1. Introduction

In order to improve the spectral efficiency of wavelength division multiplexing (WDM) network, elastic optical networks (EONs) emerged with the advantages of fine spectrum granularity and flexible spectrum allocation to better meet the requirements of different traffic demand [1]. Apart from the problem of low spectral efficiency, the transmission capacity of single mode fiber (SMF) has nearly reached the limit of nonlinear Shannon theorem. Fortunately, spatial division multiplexing (SDM), realized by multi core fiber (MCF) and few mode fiber (FMF), can be adopted to fulfill the enormous demands. Therefore, SDM and EONs are regarded as two promising technologies that can jointly support high-quality transmission service. Compared with MCF, FMF has the strengths of higher transmission capacity, better power efficiency and higher nonlinearity tolerance compared to MCF [2], but it can only be used in a small network topology due to the severe physical impairment. In MCF, there are multiple single mode cores made by the same material with the same characteristics. The spacing of cores can be closer or wider, and the packing of them can be odd or even [3]. Inter core crosstalk is the main issue discussed in SDM, which is mainly related to the structure of the optical fiber, e.g. the placement of cores, core pitch, the number of cores and propagation distance [3,4]. Under the same physical conditions, the crosstalk in MCF is significantly lower than that in FMF, which means it needs lower computation complexity of MIMO DSP. Therefore, MCF is the better choice of SDM, which can be combined with EON to provide better network transmission services.

With the maturity of EON and SDM technology, SDN-EON could support a transmission rate from Gbps to Pbps, and a research shows that SDM-EON can guarantee transmission capacity at 10 Pbps per fiber [5]. It means that the occurrence of a network failure, in which all the cores in MCF and FSs of a link fail, will cause a greater amount of service loss than the traditional optical network, resulting in serious social impact and economic loss. Link failure is one of the most common failure modes for optical networks. Links can fail in many ways, ranging from amplifier failure to power outages to wayward backhoes. Therefore, it is important to improve the survivability of the SDM-EON network, propose measures for link protection. From the perspective of protection objects, the researches on network survivability are mainly divided into path-based protection and link-based protection. For path-based protection, it is mainly for traffic, to establish a reserved protection path from the source node to the destination mode without failure links. The typical protection methods are dedicated backup path protection (DBPP) and shared backup path protection (SBPP). DBPP aims to establish two paths working path and protection path for each request, which can solve the problem of multi-link failures in some situations [6]. Different from DBPP, the resources can be shared in SBPP, with lower recovery rate and better resource utilization. However, the path-based protection method will rely too much on traffic distribution characteristics. The resource demands of different scenarios with path-based protection is inconsistent. While in link-based protection, it aims to protect the target link instead of the end-to-end path. The link-based protection method has less configuration cost and better time delay in comparison to path-based protection [7]. Similar to the path-based protection, there are dedicated and shared link protection schemes. And shared link protection scheme has better resource utilization.

From the perspective of the entire network, protection method can be divided into mesh-based protection schemes and ring-based protection schemes. Mesh-based methods emerged for mesh network survivability. It tries to duplicate every transmission path, from source nodes to destination nodes. However, the costs of redundancy can be typically very high. Ring-based protection schemes are popularly used in optical networks too. There are two general types of self-healing rings (SHR) for protection methods: the bi-directional line switched ring (BLSR) and unidirectional path-switched rings (UPSR). In BLSR, if protection channel is free, the service demand will be switched to the protection channel in the reverse direction of the link failure. In UPSR, a traffic is simultaneously transmitted on working and protection fibers. The signal with better quality will be chosen at the receiver side. It is proved that BLSR can be used more efficiently than UPSR, because any link can make similar use of the shared standby capacity around the ring [6]. Though, Mesh-based methods can serve more working demand in more diverse patterns as compared to corresponding ring-based methods, mesh protection is not generally as fast as rings because of dealing with multiple-path re-routing problems. The main advantage of rings is their low cost and high speed when compared to mesh-protection schemes, especially in metro areas. Therefore, BLSR method in link protection is a good choice for bi-directional transmission.

Ring covers, c-cycle double covers and preconfigured protection cycle (p-cycle) are three most notable ring-based protection techniques which are based on BLSR in the mesh network [8]. And the recovery process is handled by the end nodes of the failed link in the three ring-based protection techniques [9]. Ring covers approach chooses a set of rings that covers every link in the mesh at least once is found. By using the SHR technique, the network can be protected against fiber cuts and node failures [10]. In [10] and [6], the authors pointed out that this approach requires a large amount of spare capacity to guarantee 100 percent protection in WDM network. Whereas, this problem can be easily addressed in optical network with flexible grid. In cycle double covers, the link can be covered only once, in this case an overall design with exactly 100% of redundancy can be achieved. While in SDM-EON network, it is impossible to find such ring covers under strict length limitation, because the crosstalk of MCF is related to the distance of routing. In p-cycle protection, the time of calculating and recovering path is spent before any failure occurs [11]. Only two nodes need real time recovery for any link failure and the other intermediate link need not any switching. Besides that, p-cycles can provide spare FSs not only on-cycle links but also straddling links. Overall, p-cycle has the ring-like restoration speed and mesh-like efficiency [12] [13]. Although the straddling links can be protected in p-cycle method, it can only be used as work links but not protection links which is a specific characteristic of p-cycle. That means, the reserved spectrum resources on straddling links may be wasted. Thus with the purpose of taking full advantages of the resources, ring covers may have better performance than p-cycles in SDM-EON network.

In this paper, we focus on the robustness of the whole network and propose a link protection scheme with shared resources and multiple backup paths by means of ring covers in SDM-EON. Compared with traditional SBPP, our scheme considers the entire network instead of a specific traffic request, so its performance will not be affected by traffic distribution. Our aim is to increase the recovery rate as much as possible. Through specific ring covers method proposed, our scheme can make full use of resources, improve switching speed and lower cost. Firstly, we calculate a set of rings under different distance constraints. Then we consider the inter core crosstalk in MCF and propose several link protection algorithms based on existing rings in SDM-EON. To satisfy the spectrum continuity and contiguity constraint, the frequency resources are divided into two or three areas. It should note that our scheme is a pre-plan in SDM-EON, which only considers static scenarios.

The rest of the paper is organized as follows. Section 2 describes the related works. In Section 3, we make a description about the network model and the physical impairment in MCF. In Sections 4, we discuss the ring covers-based protection designs. The performance of the proposed algorithms is evaluated in Section 5. Finally, Section 6 summarizes the paper.

2. Related work

In recent years, the problem of RSCA has been studied by many researchers across the world. The inter-core crosstalk in MCF makes a serious impact on the quality of transmission. Since the first formulation of crosstalk in MCF was proposed in [14], quantities of works studying RSCA problem have been further proposed based on it. In [15], the authors proposed an on-demand RSCA scheme by the way of predefining core selection priority and classification. The results showed that the crosstalk and fragmentation could be both decreased. In [16], a crosstalk-aware multi-core virtualization concatenation scheme is proposed to get lower blocking probability and higher spectrum utilization compared with SCVC. In [17], the authors discussed the routing, modulation, space and spectrum assignment (SMLSSA) in SDM-EON and established an ILP model for static traffic. In [18], the author proposed the concept of core priority, and their research proves that a reasonable order of core selection will cause less crosstalk. In [19], authors have proposed an algorithm to dynamically allocate resources with a hybrid (shared or dedicated) protection scheme named Hybrid Protection Lightpath (HybPL), defining different cost functions to choose between two schemes.

As for protection of networks, path protection and link protection are two major techniques in the protection of mesh networks [20]. Path protection refers to the method that we reserve the routings and backup resources from source nodes to destination nodes for each connection, related researches are [21] [22] [23] [24], while link protection is used to protect/restore the single link, e.g. [25] [26]. Extensive studies on both path protection and link protection have been published. Dedicate backup path protection (DBPP) and shared backup path protection (SBPP) are typical path protection methods. DBPP can be used for some extremely important traffic that need dedicated protection. SBPP allows one resource to be shared among multiple backup paths of different traffic when they failed. Most of studies have researched them, e.g. [21] [22] [23] [24]. In WDM networks, the selection of paths and allocation of wavelength resources are the major issues to be dealt with. In EONs, the wavelength allocation turns into spectrum allocation, and its complexity grows even higher due to the constraint of spectrum continuity and contiguity. Furthermore, in SDM-EON, we must consider not only the allocation of spectrum, but also the selection of cores.

For link protection, [26] proposed two algorithms named LSF-SPA and KT-SPA aimed at single link failure based on segment for multicast requests. In [25] both path protection and link protection are discussed and the numerical results indicated that, for a representative network topology, path restoration has a better restoration efficiency than link restoration, and link restoration has a faster restoration time compared with path restoration. The authors in [21] studied the shared backup path protection (SBPP) in MCF by considering inter-core crosstalk with MIMO equalization. In [22], the authors discussed DBPP and SBPP with different switching strategies which are SDM-indsw and SDM-jsw. They also studied the performance under various squeezed protection ratio. In [23], the authors provided survivability with SBPP and defined a cost function based on the shareability of frequency slots which leads to a more efficient backup resource sharing. In [24], a SBPP method based on multigraph was used to dynamically generate primary and backup paths and 100% protection ratio can be achieved. Authors in [27], have proposed a heuristic algorithm to solve dynamic RMCSA problem with shared protection scheme, which is not crosstalk-aware. In [28], authors have proposed a heuristic algorithm to solve the RMCSA problem in a large-scale scenario based on dedicated and shared path protection scheme.

Based on ring-based protection, p-cycle and ring cover are common techniques used for protection. A heuristic p-cycle algorithm called QBPCH by setting maximum length constraint was proposed in [8]. [1] selected a set of p-cycles to minimize the sum of links in order to get the highest protection efficiency. In [25], the authors adopted p-cycle for link protection, but the recovered routings had some redundancy. Authors in [29] applied ring cover protection to the mesh networks for the first time. [30] studied the robustness of link restoration algorithms using multiple ring-covers for mesh networks. Authors investigated novel approaches for establishing ring covers in optical networks with mesh topologies, while minimizing the length of the ring covers. In [31], the authors applied ring cover technique to EON, it is the first time to apply this technique to the EON. They developed an ILP model to minimize the required protection capacity and the overall link spectra used in the entire network. It is clear that a great number of papers are discussing the method of applying p-cycle to SDM-EON to provide protection,but there are fairly rare papers adopting ring cover method. To the best of our knowledge, our research applies ring cover to SDM-EON for the first time.

3. Network model

3.1 SDM-EON description

The graph of network described by $G\left ( {V,L} \right )$, $V = \left \{ {{v_1},{v_2}, \ldots ,{v_{\max }}} \right \}$ represents the nodes and $L = \left \{ {{l_1},{l_2}, \ldots ,{l_{\max }}} \right \}$ represents the links. The number of nodes and links are denoted by $\left | V \right |$ and $\left | L \right |$, respectively. Each link is composed by a MCF fiber which is represented by $C$, $C = \left \{ {{c_1},{c_2}, \ldots ,{c_{\max }}} \right \}$. There is a set of frequency slots (FSs), $F = \left \{ {{f_1},{f_2}, \ldots ,{f_{\max }}} \right \}$ in each core and $\left | F \right |$ is the number of FSs. We assume that each FS has the same bandwidth$\left ( B_{slot} \right )$. Thus, $N_{i,f}$,the number of occupied FSs of a request $r_i$, is computed with its bandwidth requirement (with BPSK) $B_i$ , the modulation level $M_i$ , and the number of guard-band slots as follows:

3.2 Physical impairment in MCF

In MCF, there exists the crosstalk which is the interference of optical power between two nearby cores [32]. Crosstalk will cause interference with the current core and then the quality of signals at the receiver side. In our network, the crosstalk only occurs when the same FSs are occupied in the neighboring cores as shown in Fig. 1.

 

Fig. 1. The crosstalk in MCF

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The crosstalk in MCF can be calculated by Eq. (2) and Eq. (3) [18].

4. Multiple backup paths and resources shared protection scheme based on ring covers

In this section, we propose a multiple backup paths and resources shared protection scheme based on ring covers. The scheme includes three parts: ring design, restore scheme and resource orchestration scheme. In the first subsection, we introduce a method to obtain a set of ring covers under several threshold values. In the next part, a rerouting scheme is put forward to restore the broken routes with multipath according to the relations among the source, destination, calculated rings, and link failures occurred. It is noteworthy that we are committed to the path protection and try the best to take full advantages of ring covers. In the last two subsections, two XT-aware distinct schemes are developed to separate spectrum resources into working area and protection area based on either cores or FSs.

4.1 Ring cover-based design

In this paper, we take NSFnet with 14 nodes and 21 links (see in Fig. 2) as an example. The distance between two different nodes is measured in kilometers. We calculate all of the rings in NSFnet by Depth First Search (DFS) and store the 139 rings into $\mathbb {C}$. Different length threshold values are set to limit the length of rings in $\mathbb {C}$, since the crosstalk in MCF is related to the distance. Our aim is to select a set of ring covers satisfying all constrains. Notations are given as below.

 

Fig. 2. NSFnet topology

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Notations:

${L}$ : The set of links in a network. ${L} = \left \{ {{l_1},{l_2}, \ldots ,{l_L}} \right \}$.

$\mathbb {C}$ : All cycles in $G(V,E)$.

$\mathbb {P}$ : An aggregate of all sets of cycles. $\mathbb {P} = \left \{ {{P_1},{P_2}, \ldots ,{P_P}} \right \}$.

${P_i}$ : The $i$-th set of cycles in $\mathbb {P}$. ${P_i} = \left \{ {{P_{i,1}},{P_{i,1}}, \ldots ,{P_{i,K}}} \right \}$.

${P_{i,k}}$ : The $k$-th cycle in the $i$-th aggregate in $\mathbb {P}$.

${d_{th}}$ : The distance threshold of a cycle. ${d_{i,k}}$ : The length of the $k$-th cycle in the $i$-th aggregate in $\mathbb {P}$.

$b_{i,k}^l$ : Represents whether the $l$ -th link can be protected by the $k$ -th cycle in the $i$ -th aggregate in $\mathbb {P}$. $b_{i,k}^l \in \left \{ {0,1,2} \right \}$, $b_{i,k}^l = 2$ if the $l$-th link is a straddling span on the k-th cycle, $b_{i,k}^l = 1$ if the $l$ -th is an on-cycle span on the $k$ -th cycle and $b_{i,k}^l = 0$ if the $l$ -th link can not be protected by the $k$ -th cycle.

$\beta _{i,k}^l$ : Represents whether the $l$-th link is an on cycle link of the $k$-th cycle in the $i$-th aggregate in $\mathbb {P}$. $\beta _{i,k}^l = 0$ if $l$-th link is an on cycle link, otherwise $\beta _{i,k}^l = 1$.

Objective:

Minimize:

Table 1. Ring covers results in NSFnet

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4.2 Rerouting scheme based on ring covers

The restoration procedure consists of two steps: one is rerouting and the other is resource assignment. We reserve proper resource to achieve better efficiency of recovery with the limitation of spectrum continuity and core continuity. The fast recovery speed is another advantage of ring cover. To take the best advantage of this point, we design a rerouting method as shown in Fig. 3.

 

Fig. 3. Rerouting scheme

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Take the example of NSFnet with ${d_{th}}$=8000km.The set of rings calculated in ring covers-based Design part is 1-2-3, 11-12-14-13, 2-3-6-5-4, 6-10-9-13-14, 1-2-4-5-7-8, and 4-5-7-8-9-12-11. The rerouting situations can be divided into four kinds:

In this algorithm, ${P_l}$ denotes the set of rings where the failed link $l$ is included and ${P_l} = \left \{ {{r_{1,l}},{r_{2,l}}, \ldots ,{r_{\left | {{P_l}} \right |,l}}} \right \}$, while ${P_n}$ denotes the set of rings where the node n is included and ${P_n} = \left \{ {{r_{1,n}},{r_{2,n}}, \ldots ,{r_{\left | {{P_n}} \right |,n}}} \right \}$. Specifically, ${P_s}$ and Pd represent the sets of rings where the source node and the destination node are located, respectively. $k$ is the number of candidate paths calculated. The main function of this algorithm is to compute multiple candidate paths for the restoration of a specific traffic request, and the shortest available path will be chosen for the allocation of resources described in the subsequent chapter. As is expressed by nested loop statements, all the positional relations of the source node, destination node and failed link, represented by the combinations of rings they are located, are taken into consideration. For each combination, according to the four scenarios described in Section 4.2, one of the four methods will be adopted for the calculation of restoring path if it fits in. At the end of the loop, a candidate path set containing k paths is obtained. Then, by sorting the paths in ascending order according to their length, shorter paths are given higher priority. Thus, the allocation of resources can be conducted afterwards based on this.

4.3 Zoning protection scheme based on cores

After selecting a protection path, available spectrum resources should be calculated and reassigned for the failed request. In this process, three constrains should be satisfied, which are spectrum continuity, spectrum contiguity and core continuity. To address this problem, we propose two kind of solutions on the basis of different zoning plans. One of them is to partition cores, and the other is to partition FSs.

From the perspective of core partition, we reserve a set of resources in the form of cores for protecting the traffics. We divided the resources into protection area, working area based on cores (P-W-C). Once a link fails, all requests passing the link are blocked. In order to restore the requests quickly, we recover these traffics by utilizing the protection area of rerouting. As Fig. 4 shows, core #1 and #2 are working area and core #3 is the protection area. $r$ with 2 FSs is routed from F to D in core #2. If the link F-E failed, the protection path F-A-C-D with 2 FSs in core #3 is used for transmission instead.

 

Fig. 4. Zoning Protection Scheme based on cores

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To get better results and reduce resources waste, we refer to [1] and divide resources into protection area, working area and hybrid area based on cores (P-W-H-C). Working area and protection area can share hybrid area, if there are no sufficient resources.

To explain the state of network resources more clearly, we define ${A_l}$ matrix of link $l$:

$\mathbb {H}$ : The set of k-shortest paths, $\mathbb {H} = \left \{ {{h_1},{h_2}, \ldots ,{h_k}} \right \}$.

${h_j}$ : The $j$-th path.

${W\_C}$ : The set of working cores, $W\_C = \left \{ {{w_1},{w_2}, \ldots ,{w_{num}}} \right \}$.

${P\_C}$ : The set of protecting cores.

$c$ : The core in ${W\_C}$ and ${R\_C}$.

$num$ : The number of working cores.

$\textrm {O}$ : A Zero Matrix.

$R\_s$ : The set of traffics which are assigned successfully.

${h_{{r_i}}}$ : The path of ${r_i}$.

$R\_r$ : The requests need to be restored.

${s_{{r_i}}}$ : The source node of ${r_i}$.

${d_{{r_i}}}$ : The destination node of ${r_i}$.

$s{p_e}$ : The cycles which can protect link $e$.

$r{t_{{r_i}}}$ : The rerouting path of ${r_i}$.

$\textrm {I}$ : A matrix that all values are 1.

Apart from those mentioned above, the order of cores should be elaborately decided because the crosstalk occurs between adjacent cores. As a concequence, how to assign the cores of working area, protection area and hybrid area has a direct impact on the final results. We number each core from 1 to 7, and define a new selection order for each core from P1-P7 as shown in Fig. 5. The normal order of cores is based on core number from small to large. The prioritized order of cores is from P1 to P7 (The core number sequence is 2-4-6-5-3-1-7) . According to prioritized order of cores, crosstalk can be avoided as far as possible. Due to the severe crosstalk caused to all the surrounding cores, Core #7 is assigned the lowest priority of use. For comparison, different algorithms are developed assigning resources in both two sequences. We named these algorithms as normal P-W-C, prior P-W-C, normal P-W-H-C and prior P-W-H-C. The prefix normal means that we select cores by the normal order of 1-2-3-4-5-6-7 while prior means we select cores by the prioritized order of 2-4-6-5-3-1-7.

 

Fig. 5. The priority order of cores

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4.4 Zoning protection scheme based on FSs

In this section, we propose the Zoning Protection Scheme from a different perspective, where FSs are separated into protection area and working area (P-W-F). As shown in Fig. 6, FS #1-#3 are working area and FS #4 -#5 are protection area. For example, a request $r$ with bandwidth requirements of 2 FSs is served by the working path F-E-D and FS #1-#2. If the link F-E fails, the protection path F-A-C-D will be used as well as the protection area FS #4-#5.

 

Fig. 6. Zoning Protection Scheme based on FSs

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Similarly, we further divide resources into protection area, working area and hybrid area based on FSs (P-W-H-F). In P-W-H-F algorithm, we firstly divide FSs into three area in a certain proportion, once a link failure happens, the connections passing through this link failed. Then the shortest backup path will be chosen and the protection FSs will be used to establish connections successfully. If there is no available FSs in protection area or working area, we can occupy hybrid area to restore the failed connections. The difference of P-W-H-F and P-W-H-C is that one is based on cores and the other on is based on frequency. However, in this algorithm, we can select the core priority as 2-4-6-5-3-1-7 since different areas do not affect each other at all. We can set priority as [18] to get better results. We name these algorithms as prior P-W-F and prior P-W-H-F.

4.5 Complexity analysis

Figure 7 shows the flow of traffics in network, we assign resources for traffics in NSFnet and get blocking probability of current network. The whole flow is divided into two steps as shown in Fig. 7. Step 1 focus on how the connections establish in network at the beginning while step 2 is the procedure of protetcion. In step 1, we generate quantities of traffics uniformly distributed with different FSs and use k-shortest algorithm to calculate routings for each request. Matrix ${A_{{r_i}}}$ should be caculated to assign spatial and spectrum resources.Then we compute the crosstalk and estimate whether the traffic can be received successfully. In step 2, in order to test the efficiency of our algorithm, we set a failed link, traffics traversed the failed link will be blocked. we first select a set of ring covers as Section.4.1. We simulate the link failure of NSFnet and judge which traffic in $R_s$ passes by specified link to classify different rerouting situations and calculate the multiple backup paths as Section.4.2. Then the shortest backup path and backup resources will be selected as a backup path. ${A_{r{t_{{r_i}}}}}$ is used to calculate current status and assign new resources in protection domain or hybrid domain. At last, we judge whether reassigned traffics will be blocked.

 

Fig. 7. The flowchart of our scheme

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The problem is a NP-hard problem. We analyze complexity based on Fig.4. In step 1, for each request, We use k-shortest algorithm whose time complexity is $\textrm {O}(\left | E \right | + k\left | V \right |\log \left | V \right |)$ where $\left | E \right |$ means the number of links, $\left | V \right |$ means the number of nodes and k means the number of shortest paths. The procedure of resources will bring a time complexity of $\textrm {{O}}(\left | H \right | \cdot \left | {W\_C} \right | \cdot \left | {W\_F} \right |)$ where $\left | H \right |$ represents the number of links of the working path, $\left | {W\_C} \right |$ represents the number of working cores and $\left | {W\_F} \right |$ means the number of working FSs in one core. Therefore, the worst complexity of step 1 is $\textrm {{O}}(\left | E \right | + k\left | V \right |\log \left | V \right | + k\left | H \right | \cdot \left | {W\_C} \right | \cdot \left | {W\_F} \right |)$. In step 2, the complexity of selecting backup path is $\textrm {O}(\left | E \right | \cdot \left | {R\_r} \right |)$. The time complexity is $\textrm {O}\left ( {\left | {r{t_{{r_i}}}} \right | \cdot \left | H \right | \cdot \left | {P\_C} \right | \cdot \left | {P\_F} \right |} \right )$ for each request in $R\_r$. ${\left | {r{t_{{r_i}}}} \right |}$ means the number of protect paths.The computational complexity of our scheme is expressed by $\rm {O}(\left | R \right | \cdot \left ( {\left | E \right | + k\left | V \right |\log \left | V \right | + k\left | H \right | \cdot \left | {W\_C} \right | \cdot \left | {W\_F} \right |} \right ) + \left | E \right | \cdot \left | {R\_r} \right | \cdot \left ( {\left | {r{t_{{r_i}}}} \right | \cdot \left | H \right | \cdot \left | {P\_C} \right | \cdot \left | {P\_F} \right |} \right ))$.

5. Performance evaluation

To demonstrate the effectiveness and efficiency of the proposed algorithm, several simulations are conducted, and the results are presented in this section.

5.1 Simulation setup and scenarios

The performance of proposed algorithm is evaluated over NSFnet topology with 14 nodes and 21 links. The topology is shown in Fig. 2. The numbers between nodes in the topology are the lengths of physical links (measured in kilometer). We assume each link has 320 FSs, and the spectral width of each slot is 12.5 GHz. The requirement of transmission capacity of each link is uniformly distributed among 50, 100, 200 and 400 GHz and the modulation format is BPSK. All source and destination pairs are uniformly distributed throughout the network. The other parameters can be found in Table 2.

Table 2. Parameters setting

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5.2 Simulation results and analysis

In this Section, we show the results of our scheme. We set the scenario as a static scenario and the traffic numbers as 1000. We assume each link of NSFnet fails in sequence. Each procedure executes 100 loops to calculate a mean value.

Figure 8(a)-(c) show the success ratio of each link in normal P-W-C when the distance threshold is set to be 8000km, we define success ratio as the number of traffics which can be received successfully divided by total number of traffics. The numbers of working cores are 4, 5 and 6, while the corresponding numbers of protection cores are 3, 2 and 1. The link index represents the failed link in Fig.3. We can get the conclusion from the three pictures that the success ratio increased with the number of working core counts, this is because that the number of traffics is set to 1000 which exceeds current network capacity. The initial success ratios of the three cases shown in Fig. 8 are 67.7%, 76.1% and 82.7%. When the link failure occurred, the link failed state line declined compared with initial state. And after protection based on ring-covers, part of the traffic recovered from the failed state. Some links can even recover original status. Thus it can be seen that our scheme works.

 

Fig. 8. (a) working core=4, protection core=3 (b) working core=5, protection core=2 (c) working core=6, protection core=1

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Figure 9(a) (d) show the success ratio of different traffic numbers from 300 to 1000 in prior P-W-C and normal P-W-C when the distance threshold is set to be 8000km, 9000km, 11000km and 12000km respectively, The number of working cores is 5 while the number of protection cores is 2. We can see from the two pictures that prior P-W-C performs better on initial state line for the reason that crosstalk decreased.However, after the protection measures are taken to recover the failed requests, it is hard to tell which one gets better results. The improvement achieved from the latter approach is trivial if any. Fig.9 (b) (e) show the success ratio of different traffic numbers from 300 to 1000 in prior P-W-H-C and normal P-W-H-C when the distance threshold is set to be 8000km, 9000km, 11000km and 12000km respectively. The number of working cores, protection cores and hybrid cores are 4, 2, 1 respectively. Fig.9 (c) (f) show the success ratio of different traffic numbers from 300 to 1000 in prior P-W-H-C and normal P-W-H-C which the distance threshold is set 8000km, 9000km, 11000km and 12000km respectively, the number of working cores, protection cores and hybrid cores is 5, 1, 1 respectively. As shown in Fig.9 (a)-(f), when ${d_{th}}$ is set to 9000km in P-W-C and P-W-H-C we can get the best result. The performance of line 12000 is the worst at low traffic loads, when the traffic loads increase, its success ratio is the second only to line 9000. Fig.9 (a)-(c) and Fig.9(d)-(f) present the performance of different schemes. On the whole, prior P-W-H-C performs better than the normal scheme. The prioritized selection of cores helps a little bit (approximately 0.2% increase of the success ratio) .

 

Fig. 9. P-W-C and P-W-H-C algorithms

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Figure 10(a) (b) show the success ratio of different traffic numbers from 300 to 1000 in P-W-F when the distance threshold is set to be 8000km, 9000km, 11000km and 12000km respectively. The numbers of working cores are 5 and 6, and those of protection cores are 2 and 1. Fig.10 (c) (d) show the success ratio of different traffic numbers from 300 to 1000 in P-W-H-F when the distance threshold is set to be 8000km, 9000km, 11000km and 12000km respectively. The numbers of working cores, protection cores and the hybrid cores are 4,2,1 or 5,1,1. On the whole, P-W-H-F performs the best among four of them and the hybrid scheme is always better than the other whether in P-W-C or P-W-F. Nevertheless, the blocking ratio of P-W-C is much lower than P-W-F. Figure 11 presents the results of success ratio of dedicated backup path protection and our scheme. In order to improve the accuracy of simulation results, the simulation setup of DPP is same with our scheme. The transmission capacity of requests is uniformly distributed among 50, 100, 200 and 400 GHz and k-shortest algorithm is adopted for backup paths. From Fig.11, we can observe that our scheme performs better than the DPP. When the traffic numbers is set to 600, our scheme is much better than DPP. The effect will be weaker in large-scale instances, because the resources are hard to satisfy all of the traffics.

 

Fig. 10. P-W-F and P-W-H-F algorithms

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Fig. 11. Compared with DPP algorithm

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6. Conclusion

In this paper, we propose a traffic protection scheme for single link failure from the perspective of the robustness of the entire network. This protection method uses ring cover to find multi backup path and shared resources to improve resource utilization for MCF- EON. In order to avoid huge extra costs, our algorithm satisfies the constraints of spectrum continuity, spectrum contiguity and core contiguity. Since our optimization method focuses on link protection and ring cover, it is not affected by traffic distribution and has certain advantages in time delay and deployment cost. In static network simulation, the proposed protection algorithm is evaluated according to the defined success ratio. We observe that prior P-W-H-C has a better performance compared to P-W-C and normal P-W-H-C, although the blocking probability of it is only 2% less than normal P-W-H-C. Besides, all the P-W-H-F algorithms have a common feature that they perform worse than their corresponding protection schemes based on cores. Remarkably, prior P-W-H-C can restore 72.8% of the traffic when the traffic number is set to 1000 and has the highest success ratio of 81% among proposed algorithms. Compared with traditional SBPP algorithm, it is clear that our algorithms have better performance. For practicality, we will study the application of proposed algorithms in dynamic networks in the future.