How Much Can Sub-band Virtual Concatenation (VCAT) Help Static Routing and Spectrum Assignment in Elastic Optical Networks?

How Much Can Sub-band Virtual Concatenation (VCAT) Help Static Routing and Spectrum Assignment in Elastic Optical Networks? (Invited) Xin Yuan, Gangxiang Shen School of Electronic and Information Engineering Soochow University, Suzhou, PR China Correspondence email: shengx@suda.edu.cn Abstract Orthogonal Frequency Division Multiplexing (OFDM) has recently been proposed as a modulation technique for optical networks due to its higher spectral efficiency and superior impairment tolerance. There have been extensive studies on routing and spectrum assignment (RSA) of the OFDM-based elastic optical network, of which most focus on a single route for each lightpath service. In this paper, we study the RSA problem for the elastic optical network considering the multi-path subband virtual concatenation (VCAT) technique that allows the sub-bands of a VCAT lightpath connection to be transmitted over different routes. We develop integer linear programing (ILP) models to optimally solve the problem. We evaluate the benefit of the multi-path sub-band VCAT technique for the RSA problem through comparing with the non-vcat case. In addition, because of the limitation of synchronization in the sub-band VCAT technique, we set a maximal distance difference among the sub-band paths of a VCAT connection to evaluate how the limitation can impact the RSA performance. We find that the multi-path sub-band VCAT technique shows a stronger benefit in a network with a higher nodal degree. Keywords elastic optical networks; routing and spectrum assignment; multi-path sub-band VCAT I. INTRODUCTION With the fast growth of Internet traffic due to the emergence of high-rate applications, such as video on demand, high definition TV, cloud computing and grid applications, Cisco predicted that IP traffic will grow at a compound annual growth rate of 9% from 11 to 1 [1] and 9% of all Internet traffic will be video in the next three years []. This requires us to pay more attention to improving the transmission efficiency of optical backbone networks. Traditional wavelength division multiplexing (WDM) optical networks follow the ITU-T fixed frequency-grid standard. This introduces low spectrum utilization in provisioning lightpath services because a full wavelength or optical channel is always assigned for each lightpath request, even if the requested data rate is only a portion of the whole capacity of an optical channel. Thus, we need a more spectrum-efficient transmission technique for better spectrum utilization. Recently, extensive research efforts have been dedicated to optical Orthogonal Frequency-Division Multiplexing (OFDM) [] as a means to enhance spectrum efficiency. Besides the advantages of low symbol rate of each subcarrier and coherent detection that can mitigate the effects of physical impairments, OFDM also brings the unique benefit of better spectrum efficiency, allowing the spectra of adjacent subcarriers to overlap owing to their orthogonal modulation feature. A connection requiring capacity higher than one OFDM subcarrier can be assigned with a number of contiguous subcarriers to obtain good spectrum efficiency. An optical transport network based on the coherent optical OFDM (CO- OFDM) transmission technique is often called CO-OFDM elastic optical network. In the elastic optical network, routing and spectrum assignment (RSA) is an important problem that has attracted much research attention recently. In this problem, two unique constraints make the RSA problem different from the traditional routing and wavelength assignment (RWA) problem []. They are spectrum contiguity and spectrum continuity. Spectrum contiguity means that all the frequency slots (FSs) that make up the bandwidth of a lightpath should be neighboring in the spectrum domain. Spectrum continuity means that all the spectra used on all the fiber links traversed by a lightpath should be the same. There exist extensive investigations on the RSA problem. Christodoulopoulos et al. [] considered k shortest paths between each pair of nodes and developed an arc-path ILP model to minimize the required number of FSs. Following this work, Velasco et al. [] developed two ILP models to solve the capacitated RSA problem. One is arc-path, and the other is node-arc, and to shorten model-solving times, two relaxed ILP models were also evaluated. To enhance the computational efficiency of node-arc ILP model, Cai et al. developed a new node-arc model [] based on the arc-path model of []. Among these studies, we find that most of them focused on the RSA problem with a single route. Recently, it has been proved physically possible for a lightpath to be made up of multiple sub-bands traversing different routes []. Such a technique is realized by virtual concatenation in the spectrum domain, and called multi-path sub-band virtual concatenation (VCAT). Some studies have been conducted in this direction. Cai et al. [8] applied the VCAT technique to the frequency domain by transmitting the sub-bands of a CO-OFDM optical channel via different routes 98-1-99-8-/1/$1. 1 IEEE

Proceedings of the 1 IEEE ICCS and showed that the VCAT technique can significantly improve lightpath blocking performance. Shen et al. [9] developed two analytical models for performance evaluation of the VCAT technique under the conditions with and without spectrum conversion in the CO-OFDM optical networks and showed that VCAT can significantly improve lightpath blocking performance over non-vcat. For the VCAT technique, though there have been some studies on dynamic lightpath service provisioning [8-9], the study on the static RSA problem to the best of our knowledge is still absent. In this study, we focus on solving the RSA problem with the sub-band VCAT technique and evaluating how sub-band VCAT can help improve spectrum utilization for the elastic optical network compared to the non-vcat case. We develop ILP models for the multi-path sub-band VCAT RSA problem. The benefit of how much the VCAT technique can help improve spectrum efficiency is evaluated through test studies based on different network topologies. The rest of this paper is organized as follows. In Section II, we introduce the concept of multi-path sub-band VCAT S Route 1 slots S slots Node A Fig. 1. A node pair with multiple sub-band paths technique. In Section III, we present the ILP models for the RSA problem under the multi-path sub-band VCAT technique. We solve the ILP models and conduct performance analyses in Section IV. Finally, we conclude the paper in Section V. II. MULTI-PATH SUB-BAND VIRTUAL CONCATINATION (VCAT) In the non-vcat case, only one path is chosen for bandwidth provisioning between a pair of nodes. In contrast, in the case of multi-path sub-band VCAT, different sub-bands can be provisioned via different routes between the node pair. Fig. 1 shows an example of multi-path sub-band VCAT. Assume that a lightpath demand between nodes A and B requires S FSs and there are n different routes between the node pair. We split the S FSs into a set of sub-bands, i.e., {S 1, S, S,, S n }. Each route carries a sub-band and these sub-bands are recombined at the receiver, i.e., node B. Depending on the transmission technique applied, the number of sub-band path making up a VCAT connection can be limited. Also, the maximal distance difference of these paths can be subject to a certain limit. hop 1 hop hop hop H-1 hop H H-1 S slots Route hop hop hop H-1 1 H-1 hop S slots Route n hop hop hop hop H-1 1 H-1 hop H hop H S slots Node B III. ILP MODELS FOR RSA WITH MULTI-PATH SUB-BAND VCAT In this section, we first define the RSA problem of multipath sub-band VCAT, which is followed by the corresponding ILP optimization models. The RSA problem of multi-path subband VCAT technique is defined as follows. With multi-path sub-band VCAT, we can split the spectrum of a lightpath into multiple sub-bands, transport the sub-bands via different routes, and finally recombine them back to a continuous spectrum at the receiver. Thus, the RSA problem with multi-path sub-band VCAT can be modelled to select routes and assign spectra for each of the routes such that a sufficient bandwidth can be provisioned for each pair of nodes. Each sub-band on a route must meet the following two constraints, i.e., spectrum contiguity and spectrum continuity. The case without VCAT can be considered as a special case of sub-band VCAT that requires all the FSs to be provisioned along a single route. Given a network topology and a lightpath traffic demand matrix, the objective of the RSA problem is to minimize the maximal index of used FSs and the sum of used FSs on each link in the whole network. These two aspects both reflect the spectrum efficiency of the network. Next, we present the ILP model for RSA with multi-path sub-band VCAT. A. ILP Model for RSA with Multi-path Sub-band VCAT Sets: V L NP Set of network nodes. Set of network links. Set of node pairs in the network. Set of candidate paths between node pair sd. Set of links traversed by path r between node pair sd. Parameters: Traffic demand in units of FSs between node pair sd. Takes the value of one if link ij is included on path r between node pair sd; zero, otherwise. M Variables: The number of links traversed by path r between node pair sd. A large value. An integer variable that denotes the starting FS index of path r between node pair sd. A binary variable that takes the value of zero if the starting frequency of path r between node pair sd is smaller than the starting frequency of path r1 between node pair sd1 (i.e., < ); one, otherwise (i.e., < ).

Proceedings of the 1 IEEE ICCS An integer variable that denotes the traffic demand in units of FSs carried by path r between node pair sd. The maximal used FS index in the whole network. Objective: Minimize (α=.1) The objective is to minimize the maximal index of the used FSs and the sum of used FSs on each link in the whole network. We consider minimizing the maximal index of the used FSs as the first priority by setting weighting factor α to be a small value, e.g.,.1. Constraints: 1) Spectrum assignment (1) Constraint (1) ensures that the sum of traffic demand provisioned on all the paths between node pair sd equals to the total traffic demand required by the node pair. For all the commodities between node pairs that have and, with r and r1 sharing at least one common link l:, the following constraints should be satisfied: () () Constraints () and () ensure that the spectra of two lightpaths that share common link(s) must not overlap. If (i.e., ), then () is activated, which becomes ; otherwise, () always holds. Note that for each node pair, the routes used to provision subbands are pre-calculated to be link-disjoint. Thus, we only need to consider spectrum non-overlapping among the routes of different node pairs that share common links. ) Other constraints () () () Constraint () ensures that the network-wide maximal used FS index c is no smaller than the ending FS index of the lightpath between any node pair. Constraint () ensures that c is no smaller than the total number of used FSs on any fiber link in the network. Constraint () ensures that c is no greater than all the traffic demand. Constraints () and () are redundant to reduce the feasible solution space of the ILP model. In this study, we assume that the guard-band between two neighboring optical channels (sub-bands) is not considered. However, the model is open to be able to incorporate the guard-band if necessary. B. ILP Model for RSA without VCAT The non-vcat RSA problem can be considered as a special case of the RSA problem with multi-path sub-band VCAT. The model of this case has the same sets and parameters as those of model A. In addition to the variables of model A, we have a new variable as follows: A binary variable that denotes whether path r between node pair sd is used for establishing a lightpath, i.e., equals one if path r is chosen; zero, otherwise. The model has the same objective as that of model A and its constraints include ()-() with two more constraints as follows: () Constraint () ensures only one path should be chosen for lightpath establishment between the node pair. (8) Constraint (8) ensures that once a path between node pair sd is chosen, all the traffic demand between the node pair is allocated onto it. C. ILP Model for VCAT RSA Considering Sub-band Path Distance Difference Physically, because of the synchronization limitation in the VCAT technique, when splitting a spectrum onto multi-paths between a pair of nodes, the maximal distance difference of these paths is not allowed to be infinite, but subject to a certain limit X. To incorporate such a limit, we develop a new ILP model as follows. Sets: in addition to V, L, NP, and as in model A, we have new sets as follows: Set of candidate path sets between node pair sd. Each element in the set corresponds to a set of paths between the node pair, whose maximal distance difference is no greater than a certain limit X. For each node pair, we list out all the possible candidate path sets that satisfy the limit X. Set of paths in candidate path set i between node pair sd. Parameters: same as the parameters in model A. Variables: in addition to variable c, we have new variables as follows: An integer variable that denotes the starting frequency of path r in candidate path set i between node pair sd. A binary variable that takes the value of zero if the starting frequency of path r in candidate path set i between node pair sd is smaller than the starting frequency of path r1 in candidate path set i1 between node pair sd1 (i.e., < ); one,

Proceedings of the 1 IEEE ICCS otherwise (i.e., < ). A binary variable denoting whether candidate path set i between node pair sd is chosen for lightpath establishment, i.e., equals to one if candidate path set i is chosen; zero, otherwise. An integer variable that denotes traffic demand in units of FSs carried on path r in candidate path set i between node pair sd. Objective: Minimize c+α* (α=.1) Constraints: 1) Path set selection (9) Constraint (9) ensures that only one set of paths should be chosen for lightpath establishment between the node pair. ) Spectrum assignment (1) (11) Constraints (1) and (11) ensure that once a path set between a node pair is chosen, all the traffic demand between the node pair is allocated onto the path set. (1) (1) Constraints (1) and (1) are similar to () and () to ensure that the spectra of two sub-band lightpaths that share common link(s) must not overlap. ) Other constraints (1) (1) (1) Constraints (1)-(1) are similar to ()-(). IV. TEST CONDITIONS AND RESULTS To evaluate the performance of the RSA problem with multi-path sub-band VCAT technique, we solve the ILP model for different test networks and compare the results with the non-vcat case. Since the result of the ILP model is optimal, the evaluation of spectrum efficiency for the two cases is accurate. We considered six test networks, including an eightnode ring network and the networks based on the eight-node ring network arbitrarily added four links each time until it is fully connected. The six networks are shown in Figs. (a)-(f), respectively. A random number of FSs required by each node pair sd is chosen uniformly between 1 and 1 FSs. We used the commercial software package AMPL/Gurobi to solve all the ILP models. All the results presented were obtained by stopping solving ILP models after two hours for each traffic demand instance or its MIPGAP has reached.1. We compare the spectrum efficiency of the VCAT case over the non-vcat case. Fig. shows the network spectrum efficiency from the perspective of the maximal index of used FSs and the sum network link capacity in units of FSs. The left y-axis corresponds to the maximal index of used FSs, and the right y-axis corresponds to the sum network link capacity. The x-axis corresponds to the above six network cases from the lowest nodal degree (d=) to the highest nodal degree (fully connected). We find that for a low network nodal degree, there is no performance improvement in the aspect of maximal index of used FSs by VCAT over non-vcat. However, with the increase of nodal degree, we see that the benefit of using the VCAT technique starts to emerge. From networks (d) to (f), we see that the VCAT case always requires a smaller number of FSs c than the non-vcat case. For example, in (f), the reduction of FSs is up to %. This is reasonable because a network with a higher nodal degree can provide more routes between each pair of nodes, which provides more opportunities for the VCAT technique to choose better sub-band paths and allocate FSs for the sub-bands. (a) (b) (c) (d) (e) (f) Fig.. Test networks. Numebr of required FSs 1 1 Fig.. Spectrum efficiency comparison between VCAT and non-vcat based on different network topologies. Test networks Non-VCAT VCAT Non-VCAT VCAT a b c d e f 1 1 Sum capacity of the whole network

Proceedings of the 1 IEEE ICCS We also consider the performance aspect of the sum network link capacity shown on the right y-axis. We can see that overall the VCAT case consumes a lower sum network link capacity than the non-vcat case though in (f) the observation is opposite. This is because minimizing the maximal index of used FSs has the first priority in the two objectives. Its improvement could lead to a worse performance in the second objective, i.e., the sum network link capacity. However, in all the other five cases, the VCAT case always shows a lower sum network link capacity than the non-vcat case. We also evaluate how the limitation of maximal allowed distance difference among sub-band paths X can affect the spectrum efficiency of the VCAT technique. Fig. shows the results under different maximal allowed distance differences. Without losing generality, we assume that the distance of each path is measured in a general unit. We consider four distance difference cases, i.e., X=1,, 9, and infinite units of distance. The y-axis and x-axis correspond to the same meanings as in Fig.. We can see that in the aspect of maximal number of used FSs, the distance difference limitation does not show any impact with four X cases converging to a single curve. However, for the aspect of sum network link capacity, we do see that the distance difference limitation shows some impact on the performance. With the increase of X, we see that the sum network link capacity reduces. This is because a larger X provides more combinations of route sets that can be used to provision VCAT connections, which therefore provide more optimization opportunities to minimize the sum network link capacity. Moreover, we see that the performance improvement becomes stronger with an increasing of network nodal degree. The explanation on this observation is the same as that for the result in Fig.. Numebr of required FSs 1 1 Test networks X=1 X= X=9 X= X=1 X= X=9 X= a b c d e f Sum capacity of the whole network Fig.. The impact of distance difference limitation on the spectrum efficiency of VCAT. 1 1 V. CONCLUSION CO-OFDM is a promising modulation technique that can provides efficient elastic bandwidth transmission. For this type of elastic optical network, we considered to apply the multipath sub-band VCAT technique to improve spectrum efficiency. We developed ILP models for the RSA problem with the multi-path sub-band VCAT technique under static lightpath traffic demand. The results show that the benefit of multi-path sub-band VCAT is closely dependent on network topologies. In a network with a low nodal degree, the benefit of VCAT is trivial, and the spectrum efficiency of multi-path subband VCAT is close to the case without VCAT. However, with an increasing network nodal degree, the multi-path sub-band VCAT technique can help improve spectrum efficiency. In addition, we consider how the maximal distance difference of the sub-band paths that make up a VCAT service impact the spectrum efficiency in the RSA problem. It is found that the limit on maximal distance difference among sub-band paths demonstrates an impact on the spectrum efficiency of the RSA problem in the aspect of sum network link capacity. Such an impact also becomes stronger with an increasing network nodal degree. REFERENCES [1] Cisco. (1, May ). Cisco visual networking index: forecast and methodology, 11 1. [Online]. Available: http://www.cisco.com/en/us/solutions/collateral/ns1/ns/ns/ns /ns8/white_paper_c11 81_ns8_Networking_Solutions_White_Paper.html. [] M. O Neill. 11, Nov. 1. Cisco predicts that 9% of all Internet traffic will be video in the next three years. [Online]. Available: http://socialtimes.com/cisco-predicts-that-9-of-all-internet-trafficwillbe-video-in-the-next-three-years_b8819. [] W. Shieh, X. Yi, Y. Ma, and Q. 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