Fragmentation and ISRS-Aware Survivable Routing, Band, Modulation, and Spectrum Allocation Algorithm in Multi-Band Elastic Optical Networks

Abstract

The C+L band elastic optical networks (C+L-EONs) increase the network capacity significantly. However, the introduction of an L band enhances the inter-channel stimulated Raman scattering effect (ISRS), consequently deteriorating the quality of transmission (QoT) of the signal. Furthermore, spectrum allocation leads to spectrum fragmentation inevitably, which escalates the bandwidth blocking rate. In addition, in C+L-EONs, a single fiber carries more services, and once one of the links fails, a huge number of requests will be interrupted, resulting in huge economic losses. Therefore, this paper proposes a survivability routing, band, modulation, and spectrum allocation (RBMSA) algorithm that effectively guarantees service survivability and reduces the impact of ISRS and spectrum fragmentation. The algorithm employs shared backup path protection and a band partitioning method, whereby the spectrum resource of the primary path is assigned in the L band and the backup path is assigned in the C band in order to minimize the impact of ISRS on the QoT of the request while ensuring the survivability of the network. Furthermore, a fragmentation metric accounting for both the free and shared spectrum resource is proposed to mitigate both free and shared spectrum fragmentation. The simulation results reveal that the proposed RBMSA algorithm reduces the bandwidth blocking probability (BBP) and the fragmentation rate (FR) by 47.7% and 21.3%, respectively, and improves the optical signal-to-noise ratio (OSNR) by 4.17 dB in NSFNET. In COST239, the BBP, FR, and OSNR are 22.1%, 21.5%, and 4.71 dB, respectively.

1. Introduction

In recent years, the escalating demand for traffic on transport networks, including the 5th mobile communication technology, cloud computing, and the interconnection of data centers, has triggered a continuous increase in the requirement for data traffic in transmission networks [1]. Elastic optical networks (EONs) divide the wavelength into finer frequency slots (FSs). This greatly improves the spectrum utilization efficiency and enhances the transmission capacity of the network [2]. However, the existing transmission capacity of the network remains inadequate to satisfy the escalating traffic demand, hindered by the nonlinear Shannon limit of single-mode fibers (SSMF). Band division multiplexing (BDM) offers a promising mid-term solution by broadening the available spectrum range to tens of THz through the utilization of multiple bands within already deployed optical fibers. Furthermore, C+L-EONs have the potential to expand the transmission bands from the C band to the C+L bands on existing SSMF despite the need for novel network components such as transceivers and amplifiers to cater to the demands beyond the C band [3]. Consequently, this paper focuses on the scenario of C+L-EONs.

The inter-channel stimulated Raman scattering (ISRS) effect, a nonlinear phenomenon, becomes increasingly significant, resulting in the transfer of power from higher to lower frequency components within the same optical spectrum [4]. Consequently, it is crucial to take into account the nonlinear impairments (NLI) experienced by the signal in C+L-EONs. Furthermore, the addition of a band dimension in the network necessitates the advancement of routing, modulation, and spectrum allocation considerations into a more comprehensive RBMSA problem.

Furthermore, spectrum fragmentation poses a significant challenge in the resource allocation process of C+L-EONs [5]. When a request arrives in the network, it requires not only the selection of an appropriate path based on its source and destination nodes but also the allocation of a contiguous spectrum according to its bandwidth demand [6]. Three constraints must be met during spectrum allocation: spectrum continuity, adjacency, and non-overlap. Specifically, within the transmission optical path, consecutive FSs must be utilized on each link. However, the dynamic and random arrival and departure of requests cause optical paths to be established and released dynamically, leading to the emergence of unusable free FSs known as spectrum fragmentation in the links [7]. This fragmentation not only reduces spectrum utilization in the network but also elevates the network blocking rate. Therefore, it is crucial to consider spectrum fragmentation during the spectrum allocation process.

On the other hand, in large-scale networks, there is the problem of a request interruption due to fiber failure [8]. In large-capacity networks, the failure of a single fiber can interrupt multiple established requests, resulting in huge economic losses. Therefore, it is necessary to study a survivability-based resource allocation algorithm for C+L-EONs. Common network survivability assurance methods are protection and recovery algorithms. Compared to recovery, protection takes less time and can efficiently ensure network survivability. This paper adopts the protection algorithm to ensure network survivability. Typical protection algorithms are dedicated path protection (DPP) and shared backup path protection (SBPP) [9]. DPP allocates a dedicated backup path for each primary path. While this protection mechanism offers faster fault recovery times, it consumes more network resources, potentially leading to lower resource utilization. For SBPP, the backup resource in the primary paths where the links do not intersect can be shared, which reduces resource redundancy [10]. Therefore, to optimize resource utilization and efficiency, SBPP is used to guarantee the network survivability in this paper.

In summary, we propose a survivable RBMSA algorithm in C+L-EONs, which considers the fragmentation and ISRS issues comprehensively. The following are the main points of this article:

First, the band partitioning method is adopted, which allocates the primary path resource in the L band and backup path resource in the C band. The method reduces the ISRS impact by ensuring that the lightpaths do not establish in the C band before network failures.

Second, a path weight metric that considers the idle fragmentation within a link is proposed in the primary path selection phase, while a path weight metric that jointly considers the idle fragmentation and the shareable fragmentation within a link is proposed in the alternate path selection phase. The proposed path weight metric can select less fragmented paths for requests as much as possible in order to maximize the use of the spectrum resources of each link and thus successfully establish optical paths for more requests.

Third, in the spectrum allocation phase, two fragmentation metrics are proposed, one focusing on idle fragments within the primary path and the other jointly considering idle and shareable fragments within the alternate path. Among them, the fragmentation metric that jointly considers idle fragments and shareable fragments in the alternate path extends the scope of the spectrum fragmentation metric, which can reserve more consecutively available FSs for subsequent requests; further reduces the ISRS impact of the requests in the C band on the requests in the L band during the occurrence of faults; and guarantees the QoT of the requests.

The following parts of the study are structured as follows. In Section 2, we provide a comprehensive review of the pertinent paper pertaining to C+L-EONs. Section 3 introduces the system model and quality of transmission (QoT) estimation framework for the C+L bands. Subsequently, in Section 4, we expound upon the fundamental principles underlying the proposed algorithm. Section 5 offers a comprehensive evaluation and in-depth analysis of the performance characteristics of the proposed algorithmic approach. Subsequently, Section 6 consolidates the key conclusions derived from this investigative study.

2. Related Works

The C+L-EONs have gained popularity due to the significant surge in network traffic. The related work is summarized in three aspects: (1) ISRS-based QoT estimation, (2) spectrum fragmentation awareness, and (3) network survivability.

Exploring the impact of ISRS on QoT estimation is a crucial research issue in C+L-EONs. Several studies focused on the QoT estimation under the influence of NLI jointly with the ISRS, and they demonstrated the significant role played by transmission power and ISRS in multi-band (MB) systems [11,12,13]. D’ Amico et al. [14] comprehensively consider the ISRS, self-phase modulation (SPM), cross-phase modulation (XPM), and amplified spontaneous emission (ASE) noise in the QoT estimation process and establish the optical signal-to-noise ratio (OSNR) measurement model. The authors investigate the influence of various modulation formats on the QoT assessment process within the MB system and propose assessment methods that consider modulation formats dependently [15,16]. Venda et al. [17] demonstrate that as network load and resource utilization increase, the accuracy of the Gaussian noise (GN), and generalized Gaussian noise (GGN) models decreases. Utilizing a triangular approximation of the Raman gain, Lasagn et al. [18] develop an enhanced Christodoulides-Zirngibl (ECZ) SRS model and apply it within the GN model framework. The findings reveal that OSNR can serve as a primary QoT parameter for accurate assessment. Then, Shen et al. [19] address the physical layer impairment issue in multi-band elastic optical networks from the perspectives of routing selection and spectrum allocation, proposing a resource allocation algorithm for impairment reduction. The results demonstrate that, compared to other studies, this work effectively alleviates the impact of physical layer impairments on signal transmission quality. The aforementioned work only takes into account the impact of physical layer impairments on signal quality in the network without addressing the spectrum fragmentation and the network survivability issue.

Spectrum fragmentation-aware algorithms have been extensively studied in recent years. Luo et al. [20] propose an impairment and fragmentation-aware dynamic resource allocation algorithm for C+L-EONs using Q-learning, which integrates the effects of network fragmentation and link availability. Ravipudi et al. [21] apply a machine learning approach to propose a preventive fragmentation sorting method for C+L-EONs. This not only dramatically improves the network resource utilization but also ensures the QoT of the request. Jana et al. [22] consider the spectrum fragmentation issue and the survivability issue in EONs simultaneously and adopt a path-switching defragmentation scheme, which realizes the route redirection of the backup path by reallocating the backup path FSs. The results show that the scheme can improve network resource utilization while ensuring network survivability.

In terms of network survivability, Chatterjee et al. [23] consider the physical layer impairments suffered by the primary and backup paths of requests before and after network failures in EONs and propose a highly robust resource allocation algorithm to guarantee the QoT on the primary and backup paths of requests. In [24], the MB-space division multiplexing (SDM)-EONs scenario is explored, and a band division protection scheme is proposed to enhance OSNR by assigning resources for both primary and backup paths to distinct bands. To mitigate physical layer impairments and enhance the SNR, a band partitioning protection scheme is proposed, allocating resources for the primary and backup paths to distinct bands. Chebolu et al. [25] consider the survivability issue and the spectrum fragmentation problem in the SDM-EONs jointly and design a fragmentation-aware fragmentation metric to reduce network fragmentation. In addition, a routing strategy utilizing multipath routing is introduced to guarantee the survivability requirements of requests. Liu et al. [26] proposed a highly robust SBPP algorithm. This algorithm effectively mitigates physical layer impairments in the network by allocating primary path resources to the L band and backup path resources to the C band. The results demonstrate notable improvements in BBP and OSNR through the implementation of this algorithm.

It should be noted from the above literature that existing studies in C+L-EONs mainly focus on spectrum fragmentation, ISRS-based QoT estimation, and network survivability. However, the spectrum fragmentation issue limits the spectrum resource usage efficiently. Moreover, the influence of ISRS becomes more significant in C+L-EONs, further limiting the potential capacity improvement of C+L-EONs. Additionally, network survivability should be taken into account, as link failures can result in significant economic losses due to the interruption of numerous services. Therefore, we comprehensively consider the effect of spectrum fragmentation and ISRS impact on resource allocation based on the network survivability, and we proposed the ISRS- and fragmentation-aware survivable RBMSA algorithm to ensure the network survivability, increase the spectrum fragmentation, and mitigate the ISRS impact of requests.

3. System Model and QoT Estimation

This part centers on the network model of C+L-EONs, including the method for calculating the weight of each link, selecting request modulation formats, and estimating physical layer impairments.

3.1. Network Model

In the literature, the network topology is denoted using G(V,E), where V = {v₁, v₂, …, v_end} represents the collection of nodes and E = {e₁, e₂, …, e_end} denotes the collection of network links, each of which can satisfy bi-directional transmission requests. F_c = {f_c1, f_c2, …, f_{c_end}} denotes the collection of FSs in C band, and F_l = {f_l1, f_l2, …, f_{l_end}} denotes the collection of FSs in L band. Each FS has a bandwidth of 12.5 GHz. The requests are all unknown before arriving network, their arrival and duration obey the Poisson and negative exponential distribution, respectively. Each request r is defined as r(r_s, r_d, r_b, t_s, t_h), where r_s denotes the source node of the request, r_d denotes the destination node of the request, r_b denotes the bandwidth requirement of the request, t_s represents the request arriving time, and t_h represents the request holding time. For each request, the quantity of necessary frequency slots is dictated by the chosen modulation format and OSNR.

3.2. Link Weight Calculation Method

3.2.1. Primary Path Link Selection Method

The dynamic arrival and departure of requests as well as the three constraints that need to be satisfied for the resource allocation process lead to spectrum fragmentation. The high susceptibility of links to spectrum fragmentation significantly impacts the blocking rate of the network. Therefore, the spectrum fragmentation on different links should be taken into account when selecting links for requests. The fragmentation of the spectrum on the primary path can be determined by Equations (1) and (2).

$$F_{P,primary}={\displaystyle \sum _{l_{primary}\in P_{primary}}{F}_{l,primary}},$$

(1)

$$F_{l,primary}=({\displaystyle \sum _{i=1}^n{f}_i})\cdot \sqrt{{\displaystyle \sum _{i=1}^n{f}_i}}\cdot \frac{{\displaystyle \sum _{i=1}^n（f_i\cdot \sqrt{f_i}}）}{n},$$

(2)

where n denotes all of the available blocks of the current request, f_i denotes the free FSs in the ith available blocks, l_primary represents the link in primary path, F_l,primary indicates the level of fragmentation on the primary path link l, and F_P,primary represents the degree of fragmentation of the chosen primary path. The smaller n is, the more closely the free spectrum blocks on the link are distributed, and the larger f_i is, the more available FSs the free frequency blocks on the link contain. Therefore, a higher value of F_l,primary means that in this link, there are fewer blocks of free spectrum within the link and a greater concentration of available spectrum resources, and the degree of fragmentation is smaller for the current service. It can better meet the needs of the arriving service requests.

3.2.2. Backup Path Link Selection Method

To minimize the redundancy of a network resource, we used the SBPP scheme [10] to allocate backup resource for requests. In addition, spectrum fragmentation is further considered in the backup path link selection process. Equations (3) and (4) calculate the spectrum fragmentation of the backup path.

$$F_{P,backup}={\displaystyle \sum _{l_{backup}\in P_{backup}}{F}_{l,backup}},$$

(3)

$$F_{l,backup}=({\displaystyle \sum _{i=1}^n{f}_i})\cdot \sqrt{{\displaystyle \sum _{i=1}^n{f}_i}}\cdot \frac{{\displaystyle \sum _{i=1}^n（f_i\cdot \sqrt{f_i}）}}{n}+({\displaystyle \sum _{p=1}^m{s}_p})\cdot \sqrt{{\displaystyle \sum _{p=1}^m{s}_p}}\cdot \frac{{\displaystyle \sum _{p=1}^m（s_p\cdot \sqrt{s_p}}）}{m},$$

(4)

where f_i denotes the number of free FSs in the ith available block, s_p stands for the number of shareable FSs in the pth shareable spectrum block for r, m represents the total count of available shareable blocks, l_backup represents the link in backup path, F_l,backup quantifies the spectrum fragmentation on the backup path link l, and F_P,backup measures the fragmentation level of the selected backup path. A larger s_p means that the number of frequency slots contained in the shareable frequency blocks is greater, and a smaller m means that the shareable frequency blocks are more densely distributed. Therefore, the higher the F_l,backup value, the more free and shareable spectrum resources are available to the link and the less free and shareable fragmentation there are for the current service.

Figure 1 illustrates the process of selecting the primary and backup paths for the request. As shown in Figure 1, we assumed that the FSs of request was 2, with nodes A and D serving as the source and destination, respectively. From Equations (1) and (2), we calculated that the primary path weights of P1, P2, and P3 are 16, 52.9, and 125, respectively. Therefore, path P3 was selected as the primary path of request. According to the principle of link disjointness, P1 and P2 can be selected as alternative backup paths; then, according to Equations (3) and (4), the backup path weights of P1 and P2 were 126 and 107, respectively. Therefore, path P1 was selected as the request alternate path.

3.3. Modulation Format Selection

For each dynamically arriving request, a suitable modulation format can be selected for it based on the length of its selected path using distance adaptive modulation, which can be calculated by Equation (5).

$$RF{S}_s=[\frac{r_b}{M\cdot Slot}]+Gb,$$

(5)

where M represents the modulation level associated with a given request r, while RFS_s represents the FSs allocated to that request. The paper took into account four modulation formats: binary phase-shift keying (BPSK), quadrature phase-shift keying (QPSK), 8-QAM, and 16-QAM, and their corresponding modulation levels were as follows: M = {1, 2, 3, 4}. The modulation format selected by a request was determined by the distance between its selected paths. The slot denotes the optical network channel capacity whose size is 12.5 GHz. Gb denotes the guarded bandwidth between the neighbor lightpaths. The correlation between modulation format and transmission distance are summarized in paper [19].

3.4. Physical-Layer Impairments Estimation

In C+L-EONs, the deployment and maintenance of Raman amplification across all links bring significant challenges. Therefore, for long-haul transmission, the optical signals in both C and L bands are amplified solely by EDFA. Given the distinct characteristics of these bands, it was necessary to configure different parameters for EDFA in each band. Additionally, we employed the generalized GN model, as described in [21], to accurately assess the OSNR. This model comprehensively considers various factors, including ISRS, ASE noise, SPM, and XPM. Consequently, the OSNR of a given request, designated as r, can be accurately determined by Equation (6).

$$OSN{R}_r=\frac{P_r}{{\sigma }_{\mathrm{ASE}}^2(f_r)+{\sigma }_{\mathrm{NLI}}^2(f_r)},$$

(6)

The transmit power of request r is denoted as P_r. The ASE noise variance is represented as ${\sigma }_{\mathrm{ASE}}^2$(f_r), which can be determined through Equation (7). Furthermore, the NLI variance is designated as ${\sigma }_{\mathrm{NLI}}^2$(f_r) and can be calculated by Equation (8). These parameters play a crucial role in accurately assessing the performance of the system.

$${\sigma }_{\mathrm{ASE}}^2(f_r)=2n_{sp}\mathrm{h}{f}_r{B}_r(\alpha L-1),$$

(7)

$${\sigma }_{\mathrm{NLI}}^2(f_r)={\sigma }_{\mathrm{SPM}}^2(f_r)+{\sigma }_{\mathrm{XPM}}^2(f_r),$$

(8)

The spontaneous emission noise on EDFA is denoted as n_sp, while h signifies Planck’s constant, and α denotes the attenuation coefficient of the fiber. The SPM and XPM variances are designated as ${\sigma }_{\mathrm{SPM}}^2$(f_r) and ${\sigma }_{\mathrm{XPM}}^2$(f_r), respectively, and they can be computed by Equations (9) and (10).

$$\begin{array}{l}{\sigma }_{\mathrm{SPM}}^2(f_r)=\frac{4}{27}N\frac{P_r^3}{B_r^2}\frac{{\gamma }_{r,r}^2\pi }{{\varphi }_r{\alpha }^2}{e}^{2C_r\overline{k}{L}_{eff}(L)f_r}\\ [\frac{{(2\alpha -C_r{f}_r)}^2-{\alpha }^2}{\alpha }\arcsin \mathrm{h}(\frac{{\varphi }_r{B_r}^2}{\alpha \pi })+\\ \frac{4{\alpha }^2-{(2\alpha -C_r{f}_r)}^2}{2\alpha }\arcsin \mathrm{h}(\frac{{\varphi }_r{B_r}^2}{2\alpha \pi })]\end{array},$$

(9)

$$\begin{array}{l}{\sigma }_{\mathrm{XPM}}^2(f_r)=\frac{32}{81}{P}_{r}N{\displaystyle \sum _{k=1,k\ne r}^{N_{s,l}}\frac{P_k^2}{B_k}\frac{{\gamma }_{r,k}^2}{{\varphi }_{r,k}{a}^2}{e}^{2C_r\overline{k}{L}_{eff}(L)f_k}}\\ [\frac{{(2\alpha -C_r{f}_k)}^2-{\alpha }^2}{\alpha }\arctan (\frac{{\varphi }_{r,k}{B}_r}{\alpha })+\\ \frac{4{\alpha }^2-{(2\alpha -C_r{f}_k)}^2}{2\alpha }\arctan (\frac{{\varphi }_{r,k}{B}_r}{2\alpha })]\end{array},$$

(10)

In Equations (9) and (10), the variable N represents the total number of spans within the system. P_r denotes the transmit power associated with request r. γ_r,r denotes the nonlinear coefficient on the fiber. Furthermore, C_r signifies the linear regression slope pertaining to the normalized Raman gain spectrum. N_s,l denotes the count of requests present in link l, excluding request r. The request transmit power within link l is represented by P_k. The required bandwidth of request is denoted as B_k. f_k represents the request center frequency. The effective length L_eff(L), nonlinear coefficient γ_r,k, phase rotation Φ_r, and cross-phase modulation Φ_r,k can be calculated by Equations (11)–(14), respectively.

$$L_{eff}(L)=\frac{1-e^{-\alpha L}}{\alpha },$$

(11)

$${\gamma }_{r,k}=\frac{2\pi }{{\lambda }_r}\frac{2n_2}{A_{eff}({\lambda }_r)+A_{eff}({\lambda }_k)},$$

(12)

$${\varphi }_r=\frac{2}{3}{\pi }^2({\beta }_2+2\pi {\beta }_3{f}_r),$$

(13)

$${\varphi }_{r,k}=2{\pi }^2(f_k-f_r)[{\beta }_2+\pi {\beta }_3(f_k+f_r)],$$

(14)

where λ_r represents the wavelength associated with request r. The nonlinear refractive index of the fiber is denoted as n₂. The effective areas of the fiber at wavelengths λ_r and λ_k are designated as A_eff(λ_r) and A_eff(λ_k), respectively. β₂ corresponds to the parameter pertaining to group velocity dispersion (GVD), while β₃ represents the linear slope of GVD. These parameters play a crucial role in accurately characterizing the nonlinear effects and dispersion properties of the optical fiber within the system.

4. Fragmentation and ISRS-Aware Survivable RBMSA Algorithm

In this section, we propose the fragmentation and ISRS-aware survivable RBMSA (FISRSA-S RBMSA) algorithm. The proposed algorithm ensures end-to-end QoT in fault-free or single-link failure scenarios while improving spectrum resource utilization efficiency and reducing the bandwidth blocking rate.

The pseudocode of our proposed algorithm is given in Algorithm 1. When requests arrive in the network, they should be assigned primary and backup path resources based on their source and destination nodes, bandwidth, and other requirements. For the primary path, Equation (15) is used to calculate congestion weights for links to minimize the interference between requests.

$$W_C=\frac{F_{used}}{F_{total}}.$$

(15)

The link weight is set based on the resource occupancy situation of the link, where W_C represents the congestion level of the link. F_total and F_used represent the total and occupied FSs within the L band on the link. Then, k paths are found for requests using minimum congestion routing according to the W_C, which in turn reduces the interference between requests effectively. The spectrum fragmentation of k paths can be calculated by Equation (1). The k paths are ascended based on the degree of spectrum fragmentation. The path that has the least spectrum fragmentation is selected to allocate resources for the request. Finally, we need to choose a spectrum block that has minimum impact on subsequent requests from all free spectrum blocks. Equation (16) is used to calculate the impact on subsequent requests after the free block is occupied.

$$F_{free}={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{k=1}^a\frac{(f_i-f_r)\cdot \sqrt{f_i-f_r}}{f_k\cdot \sqrt{f_k}+1}}},$$

(16)

where F_free represents the impact on subsequent requests after the spectrum block is occupied, f_r denotes the quantity of FSs necessitated by the present request r, k represents the number of spectrum blocks which is partitioned after allocation of requests, and f_k denotes the number of FSs in each partition. The spectrum block that has the least impact on the subsequent request are calculated according to the relationship between the current request demand and the free spectrum blocks. Then, the OSNR of these spectrum blocks are calculated according to Equation (4). If there is more than one spectrum block that meets OSNR demand of the request, then first fit (FF) [27] is used to allocate spectrum resources. Also, if the path cannot find the free spectrum blocks, the next alternate path is selected until all the paths have been traversed. After finding the free spectrum resource for the request in the primary path, the disjoint links [10] are selected for backup paths. Equation (17) is used to calculate the shareability of links.

$$W_{Share}=\frac{N_{sharable}}{N_C},$$

(17)

where W_Share represents the shareability of links, N_c represents the total number of FSs in C band on link l, and N_sharable represents the total number of FSs in C band on link l that can be shared by the current request. k paths with maximum shareability are selected for the request. Then, the fragmentation of all the alternate backup paths is calculated according to Equation (18). F_shareable represents the fragmentation degree of the backup path. p denotes the pth sharable spectrum block in link l. The alternate backup paths are ranked according to the fragmentation degree, and the path with the least fragmentation degree is selected. Based on a distance-adaptive modulation format, the suitable modulation format is chosen for the requests. It should be noted that the 1 of Equations (17) and (18) is intended to avoid a denominator of 0 if there are no blocks of free spectrum in the selected link to satisfy the demand for the requested FSs.

Algorithm 1: Fragmentation and ISRS-aware survivable RBMSA algorithm
Input: G(V,E), request r(rs,rd,rb,ts,th), transmit power Pr.
Output: The result of RBMSA.
1:	Calculate link weight WC for each link according to Equation (15)
2:	Select the alternative route pr according to the larger link weight, and save pr to alternative set Pr
3:	for each alternative pr ∈ Pr do
4:	Calculate the route fragmentation ratio FP,primary for pr according to Equations (1) and (2)
5:	Sort pr in descending order of FP,primary
6:	for each free FS in pr do
7:	Search the contiguity free FSs that meet request r
8:	Calculate the fragmentation ratio Ffree of pr according to Equation (16)
9:	If sufficient FSs exist then
10:	Calculate the OSNRr for request r according to the Equations (6)–(14)
11:	If OSNRr > OSNRm then
12:	Establish the lightpath
13:	End if
14:	Else
15:	Block r
16:	End if
17:	End for
18:	End for
19:	Delete all links according to the primary path
20:	Calculate link weight WShare for each link according to Equation (17)
21:	Select the alternative route pb according to the larger link weight, and save pr to alternative set Pb
22:	For each alternative pb ∈ Pb do
23:	Calculate the route fragmentation ratio FP,backup for pb according to Equations (3) and (4)
24:	Sort pb in descending order of route fragmentation ratio
25:	For each free FS in pr do
26:	Identify free spectrum blocks based on the given rb
27:	Calculate the fragmentation ratio Fshareable of pb according to Equation (18)
28:	If there are sufficient FSs then
29:	Calculate the OSNRr for request r according to the Equations (6)–(14)
30:	If OSNRr > OSNRm then
31:	Establish the lightpath
32:	End if
33:	Else
34:	Block r
35:	End if
36:	End for
37:	End for

$$F_{shareable}={\displaystyle \sum _{p=1}^m{\displaystyle \sum _{k=1}^a\frac{(s_p+f_{nei}-f_i)\cdot \sqrt{s_p+f_{nei}-f_i}}{f_k\cdot \sqrt{f_k}+1}}}+{\displaystyle \sum _{p=1}^m{\displaystyle \sum _{k=1}^a\frac{(s_p-f_i)\cdot \sqrt{s_p-f_i}}{f_k\cdot \sqrt{f_k}+1}}}.$$

(18)

Finally, the FSs on the path are evaluated by Equation (1), the FSs that have the least impact on the subsequent requests are identified, and the OSNR of these spectrum resources are calculated by Equation (4). If there are more than one FSs that satisfy the OSNR threshold, then the last fit (LF) method is used to select the FSs for the request, and the next alternate path is selected if no FSs can be found in this path until all alternate paths have been traversed. If multiple FSs meet the OSNR threshold, the LF is adopted.

The time complexity of the proposed algorithm is summarized as follows: For the routing calculation, a complex algorithm utilizing link weights is utilized, and its time complexity can be represented by O(|K||V||E| + |E||N_l| + |E|²|N_l|²), where |K| represents the number of the alternative paths. |E| and |V| represent the number of nodes and links in the network, respectively. |N_l| denotes the number of FSs in the L band. The time complexity of backup route selection can be represented by O(|K||V||E|² + |E|²|N_c|²), where |N_c| represents the number of total FSs in the C band. Therefore, the time complexity of the algorithm is O(|K||V||E| + |E||N_l| + |E|²|N_l|² + |K||V||E|² + |E|²|N_c|²).

5. Simulation Results and Analysis

In this section, we present the performance evaluation of the proposed FISRSA-S RBMSA algorithm within a dynamic traffic scenario. We use PyCharm as a dedicated Python-integrated development environment for the implementation. The simulations are performed on a PC with a 3.2 GHz Intel Core i9 and 16GB RAM. In our previous work [26], we have confirmed that by allocating primary and backup paths to different bands, it alleviates physical layer impairments in the network, thereby ensuring the OSNR of signals while guaranteeing the survivability of services. Building upon this, our current study additionally takes into account the spectrum fragmentation issue during the resource allocation process. In comparing algorithmic fragmentation metric schemes, we choose the classical entropy-based fragmentation metric (EFM) [21]. Furthermore, we compare the impact of DDP [9] and SBPP [10] algorithms on network resource utilization. To further validate the efficacy of the algorithm, we also introduce a comparative algorithm where the primary path is allocated to the C band and the backup path is allocated to the L band. Our analysis focuses on two distinct network topologies: the NSFNET network [28] and the COST239 network [29]. All links within these networks are bidirectional and constructed using SSMF. As depicted in Figure 2, the numerical value adjacent to each link represents its length. A single FS serves as a guard band, separating individual requests [30]. The total FS of the C band is 358, while the L band is 558 [31]. It is assumed that the arrival process λ adheres to the Poisson process, and the holding time μ of each request follows a negative exponential distribution [32]. The range of the data rate for each request is 20–100 Gb/s, which follows uniform distribution. For each request, we compute K = 3 primary paths, and for each primary path, K_b = 3 backup paths (disjoint from the primary path) are determined. Additionally, other pertinent physical parameters are concisely summarized in paper [33].

5.1. Performance of Bandwidth Blocking Probability and Resource Utilization

In this section, we evaluate the performance of our proposed algorithm in terms of BBP and RU. These metrics can calculated as given in Equations (19) and (20) [34]:

$$BBP=\frac{B_{\mathrm{block}}}{B_{\mathrm{total}}},$$

(19)

$$RU=\frac{\mu \cdot N_{\mathrm{FS},\mathrm{occupied}}}{N_{\mathrm{FS},\mathrm{total}}\cdot t_{\mathrm{network}}},$$

(20)

In the above formula, μ denotes the holding time for all requests, which follows a negative exponential distribution. N_FS,occupied refers to the quantity of frequency slots currently in use by successfully established lightpaths, and N_FS,total signifies the total available FSs within the network; t_netwrok represents the network runtime.

Figure 3 compares the BBP between the proposed algorithm and the benchmark algorithms. The traffic load increases in both the NSFNET network and COST239 network, and the BBP also rises. This trend is attributable to the fact that a higher traffic load translates into a greater number of incoming requests per unit time, subsequently depleting the available FSs within the network. Consequently, a significant proportion of requests are either blocked or rejected, ultimately leading to a degradation in network performance.

In comparison to benchmark algorithms, the proposed algorithm exhibits a lower BBP. Specifically, in the NSFNET network topology, under a traffic load of 600 Erlang, the BBP of the proposed algorithm is reduced by approximately 47.7% compared to the KSP(L)-MSP(C)-EFM algorithm. This is because the KSP(L)-MSP(C)-EFM algorithm employs the KSP routing strategy for the primary path selection, which, compared to the minimum congestion-based routing method, tends to facilitate an excessive concentration of single-link services. This significantly elevates the BBP. The primary path selection in the LC(L)-DP(C)-EFM algorithm employs the minimum congestion-based routing strategy, leading to a lower BBP compared to the KSP(L)-MSP(C)-EFM algorithm. However, its backup path selection involves DPP, requiring one-to-one backup resources for the primary path, thereby increasing network resource consumption. As a result, its BBP is higher than that of the LC(L)-MSP(C)-EFM and LC(C)-MSP(L)-EFM algorithms, which employ SBPP. The comparison between the LC(L)-MSP(C)-EFM algorithm and the LC(C)-MSP(L)-EFM algorithm demonstrates that assigning the primary path to the L band and the backup path to the C band is superior to the reverse allocation of the primary path to the C band and the backup path to the L band. The proposed algorithm not only integrates both the minimum congestion and maximum sharing path selection methods but also refines the fragmentation measurement process. In comparison to entropy-based fragmentation measurement methods, the proposed algorithm enables a more precise quantification of path fragmentation, thereby facilitating the selection of optimal paths for services. Consequently, the chosen algorithm exhibits the lowest bandwidth blocking rate. Similarly, in the COST239 network, at a traffic load of 4200 Erlang, the BBP is reduced by approximately 22.1% compared to the LC(L)-DP(C)-EFM algorithm. This is due to the fact that the backup path of the LC(L)-DP(C)-EFM algorithm employs the DPP routing method. In contrast to the SBPP routing method, the DPP routing method consumes a greater amount of spectrum resources, significantly increasing the blocking rate. The KSP(L)-MSP(C)-EFM algorithm employs the KSP routing method for its primary path. In comparison to the minimum congestion routing method, the KSP routing method is prone to the phenomenon of an excessive number of single-link services, significantly escalating the BBP. Therefore, its level of BBP is inferior to algorithms employing the minimum congestion routing method. The proposed algorithm not only considers the routing process but alao takes into account the level of spectrum fragmentation on each link, favoring the allocation of spectrum resources with minimal fragmentation for subsequent requests. This strategy promotes the efficient utilization of spectrum resources, thus mitigating the risk of request blocking.

Figure 4 clearly demonstrates that the proposed algorithm offers the highest RU when compared to benchmark algorithms. In the NSFNET network, under the traffic load of 800 Erlang, the proposed algorithm exhibits a significant improvement in RU, achieving an improvement of approximately 23.9% compared to the KSP(L)-MSP(C)-EFM algorithm. The primary path of the KSP(L)-MSP(C)-EFM algorithm utilizes the KSP routing method, which, compared to the minimum congestion routing method, is more prone to service congestion. This will lead to service blocking, thereby reducing the RU. The backup path of the LC(L)-DP(C)-EFM algorithm employs a DPP routing method, which significantly increases the level of resource redundancy. Therefore, its RU is inferior to algorithms that adopt SBPP. The proposed algorithm not only considers the issue of resource utilization in routing but also selects the optimal spectrum positions for services through a more precise fragmentation metric in order to minimize the impact on future services. Therefore, the proposed algorithm achieves optimal resource utilization RU. In COST239, the RU of the proposed FISRSA-S algorithm has improved by approximately 13.2% compared to the LC(L)-DP(C)-EFM algorithm under 3800 Erlang. The superior performance of the proposed algorithm can be attributed to several key factors.

The algorithm employs a maximum sharing scheme for selecting backup paths. This approach effectively mitigates resource redundancy, thereby significantly enhancing RU. Second, our algorithm takes into account the spectrum fragmentation on each link during the resource allocation process, thus enhancing overall network spectrum resource utilization.

5.2. Performance of OSNR

In Section 5.2, we evaluate the performance on the FISRSA-S algorithm through the OSNR. Specifically, the calculation of the OSNR is conducted in accordance with the mathematical formula provided in Equation (21):

$$OSN{R}_{\mathrm{average}}=\frac{{\displaystyle \sum OSN{R}_{r,\mathrm{success}}}}{N_{r,\mathrm{total}}},$$

(21)

where OSNR_r,success denotes the OSNR on a successfully allocated request, whereas N_r,total signifies the number of arriving requests.

The results presented in Figure 5 demonstrate that the proposed algorithm surpasses benchmark algorithms in terms of OSNR. Specifically, in the NSFNET network topology, at a traffic load of 400 Erlang, the proposed algorithm exhibits an improvement in OSNR by approximately 4.17 dB. Similarly, in the COST239 network, under a traffic load of 3800 Erlang, the OSNR is enhanced by approximately 4.71 dB. The primary path of the KSP(L)-MSP(C)-EFM algorithm employs the KSP routing method, and compared to the minimum congestion routing method, the algorithm based on KSP routing is more prone to traffic aggregation, which significantly aggravates the physical layer impairment among services. Therefore, the OSNR of the KSP(L)-MSP(C)-EFM algorithm is poor. The backup path of the LC(L)-DP(C)-EFM algorithm utilizes the DPP routing approach. Compared to algorithms that employ SBPP routing, the backup path resources of the LC(L)-DP(C)-EFM algorithm cannot be shared, resulting in increased resource consumption as well as an augmentation of physical layer impairments among wavelength bands. Consequently, the OSNR performance of the LC(L)-DP(C)-EFM algorithm is inferior to algorithms that utilize SBPP routing. The proposed algorithm’s significant enhancement can be attributed to the implementation of a least congestion routing algorithm, which effectively distributes primary path requests across diverse paths. Additionally, the utilization of a maximum shared routing algorithm for discovering backup paths serves to minimize the occupation of backup resources. Therefore, it reduces the ISRS between requests significantly, leading to improved network performance.

5.3. Performance of Fragmentation Ratio

In this section, we compare our proposed algorithm with benchmarks in terms of fragmentation. The fragmentation is calculated as given in Equation (22):

$$\mathrm{Fragmentation}=1-\frac{N_{\mathrm{FS},\mathrm{largest}}}{N_{\mathrm{FS},\mathrm{total}}}$$

(22)

where N_FS,largest represents the number of FSs in the largest free block.

The results presented in Figure 6 demonstrate that the proposed algorithm outperforms benchmark algorithms in terms of the fragmentation ratio. Specifically, in the NSFNET network topology, under a traffic load of 400 Erlang, the fragmentation ratio of the proposed algorithm is reduced by approximately 21.3% compared to the LC(L)-DP(C)-EFM algorithm. In the COST239 network, under a traffic load of 3800 Erlang, the fragmentation ratio of the proposed algorithm is reduced by approximately 21.5% compared to the LC(L)-DP(C)-EFM algorithm. The backup path of the LC(L)-DP(C)-EFM algorithm employs the DPP routing method. Compared to algorithms that utilize the SBPP routing approach, the backup path resources of the LC(L)-DP(C)-EFM algorithm cannot be shared, which increases resource consumption and also elevates the probability of encountering unusable frequency slots on the link, thereby increasing spectral fragmentation in the network. The primary path of the KSP(L)-MSP(C)-EFM algorithm utilizes the KSP routing method. Compared to the minimum congestion routing approach, the algorithm based on KSP routing is more prone to traffic aggregation, which increases the probability of encountering unusable frequency slots on the main path. Therefore, compared to the minimum congestion algorithm, the KSP(L)-MSP(C)-EFM algorithm has a higher fragmentation rate. The primary and backup paths of the LC(L)-MSP(C)-EFM algorithm are the same as the proposed algorithm. However, in the crucial aspect of the fragmentation measurement, the LC(L)-MSP(C)-EFM algorithm utilizes an entropy-based approach, which can only measure external fragments. The proposed algorithm can measure the overall situation of the link more accurately. Therefore, the proposed algorithm exhibits superior performance over the LC(L)-MSP(C)-EFM algorithm. The proposed algorithm not only computes primary and backup paths based on the principles of least congestion and maximum shareability, respectively, but also takes into account fragmentation to select optimal paths. Furthermore, the proposed algorithm comprehensively considers both free fragmentation in the primary path and free as well as shareable fragmentation in the backup path, leading to improved network resource utilization and reduced fragmentation overall.

6. Conclusions

This paper presents a comprehensive investigation on survivable RBMSA, focusing on fragmentation and ISRS awareness in C+L-EONs. The proposed algorithm incorporates the SBPP to ensure network survivability for requests. To mitigate the impact of ISRS on the OSNR of services, the primary and backup paths are selected using the minimum congestion and maximum sharing algorithms, respectively. In the spectrum allocation phase, the algorithm takes into account both free fragmentation on the primary path and shared fragmentation on the backup path to minimize spectrum fragmentation. The simulation results demonstrate that the proposed algorithm outperforms other algorithms in terms of reducing the spectrum fragmentation rate and bandwidth blocking rate while simultaneously ensuring network survivability and request OSNR.