Availability Analysis for Elastic Optical Networks with Multi-path Virtual Concatenation Technique

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1 Progress In Eectromagnetics Research Symposium Proceedings, Guangzhou, China, Aug , Avaiabiity Anaysis for Eastic Optica Networks with Muti-path Virtua Concatenation Technique Xiaoing Wang 1, Limei Peng 2, and Gangxiang Shen 1 1 Schoo of Eectronic and Information Engineering, Soochow University, China 2 Department of Industria Engineering, Ajou University, Suwon, South Korea Abstract Due to high spectrum efficiency and fexibiity in bandwidth aocation, eastic optica networks receive extensive research interest in recent years. Avaiabiity is one of the most important Service Leve Agreement (SLA) metrics in teecommunication networks. In the paper, we appy the sub-band Virtua Concatenation (VCAT) technique to enhance the avaiabiity of eastic optica networks. Our study shows that the VCAT technique can greaty enhance the avaiabiity of the eastic optica networks, different spectrum distributions of sub-bands (i.e., numbers of frequency sots (FSs)) on mutipe paths of a VCAT ight path service can greaty impact the network avaiabiity, and a higher avaiabiity can be expected for a smaer VCAT sub-band granuarity. 1. INTRODUCTION Because of the unique merits, such as high spectrum efficiency and fexibiity in bandwidth aocation, eastic optica networks receive extensive research interest in recent years. Avaiabiity is one of the most important SLA metrics in teecommunication networks. Different from reiabiity that is concerned about how ikey a system wi operate for a certain time period without a serviceaffecting faiure occurring, avaiabiity considers externa repair and maintenance to recover from faiures, which is concerned about the state probabiity of finding a system in an operating state at any time when we want its service [1]. For the avaiabiity anayses of optica transport networks, the majority of existing studies focus on Waveength Division Mutipexing (WDM) optica networks [2]. Different network protection techniques have been appied to enhance service avaiabiity in WDM networks [3 5]. However, to the best of our knowedge, there is sti no study dedicated to the avaiabiity anaysis for the eastic optica networks. On the other hand, in the traditiona Optica Transport Network (OTN), VCAT is an important technique to fexiby spit the bandwidth of a compete service connection into mutipe Virtua Containers (VCs) in the time domain, transport the VCs via different end-to-end paths, and finay recombine them at the receiver [6]. The VCAT technique can we baance the traffic oad in the network, thereby significanty improving network capacity utiization. For the eastic optica network, it is aso possibe to extend this concatenation technique in the spectrum domain to spit a compete ight path into mutipe sub-bands, transport the sub-bands via different paths, and finay recombine them at the receiver [7]. This technique is caed sub-band VCAT or spectrum spit. The distribution of sub-bands on mutipe different paths enabes partia bandwidth to survive when a network incurs faiure(s). Thus, the sub-band VCAT technique is expected to enhance ight path service avaiabiity for the eastic optica network. This paper evauates the benefit of appying the sub-band VCAT technique in enhancing the avaiabiity of the eastic optica networks. We deveop anaytica modes specificay for two cases, i.e., (1) a singe ink-based node pair, between which mutipe parae inks connect, and (2) a genera mesh network, in which mutipe disjoint end-to-end paths are empoyed for each node pair to provision ight path services through the VCAT technique, and a network-wide average end-toend connection avaiabiity is cacuated. We assume that a the remaining capacity is avaiabe when one or mutipe paths of a muti-path VCAT service are affected. Our study indicates that the sub-band VCAT technique can greaty enhance the avaiabiity of the eastic optica networks, and different distributions of sub-bands (i.e., numbers of FSs) on different paths of a VCAT ight path service can greaty impact the network avaiabiity. For the singe-ink case, under the assumption of an equa ink ength of a the parae inks, an even distribution of FSs on the inks can achieve the highest avaiabiity. For the network case, the distribution of FSs that ensures the highest network avaiabiity depends on the network topoogy. Aso, a higher avaiabiity can be expected for a smaer VCAT sub-band granuarity. The rest of the paper is organized as foows. In Section 2, we give the assumption and a new avaiabiity definition, on which our anayses are based. In Section 3, we evauate the avaiabiities

2 850 PIERS Proceedings, Guangzhou, China, August 25 28, 2014 for two cases, i.e., a singe ink-based node pair and a genera mesh network containing mutipe end-to-end node pairs. We concude the paper in Section ASSUMPTIONS AND NEW AVAILABILITY FORMULA Network outages can be caused by both fiber cabe cuts and invaidity of network node equipment (i.e., node faiures). However, according to the statistics, the main reason for network faiures is due to fiber cabe cuts [2]. Thus, in this study we mainy focus on ink faiures (arising from fiber cabe cuts) when anayzing network avaiabiity. We have the foowing four key assumptions for the anayses, incuding (1) network inks are either working or in the outage state, (2) inks fai independenty, (3) both the in-service time and repair time of fiber cabes foow independent memoryess processes with a constant mean, and (4) the repair rate is much greater than the faiure rate [2]. The most widey known equation for the avaiabiity of a ink is A =MT T F /(MT T F +MT T R ), where A is the ink avaiabiity, MT T F is the Mean Time To Faiure of the ink per km, and MT T R is the Mean Time To Repair, is the ength of the ink. FIT is the Faiure In Time, which is a standard unit for measuring or specifying faiure rates, and 1 FIT means 1 faiure in 10 9 hours. Without osing generaity, in this paper, we assume that MT T F = 1 km/(200 FIT), and MT T R= 6 hours [2]. Because a network as a whoe is neither entirey avaiabe nor entirey faied, it is meaningess to directy estimate network avaiabiity. Rather, it is more meaningfu and practica to characterize the ink avaiabiity, path avaiabiity, and then based on these avaiabiities we can anays is a network-wide average end-to-end connection avaiabiity. If a path contains M continuous inks, the path avaiabiity is A p = M A i, which requires a the contained inks are avaiabe and where i=1 A i is the avaiabiity of the ith ink on the path as defined before. In the eastic optica network, the sub-band VCAT technique enabes a connection (with mutipe sub-bands on different paths) to survive partia bandwidth when a network incurs faiure(s). Considering the partia avaiabe bandwidth with the VCAT technique, we define a new ink avaiabiity as foows: Ae = (MT T F B t + MT T R B r A r ) /(MT T F + MT T R ) B t (1) where B t denotes the tota bandwidth of the VCAT connection between a pair of source and destination nodes, B r denotes the remaining bandwidth when ink faiure(s) occur, and A r is the avaiabiity of the remaining capacity B r. The numerator in the equation finds the tota avaiabe bandwidth, in which the first part corresponds to the bandwidth when there is no faiure and the second part corresponds to the remaining bandwidth when ink faiure(s) occur. The denominator in the equation finds tota bandwidth if there is no ink faiure in the period of MT T F +MT T R. 3. AVAILABILITY ANALYSES This section anayzes the avaiabiities for two cases: a singe ink-based node pair connected with mutipe parae inks and a genera mesh network with mutipe end-to-end VCAT ight path connections A Singe Link-based Pair Connected by Mutipe Parae Links Two Parae Links We first consider the case of two parae inks. Fig. 1 shows a situation where a singe node pair is connected by two parae inks. Assume that B 1 is the bandwidth of first ink, B 2 is the bandwidth of second ink, and B t is the tota bandwidth between the two nodes, where B t = B 1 + B 2, and their units are FS. When the first ink fais, B 2 is the remaining capacity between the node pair. Simiary, when the second ink fais, B 1 is the remaining capacity between the node pair. Based on Equation (1), the avaiabiity for the first and second inks with the VCAT technique can be cacuated as (2) and (3). Ae 1 = ( MT T F B t +MT T R 1 A 2 B 2) / (MT T F +MT T R 1 ) B t (MT T F B t +MT T R 1 B 2 ) /(MT T F +MT T R 1 ) B t (2) Ae 2 = ( MT T F B t + MT T R 2 A 1 B 1) / (MT T F + MT T R 2 ) B t (MT T F B t + MT T R 2 B 1 ) /(MT T F + MT T R 2 ) B t (3)

3 Progress In Eectromagnetics Research Symposium Proceedings, Guangzhou, China, Aug , where 1 and 2 are the physica engths of the two inks, respectivey, and A 1 and A 2 are the avaiabiities of the two inks based on the origina avaiabiity definition, respectivey, which are typicay very cose to 1. For the two end nodes, the VCAT connection avaiabiity can be formuated as (4), and the unavaiabiity of the connection is formuated as (5). Ae c = ( Ae 1 B 1 + Ae 2 B 2) / Bt (4) U c = 1 A c (5) Given the physica engths of the two inks, Equation (4) is soey dependent on the two variabes B 1 and B 2, which means that different distributions of sub-bands (i.e., numbers of FSs) on the two inks can impact the connection avaiabiity. To achieve a maxima avaiabiity, we need to find the combination of B 1 and B 2 that can make the first derivative of (4) equa zero. We find that when B 1 satisfies Equation (6), we can achieve maxima connection avaiabiity. ( MT T F MT T R MT T R 2 ) 1 2 Bt B 1 = ( MT T F MT T R (1 + 2 ) + 2 MT T R 2 ) (6) 1 2 Based on (6), we consider a the combinations of B 1 and B 2 to find maxima connection avaiabiities for various ink ength situations. Assume that the ength of the first ink equas 1,000 km and the tota bandwidth of the connection is 10 FSs (i.e., B 1 + B 2 = 10 FSs), we find different connection avaiabiities considering different engths of the second ink (Len2) and combinations of B 1 and B 2. Fig. 2 shows the connection unavaiabiities for these different situations, in which each curve corresponds to a certain ength of the second ink and the horizonta axis shows variabe numbers of FSs on the first ink. We can see that for each ength of the second ink, there exists minima connection unavaiabiity for a certain combination of B 1 and B 2. For exampe, when the ength of the second ink is 500 km, the minima connection unavaiabiity occurs when the combination of B 1 and B 2 is (3, 7) FSs, and simiary, when the ength of the second ink is the same as the first ink, i.e., 1,000 km, the minima connection unavaiabiity occurs when the combination of B 1 and B 2 is (5, 5) FSs, which means that speciay for the equa ink case, we shoud eveny spit the tota bandwidth onto the two inks so as to achieve a maxima connection avaiabiity. Based on the above resuts, we can concude that when the ength of second ink is onger, the maxima achievabe avaiabiity is ower and the first ink shoud be distributed with more FSs so as to achieve higher avaiabiity. We aso anayze how the range of ength of the second ink affect the combinations of B 1 and B 2 when achieving minima unavaiabiity. The resuts are shown in Tabe 1. We can see that the resuts are in ine with those in Fig. 2, i.e., when the ength of second ink is onger, the first ink shoud be distributed with more FSs to achieve the minima connection unavaiabiity.... Figure 1: A simpe demonstration for two nodes. Figure 2: Connection unavaiabiity for Len Mutipe Parae Links We next consider a singe ink-based node pair with mutipe (more than two) parae inks as shown in Fig. 3. Considering the remaining capacity when a ink faiure occurs, the ink avaiabiity

4 852 PIERS Proceedings, Guangzhou, China, August 25 28, 2014 is given by Equation (7), and the connection avaiabiity is given by Equation (8). ( Ae k = MT T F B t + MT T R k ) / N i=1,i k Ai B i (MT T F + MT T R k ) B t (7) Ae c = N ( Ae k i) / B B t (8) i=1 where i denotes the ength of the ith ink, N denotes the number of parae inks between the two nodes, A i is the avaiabiity of the ith ink not considering the remain capacity, which can be cacuated by A i = MT T F/(MT T F + MT T R i ), B t denotes the tota number of FSs, and B i denotes the number of FSs on the ith ink. Because the connection avaiabiity is dependent on the number of parae inks and the distribution of FSs, given the set and parameters of N, MT T R, MT T F, i, A i, and B t as defined before, we deveop an optimization mode to find the maxima connection avaiabiity as foows: Variabes: Ae i is the new avaiabiity of the ith ink, which is cacuated by (7). B i is the number of FSs on the ith ink. Objective: MaximizeAe c = N ( ) / i=1 Ae i B i B t. (i.e., maximize the average connection avaiabiity under different ink faiure situations) Constraints: N i=1 B i = B t. (i.e., the sum of FSs distributed on a the parae inks equas to the tota number of FSs of the connection). Tabe 1: FS combinations of different ranges of Len2for minima unavaiabiity. Range of Len2 (km) Optima FSs Optima FSs Min Max of 1st ink of 2nd ink Infinity 10 0 Tabe 2: Minima unavaiabiity under different numbers of inks. Num Links Minma Unavaiabiity Optima FSs distribution on different inks If the engths of the inks are different, the objective formua has quadratic components. In order to inearize the mode, we assume that the engths of a the inks are the same, i.e., 1 = 2 =... = N =, and thus A 1 = A 2 =... = A N = A. We evauate the avaiabiity of the connection between the two nodes with different parae inks. Assume that the engths of a inks are 1,000 km, MT T R = 6 hours, MT T F = hours*km, and B t = 10 FSs, Tabe 2 shows the minima unavaiabiity to be achieved under different numbers of inks and corresponding FSs distributions. We observe that an even distribution of FSs on different inks can achieve a maxima avaiabiity. In addition, we can see that a higher avaiabiity can be expected for a smaer VCAT sub-band granuarity. The resut is reasonabe because when the ength of a inks are the same, and the number of inks is fixed, an even distribution of FSs can make the probabiity of faied FSs minima, and therefore the connection avaiabiity maximized. Aso, with the increase of the number of parae inks, there are fewer FSs affected when a singe ink faiure occurred, and thus the probabiity of faied FSs is ower. Figure 4 shows the minima unavaiabiity of the connection between two nodes under different numbers of parae inks. Each curve corresponds to a certain ink ength. We observe that the shorter ength of a ink shows a ower unavaiabiity. In addition, we see that a ower unavaiabiity can be expected for a smaer VCAT sub-band granuarity Genera Mesh Network In this section, we estimate the avaiabiity of service connections for a genera mesh network under the sub-band VCAT technique. We first consider a singe end-to-end node pair, which is then used

5 Progress In Eectromagnetics Research Symposium Proceedings, Guangzhou, China, Aug , First ink B 1 Source B 2 Second ink B t =B 1 +B 2 + +B N Destination N th ink B N Figure 3: A singe node pair connected with mutipe parae inks. Figure 4: Minima unavaiabiity under different numbers of parae inks. to cacuate the avaiabiity for a the node pairs in a network. We average the avaiabiities of end-to-end ight paths for a the node pairs to obtain average network-wide connection avaiabiity. Figure 5 shows a singe node pair connected by mutipe disjoint end-to-end paths. Considering the remaining capacity upon a ink faiure, the avaiabiity of the ith ink on the kth path is given by Equation (9), where ki denotes the ength of the ith ink on the kth path, N denotes the number paths between the source and destination nodes. A j p is the avaiabiity of the jth path not considering the remaining capacity, cacuated as A j p = M j i=1 A ji, where Aji is the avaiabiity of the ith ink on the jth path not considering the remain capacity, i.e., A ji = MT T F/(MT T F +MT T R ji ), and M j denotes the number inks that the jth path traverses. The path avaiabiity is given by Equation (10), and the overa connection avaiabiity is given by Equation (11), where B t is the tota number of FSs, and B k denotes the number FSs aocated on the kth path. The enhanced avaiabiity considers a the singe-ink faiure situations and averages path avaiabiity considering the remaining capacity. / N Ae ki = MT T F B t + MT T R ki A j p B j (MT T F + MT T R ki ) B t (9) Ae k p = M k Ae c = N i=1 Aeki k=1 j=1,j k (10) ( ) / Ae k p B k B t (11) As shown in Fig. 5, assume that there are two paths between a pair of nodes. The first path traverses two inks with engths of 500 km and 1,000 km, respectivey, and the second path traverses three inks with engths of 500 km, 1,000 km, and 2,000 km, respectivey. We can empoy the avaiabiity cacuation equations from (9) to (11) to estimate the end-to-end connection avaiabiity. The resuts are shown in Fig. 6, in which unavaiabiity is considered. We compare the connection unavaiabiity for the cases of singe path and two paths. We see that the minima connection unavaiabiity of the two-path case with VCAT is ower than that of any singe path case without VCAT. This is because the VCAT technique can integrate the sub-bands on mutipe paths to make up an end-to-end ight path service, which can ensure some bandwidth to survive when incurring a faiure and therefore greaty enhance the connection bandwidth avaiabiity. We appy the above end-to-end connection avaiabiity anaysis approach to a the node pairs in a mesh network and cacuate a network-wide average end-to-end service avaiabiity. We use a modified Dijkstra s agorithm to find two ink-disjoint shortest routes between each node pair. For performance comparison, we evauate the minima unavaiabiity of the first shortest path without VCAT, the second shortest path without VCAT, and the two shortest paths with VCAT. Two test networks incuding the n6s8 and SmaNet networks are considered for such an evauation. Figs. 7

6 854 PIERS Proceedings, Guangzhou, China, August 25 28, 2014 and 8 show the resuts of n6s8 and SmaNet, respectivey. Because the remaining capacity can be considered avaiabe when one (or mutipe) paths of a muti-path VCAT service is affected, it is easy to understand that the connection unavaiabiity of two paths with VCAT is ower than that of any singe path without VCAT. Source First path B N1 N2 N3 Destination N th path B N B t =B 1 +B 2 + +B N Figure 5: A singe node pair connected withmutipe paths. Figure 6: pair. Unavaiabiity comparison for a node Figure 7: Unavaiabiity comparison for the n6s8 network. Figure 8: Unavaiabiity comparison for the Sma- Net network. 4. CONCLUSIONS This paper evauates the benefit of appying the sub-band VCAT technique in enhancing the avaiabiity of the eastic optica network. We made theoretica anayses for the situations of a singe ink-based node pair and a genera mesh network. Because the distribution of FSs on different inks between a ink-based node pair can affect the connection avaiabiity, we aso deveoped an optimization mode to maximize the connection avaiabiity for the node pair. We found that under the assumption that the engths of a inks are the same, an even distribution of FSs on different inks can achieve the highest avaiabiity, and a higher avaiabiity can be achieved for a smaer VCAT sub-band granuarity. For the case of end-to-end paths in a mesh network, the sub-band VCAT technique can aso greaty enhance the avaiabiity of service connections. It is aso found that the distribution of FSs that can achieve the highest avaiabiity depends on the network topoogy, and a higher avaiabiity can aso be expected for a smaer VCAT sub-band granuarity. ACKNOWLEDGMENT This work was jointy supported by the Nationa 863 Project of China (2012AA011302), Nationa Natura Science Foundation of China (NSFC) ( , ), Research Fund for the Doctora Program of Higher Education of China ( ), and Natura Science Foundation of Jiangsu Province (BK , BK ).

7 Progress In Eectromagnetics Research Symposium Proceedings, Guangzhou, China, Aug , REFERENCES 1. Biinton, R. and R. N. Aan, Reiabiity Evauation of Engineering Systems, 2nd Edition, Penum Press, Grover, W. D., Mesh-based Survivabe Networks: Options and Strategies for Optica, MPLS, SONET, and ATM Networking, Prentice Ha Professiona, Couqueur, M. and W. D. Grover, Avaiabiity anaysis of span restorabe mesh networks, IEEE Journa on Seected Areas in Communications, Vo. 20, No. 4, , May Arci, D., D. Petecchi, G. Maier, et a., Avaiabiity modes for protection techniques in WDM networks, Proc. DRCN, Grover, W. D., High avaiabiity path design in ring-based optica avaiabiity, IEEE/ACM Transactions on Networks, Vo. 7, No. 1, , Aug Choy, L., Virtua concatenation tutoria: Enhancing SONET/SDH networks for data transport, Journa of Optica Networking, Vo. 1, No. 1, 18 29, Jan Shen, G., A. Cai, and L. Peng, Benefits of sub-band Virtua Concatenation (VCAT) in CO- OFDM optica networks, Proc. ICTON, 2012.