper, we have investigated the shared-path protection algorithm against multiple failures in flexible bandwidth optical networks. The traditional shared-path protection (SPP), sharedpath protection with dynamical load balancing (SPP_DLB) and

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dedicated-path protection (DPP) are also investigated, which do not consider the correlated risk among connection requests. Aiming at the correlated risk problem, a novel shared-path protection algorithm with correlated risk is proposed, named SPP_CR algorithm, to tolerate multiple failures in flexible bandwidth optical networks. By diverse routing and restricting backup resource sharing based on the correlated risk, SPP_CR algorithm can efficiently decrease the dropped traffic caused by simultaneous multiple failures. Simulation results show that, SPP_CR algorithm (i) achieves a higher successful service ratio (SSR) than SPP_DLB, SPP and DPP algorithms; (ii) makes a better tradeoff in term of blocking probability (BP), protection ratio (PR), average frequency slots consumed (AFSC) and redundancy ratio (RR) than both DPP and SPP (SPP_DLB) algorithm. Acknowledgments This work has been supported in part by 973 program (2010CB328204), 863 program (2012AA011301), NSFC project (61271189, 61201154, 60932004), RFDP Project (20090005110013) and 111 Project (B07005) of China, and the Fundamental Research Funds for the Central Universities (2011RC0406). References [1] M. Jinno, H. Takara, B. Kozicki, Y. Tsukishima, Y. Sone, S. Matsuoka, Spectrumefficient and scalable elastic optical path network: architecture, benefits, and enabling technologies, Commun. Magaz. 47 (2009) 66–73. [2] M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, A. Hirano, Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network, Commun. Magaz. 48 (2010) 138–145. [3] K. Christodoulopoulos, I. Tomkos, E. Varvarigos, Elastic bandwidth allocation in flexible OFDM-based optical networks, J. Lightw. Technol. 29 (2011) 1354– 1366. [4] Y. Sone, A. Watanabe, W. Imajuku, Y. Tsukishima, B. Kozicki, H. Takara, M. Jinno, Bandwidth squeezed restoration in spectrum-sliced elastic optical path networks (Slice), J. Opt. Commun. Network. 3 (2011) 223–233. [5] A.N. Patel, P.N. Ji, J.P. Jue, T. Wang, Survivable transparent flexible optical WDM (FWDM) networks, OFC/NFOEC2011, OTuI2, pp. 1–3.

[6] X. Shao, Y. K. Yeo, Z. Xu, X. Cheng, Shared-path protection in OFDM-based optical networks with elastic bandwidth allocation, OFC/NFOEC2012, OTh4B. 4, pp. 1–3. [7] B. Chen, J. Zhang, Y. Zhao, et al., Multi-link failure restoration with dynamic load balancing in spectrum-elastic optical path networks, Opt. Fib. Technol. 18 (1) (2012) 21–28. [8] S. Ramamurthy, L. Sahasrabuddhe, B. Mukherjee, Survivable WDM mesh networks, J. Lightw. Technol. 21 (2003) 870–883. [9] C.S. Ou, J. Zhang, H. Zang, L.H. Sahasrabuddhe, B. Mukherjee, New and improved approaches for shared-path protection in WDM mesh networks, J. Lightw. Technol. 22 (2004) 1223–1232. [10] C. Cavdar, M. Tornatore, F. Buzluca, B. Mukherjee, Shared-path protection with delay tolerance (SDT) in optical WDM mesh networks, J. Lightw. Technol. 28 (14) (2010) 2068–2076. [11] X. Shao, Y.K. Yeo, Y. Bai, J. Chen, L. Zhou, L.H. Ngoh, Backup reprovisioning after shared risk link group (SRLG) failures in WDM mesh networks, Opt. Commun. Network., IEEE/OSA J. 2 (8) (2010) 587–599. [12] E. Oki, N. Matsuura, K. Shiomoto, N. Yamanaka, A disjoint path selection scheme with shared risk link groups in GMPLS networks, Commun. Lett. IEEE 6 (9) (2002) 406–408. [13] D. Xu, Y. Xiong, C. Qiao, G. Li, Trap avoidance and protection schemes in networks with shared risk link groups, J. Lightw. Technol. 21 (11) (2003) 2683–2693. [14] D. Xu, Y. Xiong, C. Qiao, A new PROMISE algorithm in networks with shared risk link groups, IEEE Globecom’03, vol. 5, IEEE Press, 2003, pp. 2536–2540. [15] X. Shao, Y. Bai, X. Cheng, Y.K. Yeo, L. Zhou, L.H. Ngoh, Best effort SRLG failure protection for optical WDM networks, Opt. Commun. Network. IEEE/OSA J. 3 (9) (2011) 739–749. [16] L. Shen, X. Yang, B. Ramamurthy, Shared risk link group (SRLG)-diverse path provisioning under hybrid service level agreements in wavelength-routed optical mesh networks, IEEE/ACM Trans. Network. 13 (2005) 918–931. [17] L. Guo, L. Li, A novel survivable routing algorithm with partial shared-risk link groups (SRLG)-disjoint protection based on differentiated reliability constraints in WDM optical mesh networks, J. Lightw. Technol. 25 (2007) 1410–1415. [18] Y. Zhu, J.P. Jue, Reliable collective communications with weighted SRLGs in optical networks, IEEE/ACM Trans. Network. 20 (3) (2012) 851–863. [19] S.S. Ahuja, S. Ramasubramanian, M. Krunz, SRLG failure localization in optical networks, IEEE/ACM Trans. Network. 19 (4) (2011) 989–999. [20] C. Gao, Y. Zhu, J.P. Jue, SRLG-Aware Topology Aggregation for Survivable MultiDomain Optical Networks, ICC2011, pp. 1–5. [21] M.H. Mohammad, J.P. Jue, SRLG-Aware Partitioning for Scalability and Survivability, OFC2009, JThA65, pp. 1–3. [22] X. Shao, Y.K. Yeo, X. Cheng, L. Zhou, Availability-Aware SRLG Failure Protection in Survivable WDM Mesh Networks, OFC2011, NThC5, pp. 1–3.