Applying p-cycle Technique to Elastic Optical Networks

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1 Applying p-cycle Technique to Elastic Optical Networks Yue Wei, Kai Xu, Heming Zhao, Member, IEEE, Gangxiang Shen, Senior Member, IEEE Abstract This paper considers the p-cycle network protection technique in comparison with the ring cover technique for elastic optical networks. We develop an Integer Linear Programming (ILP) model to minimize required protection capacity and used link spectra in the entire network. We also apply the Bandwidth Squeezed Restoration (BSR) technique to obtain the maximum restoration levels for the affected service flows subject to limited frequency-slot capacity on each fiber link. Our studies show that the proposed p-cycle technique requires much less spare capacity than the ring cover technique. In addition, it is seen that as the number of candidate cycles used in the design increases, the spare capacity efficiency saturates. Index Terms Elastic optical network, p-cycles, ring cover, network protection, bandwidth squeezed restoration E I. INTRODUCTION lastic optical networks receive much attention due to the flexibility in bandwidth allocation and efficiency of fiber spectrum utilization []-[]. Many studies have been performed for the design and performance evaluation of this type of networks []-[]. However, few of them focus on the issue of network protection []-[]. Network protection is important for the elastic optical network since it carries a large amount of traffic demand and any network failure such as a fiber cut can affect a significant amount of traffic. Among many network protection techniques [], the p-cycle technique is considered promising for an optical network due to its ring-like restoration speed and mesh-like spare capacity efficiency. The concept of p-cycles was first introduced by Grover and Stamatelakis in [], which are characterized as pre-configured protection cycles in mesh networks. The key difference of the p-cycle technique from the ring cover technique is that the former can support the protection of both on-cycle and straddling spans, while the latter can protect only on-cycle spans. The protection of straddling span enables each p-cycle to provide two protection paths for failure recovery of a straddling span. This significantly enhances spare capacity efficiency of the p-cycle technique compared to the ring cover technique. Most of the prior works on p-cycles focused on the SONET/SDH and WDM networks []. In this paper, we apply this technique to the elastic optical network. We particularly Y. Wei, H. Zhao, and G. Shen are with School of Electronic and Information Engineering, Soochow University, Suzhou, Jiangsu Province, P. R. China, 00; K. Xu is with School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan Province, P. R. China, (correspondence shengx@suda.edu.cn). consider the constraints of spectrum continuity, referred to as the requirement that the same set of frequency slots (FSs) should be used on all the links traversed by a lightpath, and spectrum contiguousness, referred to as the requirement that all the FSs assigned to a lightpath must be spectrally neighboring []. These new special features do not allow us to directly employ the traditional p-cycle optimization models to design for the p-cycle-based elastic optical networks. Rather, a significant extension is required to support these elastic network features, which forms the key contribution of this paper. To minimize required protection capacity and used link spectra in the entire network, we develop an Integer Linear Programming (ILP) model for the p-cycle-based elastic optical network. Also, to evaluate the capacity efficiency of the p-cycle technique, we compare the results of the p-cycle technique with the ring cover technique in terms of protection capacity and used link spectra. The terms of link and span are interchangeable in this paper. II. P-CYCLE TECHNIQUE IN ELASTIC OPTICAL NETWORKS We use an example in Fig. to explain the concept of p-cycle in elastic optical networks, where there are three p-cycles, i.e., (------), (----), and (----). Consider span (-), on which there are three traversing working flows. The assigned FSs for these working flows are in different colors, namely FS (-), FS (-), and FS (8-9), respectively. With the p-cycle technique, the three cycles can jointly recover the affected working flows on span (-). Specifically, we use cycles (----) and (----) to recover the working flows with FS (-) and FS (-), respectively, by considering span (-) as on-cycle span of the two cycles. Also, we use cycle (------) to recover the working flow with FS (8-9) by considering span (-) as a straddling span of the cycle since its two end nodes are on the cycle while itself is not on the cycle. In this case, though the cycle can provide two protection paths for failure recovery, the requirement of spectrum contiguousness prohibits the FSs of an affected working flow from being split onto multiple routes, but only one protection path can be used for recovery. We use the upper-half cycle to recover the working flow with FS (8-9) in this example. Compared to the ring cover technique that can only recover on-cycle spans, the p-cycle technique provides more options for span failure recovery, which therefore leads to more efficient spare capacity sharing. 0 copyright by IFIP

2 Flow Flow Flow 8 9 Fig. : An example of p-cycles. The requirement of spectrum contiguousness restricts all the FSs of any affected working flow to be recovered along a single route, not splittable. This requirement is one of the key differences of the current technique from the traditional p-cycles under which the restored capacity units can be split onto different eligible cycles. In addition, under the p-cycle technique, all the protection capacity deployed for a cycle is dedicated; different cycles cannot share spare capacity on their common spans as in span restoration [] or path protection []. Lastly, due to the constraint of spectrum continuity, two pairs of opposite fibers should be deployed on each physical link as shown in Fig. with one functioning as working fibers and the other as protection fibers. Because the affected working flow and the recovering cycle always share a common span, two separate fiber pairs are necessary to avoid spectrum confliction. III. ILP OPTIMIZATION MODEL In this section, we present the ILP models for both the p-cycle and ring cover protection techniques. For the ring cover technique, we specially consider the case of with full spectrum conversion, which can provide lower bounds on the spare capacity redundancy and the number of required FSs for the ring cover technique without spectrum conversion. Thus, if the p-cycle technique (without spectrum conversion) can outperform the ring cover technique with spectrum conversion, we can easily verify that the p-cycle technique should also outperform the ring cover technique under the condition without spectrum conversion. We first present the models for the p-cycle technique (without spectrum conversion), followed by the models for the ring cover technique (with full spectrum conversion). Given a set of lightpath requests with each requiring a predefined number of FSs, we minimize required protection capacity and used link spectra in the entire network. We assume that the elastic optical networks are operated under the flexi-grid mode []; this assumes that each fiber spectrum is divided into many FSs with a constant small granularity. We also assume that between each pair of nodes there is only one single shortest route employed to establish the working lightpath. The related sets and parameters of the ILP models are as follows. 8 9 Working fibers Protection fibers A. Models for p-cycles and ring cover Sets: : Set of links in the network. : Set of node pairs in the network. : Set of candidate cycles in the network. : Set of eligible cycles for the recovery of the link failure. : Set of node pairs whose working routes traverse link i. Parameters: : The working demand units (in FS) between node pair r. : A binary parameter that equals if cycle p crosses link i; 0, otherwise. : A binary parameter that equals if the working path between node pair r and the working path between node pair t share common link(s); 0, otherwise. : A binary parameter that equals if cycles p and q share common link(s); 0, otherwise. : A large value. : A weight factor. Variables: : A binary variable that equals if the eligible cycle that can help the working flow between node pair r be recovered from the link failure i is chosen; 0, otherwise. : An integer variable denoting the starting FS index of cycle p. : An integer variable denoting the starting FS index of the working lightpath between node pair r. : The number of spare capacity units (in FS) assigned for cycle p. : A binary variable that equals if the starting frequency of cycle p is larger than the starting frequency of cycle q, i.e., > ; 0, otherwise. : The total number of spare capacity units (in FS) that should be reserved on link. : A binary variable that equals if the starting FS index of the working lightpath between node pair r is larger than that of the working lightpath of node pair t, i.e., > ; 0, otherwise. : The maximum index of the used FSs on all the fiber links in the network. Objective: Minimize () Subject to: () () () 0 copyright by IFIP

3 () () ( ) () (8) (9) (0) () () Objective () is to minimize the total required protection capacity in unit of FS and the maximal index of used FSs in the entire network. We set to be a small value (e.g., 0.0) such that minimizing the total spare capacity becomes the first priority. Constraints () and () say that the maximal FS index should be always greater than the ending FS index of any working lightpath and p-cycle in the network. Due to the requirement of spectrum contiguousness, constraint () ensures that there is only one eligible cycle chosen for any node pair whose working lightpath is affected by link failure i. Constraint () ensures that the protection capacity provided by cycle p is sufficient to recover the failure of lightpath between node pair r upon link failure i. Constraint () counts the total number of spare capacity units in FS that should be reserved on link j so as to ensure successful establishment of all the p-cycles. Constraints () and (8) ensure that the cycle chosen for recovery of working lightpath between node pair r upon link failure i can provide sufficient recovering spectra, i.e., the starting and ending FS indexes of the working lightpath is bounded by the starting and ending FS indexes of the cycle. Constraints (9) and (0) ensure that the allocated spectra for the working lightpaths between different node pairs do not overlap on any common link (since all the working lightpaths are established in the same pair of fiber links). In other words, if the starting FS index of working lightpath A is larger than that of working lightpath B, the starting FS index of lightpath A should also be larger than the ending FS index of lightpath B. Constraints () and () are a version of constraints (9) and (0) for the cycles that share common link(s). For the model of the ring cover technique with full spectrum conversion, we have the same sets and parameters as in the model of the p-cycle technique. For the variables, we only need to keep four variables (i.e.,,,, and ). We have the same objective function as in equation (). In addition to constraints (), (), and (), the model has two more constraints as follows. () () B. p-cycles and ring cover protection under Bandwidth Squeezed Restoration (BSR) We have introduced the ILP models for 00% failure recovery for the two protection techniques. In an elastic optical network, when there is no sufficient bandwidth for complete restoration, we may partially restore affected service flows. This technique is referred to as Bandwidth Squeezed Restoration (BSR) [9]-[0]. The BSR technique would be especially useful in a network which does not have sufficient protection capacity for full restoration. Fig. shows an example of BSR. When span (-) fails, all the working flows on the span are affected. Without BSR, eight FSs are required on the protection cycle (------) for failure recovery. However, by applying BSR, we can partially (0%) recover the failure, e.g., through providing four FSs on the protection cycle (via either upper or lower half cycle) as shown in Fig.. Note that it is not allowed to simultaneously use both upper and lower half cycles to recover the failure due to the constraint of spectrum contiguousness in the elastic network. Protection = FSs Switch-over Fig. : p-cycle technique with bandwidth squeezing. Working = 8 FSs To plan for the p-cycle and ring cover techniques with BSR, we extend the optimization models in the previous subsection. For BSR, we define as the ratio of bandwidth squeezing. This would imply that for all the service flows we need to ensure the recovery of at least a fraction of the original bandwidth. Specifically, corresponds to the case without restoration, while corresponds to the case of full restoration. For the example in Fig., is 0. as four FSs can only recover 0% of the original 8-FS working capacity. The objective of the model with BSR is the same as (), i.e., to minimize both the total spare capacity required in unit of FS and the maximal FS index used in the entire network. Some modifications to the constraints of the two protection technique are as follows. For the model of the p-cycle technique, we replace constraints (), (), (8), and (0) with new constraints ( ), ( ), (8 ), and (0 ) as follows. These constraints ensure that only units of traffic demand are restored. ( ) ( ) (8 ) 0 copyright by IFIP

4 (0 ) 0 For the model of the ring cover technique with full spectrum conversion, in addition to (), ( ), (), and (), we need to replace constraint () with new constraint ( ) given below. ( ) In contrast to minimizing the total spare capacity required in unit of FS subject to the condition that all the lightpath demands are recovered, under BSR we may also plan to maximize service restorability (corresponding to bandwidth squeezing ratio ) given a limited spectrum capacity in each fiber link (i.e., a limited number of FSs, c). In this design scenario, becomes a variable and the maximal index of used link FSs c changes to a given parameter. The optimization models have the same sets of constraints as those for the BSR capacity minimizing designs, while maximizing the bandwidth squeezing ratio (or restoration level) becomes the new objective to replace objective () for the two protection techniques. 8 9 (a) 0-node -link SmallNet network IV. TESTS AND PERFORMANCE ANALYSES To evaluate the performance of the p-cycle technique, we consider two test networks: (a) the 0-node -link SmallNet network and (b) the -node -link COST9 network. The two test networks are shown in Fig.. The traffic demand between each pair of nodes is random with a uniform distribution within a certain range between and X FSs. We set X to be five in our study. In addition, we employ a measure called A Priori Efficiency (AE,, where refers to the number of useful paths that cycle can provide if span fails and can take the values of 0,, or, is a parameter as defined before, and is the cost of link k) as in [] to rank the set of all distinct candidate cycles, and use different limited numbers of top-ranked candidate cycles (with AE as the ranking criterion) for our ILP designs. AE is a parameter used to measure the protection efficiency of each candidate cycle. A larger AE corresponds to better protection efficiency. We start from a certain number (i.e., 00) of top-ranked cycles and then gradually increase the number of top-ranked cycles for the following testing points until the entire set of candidate cycles are considered or performance saturation is observed. We used the commercial software AMPL/Gurobi. [] to solve all the ILP models. The MIPGAPS of all the optimization models were set to be no greater than %. Fig. : Test networks. (b) -node -link COST9 network A. Spare capacity efficiency and maximal number of frequency slots used In this section, we evaluated the performance of the p-cycle and ring cover techniques for the elastic optical network in terms of their spare capacity redundancies and maximal FS indexes used. Fig. shows the result of spare capacity redundancy which is defined as the ratio of total protection capacity to total working capacity in the entire network. Because the AMPL/Gurobi cannot solve the ILP model of the ring cover design under the constraint of spectrum continuity when the number of candidate cycles is large, we employed the ILP model of the ring cover design with full spectrum conversion to find the spare capacity redundancy. With the capability of spectrum conversion, such a result can function as a lower bound on spare capacity redundancy and the maximal number of used FSs for the case with spectrum continuity. Comparing the spare capacity redundancies of the two protection techniques, we find that the redundancy of the p-cycle technique is always lower than the ring cover technique even though the latter has spectrum conversion capability. This is reasonable since the p-cycle technique offers the protection capability by the straddling spans in addition to the on-cycle spans, while the ring-cover technique can only offer the protection capacity same as that of the on-cycle spans. We also observe a saturated trend between the spare capacity redundancy and the number of candidate cycles used for the designs. At the beginning, the increase of the number of candidate cycles can significantly reduce the spare capacity redundancies for the two techniques; however, when a certain number of cycles are exceeded, a further increase of candidate cycles will not lead to any reduction of spare capacity redundancy. For the COST9 network, such saturation occurs 0 0 copyright by IFIP

5 at the point when the number of candidate cycles is around 000, and for the SmallNet network, the corresponding saturation number of cycles is around 00. In addition, we find that for the p-cycle technique, the spare capacity redundancy of the COST9 network is lower than the SmallNet network after the saturation is reached. This is because the COST9 network is denser in connectivity than the SmallNet network, which enables better spare capacity sharing in the network. Spare capacity redundancy COST9--Ring cover 0. COST9--p-Cycles SmallNet--Ring cover Number of candidate cycles Fig. : Spare capacity redundancy. Fig. shows the maximal number of FSs required for the failure recovery of all the spans. For the ring cover technique, we again use the results of the designs with full spectrum conversion for comparison, which is actually biased to the ring cover technique. We can see that although the p-cycle technique is subject to the constraint of spectrum continuity, it still requires fewer FSs than the ring cover technique (with full spectrum conversion). This from a different perspective verifies better spare capacity efficiency of the p-cycle technique compared to the ring cover technique in elastic optical networks. Maximum number of used FSs 0 8 COST9--Ring cover COST9--p-Cycles SmallNet--Ring cover Number of candidate cycles Fig. : Maximal number of FSs used. B. Performance with BSR In this section, we evaluate how the BSR capability can impact the design of p-cycle and ring cover protection techniques based on elastic optical networks. Here, we consider the BSR capability under specific numbers of candidate cycles when the curves reach saturations as depicted in Figs. and. Specifically, for the SmallNet network, the number of considered candidate cycles is 800; for the COST9 network, such a number is 000. All the results were obtained under the assumption that the traffic demand intensive X is. Given different levels of bandwidth squeezing ratio, we minimize the total required protection capacity in unit of FSs and the total number c of FSs required. The corresponding results for the two protection techniques are shown in Figs. (a) and (b) for the two test networks, respectively. For both the protection techniques, we find that a larger bandwidth squeezing ratio require a larger number of FSs to accommodate all the lightpath traffic demands. In addition, comparing the results of the two protection techniques, we see that under BSR, the ring cover technique always requires more FSs than the p-cycle technique and the redundancy of the p-cycle technique is always lower than the ring cover technique. These again verify the p-cycle technique can achieve better spare capacity efficiency than the ring cover technique in elastic optical networks. Maximum number of used FSs Maximum number of used FSs SmallNet--Ring cover SmallNet--Ring cover_scr _SCR 0% 0% 0% 00% Bandwidth squeezing ratio (a) SmallNet COST9--Ring cover COST9--p-Cycles COST9--Ring cover_scr COST9--p-Cycles_SCR 0% 0% 0% 00% Bandwidth squeezing ratio (b) COST9 Fig. : Maximal number of FSs required and spare capacity redundancy under different bandwidth squeezing ratios (SCR: spare capacity redundancy). Also, assuming a limited number of FSs on each fiber link, we maximize the restorability of network services, which is measured as maximum achievable bandwidth squeezing ratio. The corresponding results are shown in Figs. (a) and (b) for the two test networks, respectively. We can see that with increasing numbers of FSs on each fiber link, the maximal restoration level or bandwidth squeezing ratio grows accordingly. Such an observation can be expected as increased network bandwidth can restore more network services. Here it should be noted again that the restoration level achieved by the p-cycle technique is without spectrum conversion, while the restoration level achieved by the ring cover technique is with full spectrum conversion Spare capacity redundancy Spare capacity redundancy 0 copyright by IFIP

6 Restoration percentage/bandwidth squeezing ration Restoration percentage/bandwidth squeezing ration 00% 80% 0% 0% 0% 0% 00% 80% 0% 0% 0% 0% Maximum number of FSs on each fiber link (a) SmallNet (b) COST9 Fig. : Restoration percentage (or bandwidth squeezing ratios) under different maximal numbers of FSs in each fiber link. V. CONCLUSION We applied the p-cycle technique to the elastic optical network. We developed ILP models to minimize required protection capacity and used link spectra in the entire network. We also extended the ILP models to design elastic optical networks considering the BSR (Bandwidth Squeezed Restoration) capability. Our results showed that the p-cycle technique has much better spare capacity efficiency than the ring cover technique even under the situation that the latter is equipped with full spectrum conversion capability. In addition, performance saturation was observed between the spare capacity efficiency and the number of candidate cycles used in the design. It is not necessary to consider all the candidate cycles in order to achieve the best spare capacity efficiency in the design of p-cycle-based elastic optical networks. Rather, a limited set of top-ranked candidate cycles can achieve optimum performance. With the BSR capability, we made similar observations on how the p-cycle technique can achieve better spectrum efficiency than its counterpart, the ring cover technique. For a larger number of given FSs in each fiber link, a higher restoration level or bandwidth squeezing ratio can be achieved by the p-cycle technique than the ring cover technique in all the test cases. 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