Span Restoration for Flexi-Grid Optical Networks under Different Spectrum Conversion Capabilities

Transcription

1 Span Restoration for Flexi-Grid Optical Networks under Different Spectrum Conversion Capabilities Yue Wei, Gangxiang Shen School of Electronic and Information Engineering Soochow University Suzhou, Jiangsu Province, P. R. China, 16 Abstract Orthogonal Frequency Division Multiplexing (OFDM) has been proposed as a new modulation technique for fiber-optic transmission owing to its high spectral efficiency, flexibility in bandwidth allocation, and tolerance to the impairments such as chromatic dispersion. An optical transport network based on optical OFDM transmission technique is often called flexi-grid elastic optical network. In this paper, we investigate the span restoration (SR) technique for this type of network under three different spectrum conversion capabilities, namely, (1) without spectrum conversion, () partial spectrum conversion, and () full spectrum conversion. For all the three cases, we develop integer linear programming (ILP) models to minimize required spare capacity and maximal used link frequency slots. Our results indicate that spectrum conversion shows great benefit of improving spare capacity redundancy and spectrum efficiency for the flexi-grid elastic optical network. Keywords CO-OFDM; elastic optical network; flexi-grid; specrum continuity; spectrum conversion; span restoration I. INTRODUCTION The CO-OFDM-based elastic optical networks receive much attention due to its flexibility in bandwidth allocation and high efficiency of fiber spectrum utilization [1]. Though many studies have been performed for the design and performance evaluation of this type of network []-[6], most of them considered unprotected lightpath services. Few studies have been dedicated to network protection and survivability [7]-[1]. Network protection is of paramount importance to the optical transport networks since they carry a large amount of traffic demand and any network failure such as fiber cut can lead to a significant amount of data affected. Among various network protection techniques, span restoration (SR) is considered as one of promising techniques owing to its simple network operation, fast recovery speed, and good spare capacity efficiency. Span restoration was first proposed in 1987 [11], and its corresponding spare capacity design problem began in 199 [1]. Most of the prior works focused on the SONET/SDH networks and the wavelength division multiplexing (WDM) optical networks. For the flexi-grid elastic optical network, its specific features such as spectrum contiguousness in the spectrum domain and spectrum continuity along the route of a lightpath [][4] can cause the optimization problems of the traditional SR networks like spare capacity assignment (SCA) cannot be directly applied to the elastic optical networks. This motivated us to look into the SR problem for the elastic optical networks in the current research. Recently, we extended the SR technique to the protection of a flexi-grid elastic optical network under the assumption of full spectrum conversion [1]. The concept of spectrum conversion is similar to that of wavelength conversion which is well-studied for the traditional WDM networks. If any optical node in a network can convert the spectrum of a lightpath to any other spectrum in the fiber spectrum range, we call the case full spectrum conversion. In contrast, if a lightpath must always use the same spectrum on all the traversed links and all the intermediate nodes cannot convert the spectrum, we call the case without spectrum conversion. The requirement of the same spectrum on all the traversed links is referred to as the spectrum-continuity constraint. Finally, as an intermediate case, if a network can partially convert the spectrum of a lightpath, we call the case partial spectrum conversion. We can further categorize the partial spectrum conversion into two sub-cases. One is that an optical node can convert the spectrum of a lightpath only within a certain neighboring spectrum range, which is called limited-range spectrum conversion, and the other is that only a partial set of nodes in a network have spectrum conversion capability, which is called sparse spectrum conversion. Spectrum conversion can be realized in either all-optical or electronic domain. The principle of all-optical spectrum conversion is similar to that of all-optical wavelength conversion which employs the nonlinear characteristics of optical components to realize the conversion [14]. However, due to high cost and immaturity of the all-optical conversion, the electronic spectrum conversion is considered as a more reliable technique, under which an optical signal is first converted to an electronic format and then the latter is modulated onto an optical source that operates on a target conversion spectrum [1]. Our previous study [1] has considered a span-restorable elastic optical network under full spectrum conversion. In this paper, we perform a more complete investigation on a span-restorable elastic optical network to consider different spectrum conversion capabilities. The current study is more challenging as new constraints such as spectrum continuity and a limited range of spectrum conversion should be taken into account. Our objective is to find how the spectrum conversion 79

2 capability can affect spare capacity redundancy and fiber spectrum usage in a flexi-grid elastic optical network [16]. For each of the conversion cases, we develop an integer linear programming (ILP) optimization model to minimize required spare (protection) capacity and maximal number of used link frequency slots (FSs). The rest of this paper is organized as follows. In Section II, we introduce the span restoration technique under three different spectrum conversion capabilities. In Section III, we present the ILP models for the optimal designs of the three spectrum conversion cases. In Section IV, we show the results and discuss the benefit of spectrum conversion in the design of span-restorable elastic optical networks. Section V concludes the paper. II. CONCEPT OF SPAN RESTORATION A. Span restoration under different spectrum conversions When a span fails, the SR technique finds replacing paths directly between the two end-nodes of the failed span. This section introduces the concept of SR in the flexi-grid elastic optical networks under three different spectrum conversion capabilities. We first introduce the span restoration in an elastic optical network without spectrum conversion, which is followed by the case of full spectrum conversion, and finally the intermediate case of partial spectrum conversion. 1) Without spectrum conversion For the case without spectrum conversion, when establishing replacing paths upon a span failure, we need to ensure the constraint of spectrum continuity; that is, each restoration path must use the same spectrum as that of an affected working flow on all the traversed links. Fig. 1(a) shows an example of span restoration without spectrum conversion. If span (-) fails, two working flows between node pairs (-) and (-4) are affected. The restoration paths (-6--) and (-1-6--) take over for failure recovery. Due to the constraint of spectrum continuity, we need to assign the same spectra as those of the affected working flows to the restoration paths. Specifically, on the restoration path (-6--), spectrum slots ranging from to 4 are assigned for recovery of the working flow between node pair (-). Likewise, on the restoration path (-1-6--), spectrum slots ranging from 7 to 9 are assigned for recovery of the working flow between node pair (-4). ) Full spectrum conversion Under the full spectrum conversion capability, spectrum allocation on restoration paths is more flexible. For the establishment of a restoration path, we only need to reserve a sufficient number of frequency slots (FSs) required by an affected working flow, regardless the range of the assigned FSs as long as they are spectrally contiguous. Under full spectrum conversion, Fig. 1(b) shows an example of how we can recover affected working flows upon the failure of span (-). Different from the case without spectrum conversion, we can allocate any spectrum segment (e.g., starting from 1 or ) on the fiber spectrum as long as the number of assigned FSs is sufficient to recover the affected working flows and the FSs are contiguous. 1 4 z z1 z 7- z 7+ 6 (a) Without spectrum conversion (b) Full spectrum conversion (c) Partial spectrum conversion SC = 7 FSs Figure 1. Examples of span restoration under the different spectrum conversion capabilities. ) Partial spectrum conversion Partial spectrum conversion is an intermediate case to convert the spectrum of a working flow only within a limited neighboring spectrum range. As shown in Fig. 1(c), at the two end nodes of a failed span, we set an allowed conversion range for the starting FS index to be +, where is the starting FS index of an affected working flow, x is a new starting FS index after partial spectrum conversion, and is a limited spectrum conversion range. As shown in Fig. 1(c), the working flow with a starting FS index has a convertible spectrum range +, and the working flow with a starting FS index 7 has a convertible spectrum range For the partial spectrum conversion, we look into a simplified case; that is, we only allow partial spectrum conversion at the two end nodes of a failed span, while for the intermediate nodes on a restoration path, we assume they are not allowed to convert spectrum. Such an assumption can ensure fast recovery, low cost and good signal quality of the restoration lightpath (since spectrum conversion at intermediate nodes is minimized), and also greatly simplify ILP problem SC = FSs x1 x z z x - x + SC = FSs y y1 y - y

3 modeling. However, it should be also noted that the above assumption does not prevent us from pursuing a more general case, in which any node is capable of partial spectrum conversion. B. Spare capacity sharing under different spectrum conversions In addition to the spectrum conversion, another important feature for span restoration is spare capacity sharing on the common spans traversed by multiple restoration paths. The pre-condition for such spare capacity sharing is that there is only a single span failure for any network-failure event. To understand spare capacity sharing in a span-restorable elastic optical network, let us first see the case of full spectrum conversion as shown in Fig. 1(b), in which we consider span failures (-) and (-4). For span failure (-), we need five FSs on span (-) for failure recovery. For span failure (-4), we need three FSs on span (-) for failure recovery. Without spare capacity sparing, we need to reserve a total of eight FSs on span (-) to fully recover the span failures. For spare capacity sharing, since it is assumed that there is only a single span failure at any moment, maximally we need to reserve five FSs on span (-), which however can guarantee full failure recovery for any single span failure of span (-) or (-4). Three protection FSs are shared on span (-) by the two failure scenarios. The required protection (spare) capacity on a span is just a maximal number of spare capacity units required for recovery of any single span failure in the network. A general rule to determine such a maximal reserved number for each span is as follows: cut the network spans one by one, and for each cut, determine the required number of FSs on the spans for failure recovery. Once all the cut cases are considered, find the maximal required number of FSs on each of the spans, which is the number that should be reserved for full recovery of any single span failure. For spare capacity sparing in a network without spectrum conversion, we need to consider the constraint of spectrum continuity. More specifically, for all the restoration paths of each span failure, we consider spectrum sharing opportunities on their common spans subject to the constraint of spectrum continuity. Again, we can see the example in Fig. 1(a). For span failure (-), two restoration paths allocated with FSs ranging from to 4 and 7 to 9 traverse span (-). For span failure (4-), a restoration path allocated with FSs ranging from to 7 traverses span (-). In this case, frequency slot 7 can be shared by the two restoration situations, and a total of seven FSs should be reserved on span (-). Compared to full spectrum conversion, it is clear that a network without spectrum conversion needs more FSs: seven versus five slots. This hence implies that spectrum conversion capability is of great benefit to spare capacity sharing among restoration spans. For partial spectrum conversion, spare capacity sharing among restoration paths is dependent on the allowed spectrum conversion range. As shown in Fig. 1(c), if a spectrum conversion range is = 1, we may assign restoration path (-6--) with a spectrum ranging from 4 to, and restoration path (-1-6--) with a spectrum ranging from 6 to 8. Meanwhile, restoration path (--4) can keep using the same spectrum, ranging from to 7. In this way, we can achieve maximal spare capacity sharing among the restoration paths, requiring only five FSs from 4 to 8 on span (-), which is the same as that required by full spectrum conversion. Thus, for partial spectrum conversion, it is important to properly convert spectra for restoration paths so as to minimize the required spare capacity. III. ILP MODELS FOR SPAN-RESTORABLE ELASTIC OPTICAL NETWORKS Having introduced the span restoration concept, next we present the design problem for the span-restorable elastic optical networks. The optimization design can be imagined as a restoration rerouting mechanism that is highly adaptive and would make the best use of any available spare capacity and spectrum. An interesting question is then: under the assumption of a single-span failure at any moment and that the working demands have already been routed over the network, how would we decide just where and how much spare capacity and spectrum to invest so that such a mechanism would be able to achieve maximal restorability, but with the minimum of total spare capacity and utilized spectra possible? We use the basic arc-path formulation for SR. The arc-path approach to the SCA problem is posed as one of assigning restoration flow for each failure scenario onto a set of eligible routes so that all flow assignments are feasible under a minimum total of spare capacity and utilized spectrum [17]. We extend the SCA model for the traditional SONET/SDH and WDM networks to the current design of elastic optical networks. We develop three ILP models respectively for the three different spectrum conversion capabilities. Also, we assume that between each pair of nodes, there is only a single shortest route employed for working lightpath establishment. A. Model for no spectrum conversion 1) Sets S: Set of network spans. : Set of eligible routes for the recovery of the span failure. R: Set of node pairs in the network. _ : Set of node pairs whose working routes cross span i. _ : Set of node pairs whose working routes do not cross span i. ) Parameters : Working demand units (in FS) between node pair r., : : A binary parameter that equals one when the restoration route for span failure i traverses span j; zero, otherwise. A binary parameter that equals one when the working path between node pair r and the working path between node pair t share at least one common span; zero, otherwise. The example in Fig. shows a situation where two node pairs share a common span on their working paths, so in this case the parameter 81

4 ,, : equals one. A binary parameter that equals one when backup path b for recovery of the working path between node pair r upon span failure i shares a common span with the working path between node pair t that however does not cross span i; zero, otherwise. The example in Fig. shows a situation where backup path a of node pair r for recovery of span failure i shares a common span with the working path of another node pair t that does not cross span i. For this case, the parameter equals one. : A large value. : A weight factor. ) Variables : The maximal index of utilized frequency slots., :, : : : A binary variable that equals one if the affected node pair r upon span failure i chooses the restoration path of the failed span; zero, otherwise. The number of FSs used for recovery of affected node pair r by the restoration route of failed span i. The total number of spare capacity units (in FS) that should be reserved on span j. An integer variable denoting the assigned starting FS index of the working lightpath between node pair r. An integer variable denoting the assigned ending FS index of the working lightpath between node pair r. : A binary variable that equals one when the starting FS index of the working lightpath between node pair r is larger than that of the working lightpath between node pair t, i.e., > ; zero, otherwise. 4) Objective,, _, _ (1 +,,, ) 1,, _, _ (11) Objective (1) is to minimize the total required spare (protection) capacity in unit of FS and the maximal index of used link FSs in the entire network. In the study, we set to be a small value,.1, such that minimizing the total spare capacity becomes the first priority. Given a starting FS index of a lightpath, constraint () finds the ending FS index of the lightpath. Constraint () tells that the maximal FS index in the entire network should be always greater than the ending FS index of any lightpath in the network. Constraint (4) ensures that there is only one restorable path selected for any node pair whose working path is affected by span failure i. Note that this constraint is important as all the restored FSs must go together through the same route and thus only one restoration route can be employed to recover the affected working flow. This is also one of the key differences of the current model from the traditional span restoration. In the latter, restored capacity units are allowed to be split to go via different restoration paths for failure recovery. Constraint () counts the number of restored capacity units on backup path b for node pair r when span i fails. Constraint (6) counts the total number of spare capacity units in FS that should be reserved on span j so as to ensure successful establishment of all restoration paths. Constraints (7) and (8) ensure the allocated spectra for the working lightpaths between different node pairs do not to overlap on any common span. More specifically, if the starting FS index of working lightpath A is larger than that of working lightpath B, then the starting FS index of lightpath A should also be larger than the ending FS index of lightpath B. Fig. shows the situation where the working lightpaths between node pairs r and t overlap on a common span. Constraints (7) and (8) can ensure the allocated spectra on the two working lightpaths not to overlap on the common span. Minimize: + (1) Node pair r Common span ) Constraints = + 1 () (), = 1, _ (4), =,,, _ () _,,,, (6) (1 +1 ) 1 (7),, ( +1 ) 1,, (8) (1 +,, ) 1 (9),, _, _ ( +,,, ) 1 (1) Node pair t Figure. Node pairs whose working paths share common span(s). Constraints (9)-(11) are a version of constraints (7) and (8) for a pair of working and backup lightpaths that share common span(s). For any single span failure, if the selected backup path for recovery of a working lightpath shares common span(s) with another working lightpath that is not affected by the span failure, then the backup path and the second working lightpath should not overlap in their assigned spectra. Here for the second lightpath, we exclude all the working lightpaths that are also affected by the span failure. This is because constraints (7) and (8) have guaranteed the spectrum non-overlapping requirement for any two working lightpaths that share common span(s). In addition, because sets _ and _ for each span failure i are not symmetric, we need a total of three constraints from (9) to (11) to ensure 8

5 spectrum non-overlapping between a pair of working and backup lightpaths. Specifically, constraint (1) covers the case of >, and constraint (11) covers the opposite case of >. Fig. shows the situation where when span i fails, the selected backup path a for recovery of the working lightpath between node pair r shares a common link with another working lightpath between node pair t that however does not cross span i. Constraints (9)-(11) ensure backup path a and the second working lightpath between node pair t not to overlap in their assigned spectra. Node pair r Span i, : An integer variable that denotes the ending FS index of backup path b for recovery of the working lightpath between node pair r upon span failure i. We have the same objective as equation (1). In addition to constraints ()-(11), we need to consider the following new constraints owing to the limited-range spectrum conversion at the two end nodes of a failed span., =, + 1 _ (1), _ (1), +,, _ (14),, 1 +,,,, 1 (1) Path a,,,, _ Node pair t Common span,, ( +,,,,, ) 1,,,, _ (16) Figure. Node pairs whose restoration path and working path share common span(s). B. Model for partial spectrum conversion For the model of partial spectrum conversion, we have the same sets as those of without spectrum conversion. In addition to the parameters defined before, we define new parameters specfically for partital spectrum conversion as follows.,,, : : A binary parameter that equals one if two backup paths a and b used for recovery of affected working lightpaths between node pairs r and t respectively upon span failure i share common span(s); zero, otherwise. Fig. 4 shows such a situation where backup paths a and b of two node pairs r and t whose working lightpaths are commonly affected by a span failure i share a common span. A partial spectrum conversion range (as introduced in Section II), measured in unit of FS. Figure 4. Two backup paths used for recovery of two working lightpaths commonly affected by a span failure share a common span. In addition to the variables defined before, we define new variables for the case of partial spectrum conversion as follows., : Node pair t Node pair r Span i Common span Path a Path b An integer variable that denotes the starting FS index of backup path b for recovery of the working lightpath between node pair r upon span failure i. Given a starting FS index of a backup lightpath, constraint (1) finds the ending FS index of the backup lightpath. Constraint (1) tells that the maximal FS index in the whole network should be always greater than the ending FS index of any restoration path. Constraint (14) sets a limit on the starting FS index of a restoration path that is allowed to use for a given starting FS index of an affected working lightpath,. Constraints (1)-(16) are a version of constraints (9)-(11) for any pair of restoration paths that share common span(s) and their corresponding working lightpaths also share common span(s) as shown in Fig. 4. The constraints ensure the pair of restoration paths not to overlap in their spectra. Note that for the case without spectrum conversion, we do not need constraints (1)-(16) as the constraint of spectrum continuity enables all the restoration paths not to overlap if their corresponding working lightpaths have been required not to overlap. That is, subject to constraints (7)-(8) and the condition of spectrum continuity, constraints (1)-(16) become redundant. C. Model for full spectrum conversion For the model of full spectrum conversion, we have defined all the requried sets, parameters, and variables before. Also, we have the same objective function as eqution (1). For the constraints, in addition to constraints (4)-(6), we need one more constraint as follows. + _ (17) Constraint (17) says that the total number of FSs assigned as working and protection capacity should not exceed the maximal FS index of the whole network. We can find c by using (17) because each network node is capable of full spectrum conversion. Meanwhile, even under the assumption of full spectrum conversion, we still need to ensure the contiguous status of FSs that make up the whole bandwidth of a lightpath. Constraints (4)-() guarantee such a contiguous requirement. D. Computaitonal complexities of the three ILP models The ILP models for the different spectrum conversion 8

6 capabilities own different computational complexities. We count the dominant numbers of variables and constraints to evaluate the complexity for each ILP model. For the model without spectrum conversion, the dominant number of variables is a maxima of O( ) and O( ), and the dominant number of constraints is a maxima of O( ) and O( ), where is the average number of link-disjoint shortest routes for each pair of nodes, and represent the number of links and node pairs in the entire network, and and are the average numbers of node pairs whose working routes cross and do not cross a failure span, respectively. The model with partial spectrum conversion has the same dominant number of variables as that of the model without spectrum conversion. However, it has a larger dominant number of constraints than that of the model without spectrum conversion because the former extends the latter by adding more variables and constraints. The dominant number of constraints of the partial spectrum conversion model is a maxima of O( ), O( ), and O( ). Finally, for the model with full spectrum conversion, the dominant number of variables is O( ), and the dominant number of constraints is a maxima of O( ) and O( ). The computational complexities in terms of dominant numbers of variables and constraints for all the three ILP models are summarized in Table 1. TABLE 1. COMPUTATIONAL COMPLEXITIES OF THE THREE ILP MODELS. Models No conversion Partial conversion Full conversion Computational complexities Dominant number of Dominant number of variables constraints max{o( max{o( ),O( )} ),O( )} max{o( max{ ( ),O( ),O( )} ),O( )} max{o( O( ) ),O( )} IV. RESULTS AND DISCUSSIONS To evaluate the performance of the span-restorable elastic optical networks under the different spectrum conversion capabilities, we considered three test networks, including (1) a six-node eight-link network (n6s8, average nodal degree =.7), () the 11-node 6-link COST9 network (average nodal degree = 4.7), and () the 14-node 1-link NSFNET network (average nodal degree =.). The n6s8 network is shown in Fig. 1. The COST9 and NSFNET networks are shown in Figs. and 6, respectively. For all the networks, the traffic demand between each pair of nodes is random with a uniform distribution within a certain range. We set a maximum number of FSs, X, and each node pair can choose any number (between 1 and X) of traffic demand units (in FS). Without losing generality, this study sets X to be three, four, and five, respectively. In addition, we employed the k-disjoint shortest path algorithm to find all link-disjoint protection routes for each span failure. There exists an algorithm to find all eligible routes between a pair of nodes, regardless the constraint of link-disjointness. Although considering all eligible restoration routes can obtain better spare capacity sharing, it leads to a significant increase in the size of optimization problem. For better tractability, we have employed the k-disjoint shortest routes for the study. We used commercial software AMPL/Gurobi [18] to solve all the ILP models. For the different conversion cases, the running times of the optimization models were different. The running time of the model with partial spectrum conversion was the longest, about three hours. The model without spectrum conversion required a medium running time, about 1 seconds. The running time of the model with full spectrum conversion was the shortest, less than one second. Figure. 11-node 6-link COST9 network Figure node 1-link NSFNET network A. Spectrum efficiency We evaluated the performance for the span-restorable elastic optical networks in terms of spare capacity redundancy and the maximal FS index. All the three spectrum conversion capabilities were considered. For the case of partial spectrum conversion, we set to be five. Fig. 7 shows the results of spare capacity redundancy which is defined as a ratio of total protection capacity to total working capacity. Because we do not set a limit on the maximal number of FSs on each fiber link and minimizing the total spare capacity is the first optimization objective of the ILP models, all the three spectrum conversion cases show to have the same spare capacity redundancy, and each result point on the curves corresponds to the spare capacity redundancy of all the three spectrum conversion cases. In addition, under different traffic demand intensities, we see that there are almost constant spare capacity redundancies for all

7 the three test networks. Finally, comparing the spare capacity redundancies of the three test networks, we find that the redundancy of the COST9 network is the lowest, the NSFNET network is the second lowest, and the n6s8 network is the highest. This is because a network with a higher average nodal degree generally has more opportunities for spare capacity sharing, thereby showing a lower spare capacity redundancy. Among the three test networks, the COST9 network has the highest nodal degree, and the n6s8 network has the lowest nodal degree. Thus, the three test networks show spare capacity redundancies as observed. Spare capacity redundancy Maximal number of demand units, X n6s8 NSFNET COST9 Figure 7. Spare capacity redundancies under different spectrum conversion capabilities (All the three spectrum conversion cases show the same spare capacity redundancy under an idential traffic demand matrix). Figs. 8(a), (b), and (c) show the maximal number of FSs required for accommodating all the traffic demands under the three different spectrum conversion capabilities. We can see that the case without spectrum conversion requires the largest number of FSs, the case of full spectrum conversion requires the smallest number of FSs, and the case of partial spectrum conversion falls in the middle. This implies that the spectrum conversion capability does help improve spectrum efficiency or utilization in design of a span-restorable elastic optical network. In addition, we observe that the spectrum conversion capability shows different impacts on spectrum efficiency under different network nodal degrees. Let us compare the results of the NSFNET and COST9 networks. For the NSFNET network, the required maximal number of FSs under full spectrum conversion is smaller than a half of that of the case without spectrum conversion. In contrast, in the COST9 network, the difference of the required number of FSs between the two cases is much smaller: full conversion is only about % smaller than without conversion. The reason is as follows: The COST9 network has a higher nodal degree, and the NSFNET has a lower nodal degree, which leads the NSFNET network to have a longer average hop-length of end-to-end lightpath than that of the COST9 network. For a long route, it is often difficult to satisfy the constraint of spectrum continuity, i.e., finding a set of FSs that are commonly available on all the links. The full spectrum conversion capability is of great help to a long route in eliminating spectrum collision. This therefore explains why the full spectrum conversion capability is more helpful to the NSFNET network. In general, we can conclude that under the SR technique, the spectrum conversion capability can bring more benefit to a network with a lower average nodal degree Maxmial number of demand units, X (a) n6s8 (b) COST9 (c) NSFNET Continuity-Used spectrum Partial-Used spectrum Conversion-Used spectrum Continuity-Used spectrum Partial-Used spectrum Conversion-Used spectrum 4 Maximal number of demand units, X Continuity-Used spectrum Partial-Used spectrum Conversion-Used spectrum 4 Maximal number of demand units, X Figure 8. Maximal required FSs under the different spectrum conversion capabilities. B. Impact of spectrum conversion range Viewing the fact that the spectrum conversion capability can largely affect spectrum efficiency of a span-restorable elastic optical network, we evaluate how spectrum conversion range can affect spectrum efficiency of a SR network design. By changing the range of spectrum conversion and under three traffic demand intensities, we show the results for the three test networks in Figs. 9(a), (b), and (c), respectively, 8

8 in which = corresponds to the case of without spectrum conversion, and = corresponds to the case of full spectrum conversion X= X=4 X= 1 7 Range of partial spectrum conversion X= X=4 X= (a) n6s8 1 7 Range of partial spectrum conversion X= X=4 X= (b) COST Range of partial spectrum conversion (c) NSFNET Figure 9. Maximal number of FSs under different spectrum conversion ranges (X: maximal number of demand units in FS per node pair). Based on the results, we can see that with the increase of, the maximal number of FSs decreases for all of the test cases. This is reasonable since a larger corresponds to better flexibility in spectrum allocation on the restoration paths. In addition, we observe a saturated phenomenon between and the maximal number of FSs. For example, in the n6s8 network, when = 7, the maximal number of FSs is the same as that of full spectrum conversion, i.e., =. Similarly, in the COST9 network, under a demand intensity =, the maximal number of FSs under = 7 is also the same as that of full spectrum conversion. Finally, for the NSFNET network, due to a larger number of used FSs, the spectrum conversion range that shows to saturate is also larger to be more than =. Based on the above observations, we can therefore conclude that a span-restorable elastic optical network with partial spectrum conversion can achieve performance close to that of full spectrum conversion when a certain level of spectrum conversion range (much smaller than full spectrum conversion) is provided. V. CONCLUSION We considered the SR technique for the flexi-grid elastic optical networks under the three different spectrum conversion capabilities, namely, without spectrum conversion, partial spectrum conversion, and full spectrum conversion. For the three cases, we developed the corresponding ILP optimization models to minimize required spare capacity and maximal number of used FSs. Our results show that the capability of spectrum conversion does bring benefit to improve the spectrum efficiency for a span-restorable elastic optical network. For a network with a lower nodal degree, the spectrum conversion capability shows a stronger benefit. Also, for the case of partial spectrum conversion, we see a saturation phenomenon between network spectrum efficiency and spectrum conversion range: increasing spectrum conversion range can improve the spectrum efficiency of a SR network; however, when the conversion range reaches a certain level, the spectrum efficiency approaches that of full spectrum conversion. Finally, on spare capacity redundancy, we see that a network with a higher nodal degree generally shows a lower spare capacity redundancy owing to better spare capacity sharing opportunities. ACKNOWLEDGMENT This work was jointly supported by the National 86 Plans Project of China (1AA11), National Natural Science Foundation of China (NSFC) (61177), and the Open Project (11GZKF111) from the State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiaotong University, China. REFERENCES [1] W. Shieh and I. Djordjevic, OFDM for Optical Communications, Academic Press, 9. [] Y. Wang, X. Cao, and Q. Hu, Routing and spectrum allocation in spectrum-sliced elastic optical path networks, in Proc. IEEE ICC 11. [] Y. Wang, X. Cao, Q. Hu, and Y. Pan, Towards elastic and fine-granular bandwidth allocation in spectrum-sliced optical networks, J. Opt. Commun. Netw., vol. 4, no. 11, pp , Nov. 1. [4] K. Christodoulopoulos, I. Tomkos, and E. Varvarigos, Routing and spectrum allocation in OFDM-based optical networks with elastic bandwidth allocation, in Proc. GLOBECOM 1. [] X. Wan, L. Wang, N. Hua, H. Zhang, and X. Zheng, Dynamic routing and spectrum assignment in flexible optical path networks, in Proc. OFC/NFOEC 11. [6] M. Klinkowski and K. Walkowiak, Routing and spectrum assignment in spectrum sliced elastic optical path network, IEEE Commun. Lett., vol. 1, no. 8, pp , Aug. 11. [7] A. N. Patel, P. N. Ji, J. P. Jue, and T. Wang, Survivable transparent flexible optical WDM (FWDM) networks, in Proc. OFC/NFOEC

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