Earthquake-Tolerant Energy-Aware Algorithm for WDM Backbone Network

Abstract

Traffic on backbone communication networks is growing significantly every year. This results in an increase in both energy consumption and the carbon footprint they leave on the environment. As a response, research efforts are focused on reducing energy consumption in telecom networks. Wavelength division multiplexing (WDM) optical networks are key for addressing rising bandwidth demands in backbone networks, but this leads to a concurrent surge in energy usage. Additionally, regions with high seismic activity risk damage to backbone networks from earthquakes, causing significant bandwidth loss and service disruptions. This paper aims to reduce the energy consumption in a backbone network by implementing an algorithm that optimizes energy efficiency while preserving network connectivity and resistance to earthquake phenomena. The proposed algorithm redesigns and modifies a backbone network by deactivating the unnecessary links without affecting the network performance. The scheme is extensively evaluated through simulations using real seismic data from the Geodynamic Institute of the National Observatory of Athens, confirming earthquake resilience and energy efficiency goals, with an energy saving of up to 9% compared to existing solutions.

1. Introduction

1.1. Topic Introduction and Research Objectives

In recent years, the advent of bandwidth-hungry applications, such as file sharing, cloud storage, and video streaming, has raised energy consumption in telecommunication networks. At the same time, the global energy crisis caused by recent events, such as the war in Ukraine and the international shift to renewable energy sources to combat climate change, has created the need to reduce energy consumption in all sectors. The telecommunication sector itself accounts for over 4% of the world’s total energy consumption [1]. Its carbon footprint amounts to 2% of all carbon emissions in the atmosphere [2]. These figures are expected to continue rising in the coming decades due to the continuous growth of bandwidth demand [3]. Thus, the telecommunication sector is not and will not be an insignificant part of the total energy consumption of humanity. It cannot be an exception in the global effort to reduce the amount of energy we use.

Additionally, the telecommunications networks can be extremely vulnerable to natural disasters, such as hurricanes, tropical storms, tornadoes, earthquakes, landslides, avalanches, tsunamis, floods, fires, and animal attacks, as well as man-made or technological disasters, such as power outages, human negligence or errors, anchor drag/drops, EMP attacks, nuclear explosion, sabotage, anti-corporate attacks, cyber-attacks, terrorist attacks, or vandalism. The damage the above can cause to the telecommunications networks is of great importance. In this paper, we will focus on natural disasters, such as earthquakes. Earthquakes have devastating effects on telecommunications infrastructure. For example, the 2008 Sichuan earthquake in China destroyed more than 30,000 km of fiber optic cables and 4000 telecommunications headquarters [4], while the 2011 Great East Japan earthquake and tsunami destroyed nearly 1500 telecommunications offices and 700 telecommunications buildings [5]. The significant impact of earthquakes on communication networks necessitates measures to address the issues they cause and their inclusion in network designs. To this end, a large part of research work has focused on finding solutions, where the reduction of energy consumption, the increase of network capacity, and the tolerability of the network to the natural disaster effects, such as earthquakes, are all achieved at the same time. In our previous research work [6], we addressed these main problems of energy consumption and protection of networks from natural disasters by creating a new power-aware algorithm, which makes use of real seismic information to maintain resilient connectivity of the backbone network after a large-scale earthquake while supporting energy efficiency.

To this extent, studies of earthquake-tolerant and, at the same time, energy-aware algorithms have been introduced over the years [7,8], with the example of the EAFFB (Energy-Aware Fiber Fail Bypass) presented in [6]. In this research, an implementation is provided of a new power-aware algorithm, which makes use of real seismic information, to maintain the tolerant connectivity of the backbone network after a large-scale earthquake, while supporting energy efficiency. EAFFB is a power-aware and seismicity-aware WDM backbone network that defines the minimum number of spare links in the virtual topology to maintain connectivity tolerance. Although the EAFFB achieves its goals, it does not examine the case of deactivating links that are not necessary to achieve better energy efficiency.

The main improvements that we present in this paper with respect to [6] are the following. First, the main intent of this paper is to evaluate the possibility of achieving significantly better energy efficiency by redesigning an existing network and, at the same time, maintaining the network connectivity and resilience against earthquakes. Specifically, we examine the possibility of the deactivation of existent links in the network to accomplish better energy efficiency. We, therefore, propose a new algorithm that gives a better answer to the design and the modification of a backbone network while maintaining the functions guaranteed by the ΕAFFB algorithm developed in [6] and, at the same time, achieving significantly improved energy efficiency. This study analyzes the power consumption of a WDM network, especially the IP transmission over a WDM backbone network. The proposed scheme reduces the power consumption while at the same time ensuring network connectivity in the case of natural disasters. It does not explore aspects such as data transmission delays post-earthquake disasters.

The remainder of this article is organized as follows. In Section 1.2 and Section 1.3, background knowledge of IP over WDM networks and related work are presented, respectively. The proposed algorithm along with the energy contribution, seismic measurements, system configuration setup, and data are presented in Section 2. Section 3 includes the evaluation of the results along with the performance analysis. Finally, Section 4 concludes the article.

1.2. Background

IP over WDM networks consists of two layers: the IP layer and the optical layer, as shown in Figure 1. IP routers are responsible for routing at the IP layer, receiving aggregated traffic from peripheral routers, and interconnecting with the optical side of the network. The optical layer serves as the provider layer, offering services to the client layer through lightpaths. They consist of optical cross-connects (OXC), transponders, optical amplifiers, and multiplexers/demultiplexers [9]. The optical cross-connects (OXC) provide switching of optical signals between input and output ports. They can capture a snapshot of lightpaths and deactivate the paths dynamically. They can also support lightpath management and protection functions. They may also include wavelength conversion, multiplexing, and grooming capabilities internally [10]. Transponders are used when the format of the optical signal from the IP router needs to be adapted to another format. The transponder on the client side receives the signal from the IP router, converts it into an electronic signal, and then converts it back to the required WDM wavelength. The reverse procedure takes place on the receiving side of the network. This operation is called optical–electrical–optical (OEO) conversion. Optical amplifiers (EDFA) directly amplify optical signals without the need for converting them into electrical signals. They are placed along the fiber at intervals to compensate for the attenuation of the fiber. They are also used as amplifiers to increase the transmitting power of the transmitter or as pre-amplifiers to improve the sensitivity of the receiver [10]. Multiplexers and demultiplexers combine and separate multiple wavelengths carried through the fiber [10].

1.3. Related Work

1.3.1. Enhancing the Resilience of WDM Networks against Geographical Failures

The growing reliance on telecommunications has highlighted the importance of managing natural disasters in WDM networks. Network recovery encompasses the process of restoring and reinstating normal operations within a computer network. Various approaches to network recovery can be found in the existing literature. In their work, Tran and Saito [8] introduced a methodology for designing earthquake-resilient networks. Using a local Pareto solution approach, they identified optimal geographical routes to incorporate additional network links, fortifying the network against earthquakes through quantitative risk evaluation. In [9], the authors presented a dynamic algorithm that uses seismic hazard information and geographical maps to add new links to existing network topology, enhancing network robustness within cost constraints. Furthermore, in [11], the authors proposed a comprehensive probabilistic model for geographically correlated failures. The authors employed algorithms to identify the most vulnerable locations in a WDM network, while also introducing a set of algorithms to handle simultaneous failures. Neumayer and colleagues [12,13] used mixed-integer linear programming (MILP) to estimate the worst-case geographical locations of disasters that could maximize the capacity of disconnected links. Furthermore, the authors of [14] proposed a node relocation method within the backbone network of India, leveraging real seismic zone information to enhance network survivability through minor adjustments. In [15], the authors proposed a network availability evaluator that compares different traffic protection scenarios for advanced optical network designs, with advanced wavelength division multiplexing being included. Furthermore, the authors of [16] presented a prediction-based fair wavelength and bandwidth allocation algorithm that analyzes various wavelength allocation possibilities in hybrid passive optical networks. In [6], the authors introduced a new power-aware algorithm that uses real seismic information to maintain the tolerant connectivity of the backbone network after a large-scale earthquake. The proposed EAFFB algorithm is a power-aware and seismicity-aware WDM backbone network that defines the minimum number of spare links in the virtual topology to ensure tolerant connectivity. In the same research work, the proposed scheme was evaluated through extensive simulation results using real seismic information provided by the Geodynamic Institute of the National Observatory of Athens, and it was verified that both goals of earthquake tolerance and energy efficiency were achieved. EAFFB achieves this by calculating the minimum number of backup paths for links passing through earthquake-prone regions likely to sustain future damage. As presented in [17], high data-rate transmission over optical fibers faces challenges related to signal deterioration caused by nonlinear impairments, with four-wave mixing (FWM) being a notable concern. Particularly at elevated launch power levels necessary for long-haul transmissions spanning hundreds of kilometers, these nonlinear effects intensify, posing a significant challenge in achieving satisfactory transmission performance. The authors of [18] explored the effective implementation of DWDM in optical systems and networks, emphasizing the mitigation of four-wave mixing (FWM), a significant nonlinearity that can limit the transmission capacity. A simulation model for a 15-channel DWDM system was introduced to analyze FWM’s impact on transmitted wavelengths. Performance analyses guide the selection of practical wavelength channels for DWDM communication systems. Although the FWM effect is important, it is not considered in this study so as to have a more fair comparison with our previous work presented in [6]. In [19], the authors introduced two polynomial-time algorithms designed to choose an optimal pair of link–disjoint lightpaths between two network nodes. The objective was to maximize their minimum spatial distance (MSD), minimize the path length of the primary lightpath, and ensure that the backup lightpath maintains a specific MSD from the primary lightpath. This optimization was performed while disregarding safe regions around the source and destination nodes. Furthermore, the authors of [20] introduced a novel design framework known as geometric network augmentation (GNA). GNA identifies specific node pairs and recommends new cable routes to be implemented between each pair. This proactive approach ensures continuous network connectivity in the event of a regional failure of a specified magnitude.

1.3.2. Enhancing Energy Efficiency in WDM Backbone Networks

Extensive research efforts focus on developing survivable and energy-efficient networks. The literature presents numerous power-efficient algorithms to address this goal. In [21], two distinct protection strategies, dedicated-link and dedicated-path protection, were proposed, with a focus on energy efficiency. They introduced an integer linear programming formulation to enable power-aware network design, utilizing sleep mode for devices involved in backup path provisioning. In [22], the authors introduced an energy-efficient WDM network capable of withstanding single link and node failures. This approach achieves energy efficiency through optimized resource allocation for working and protection lightpaths, as well as the reduction of power consumption associated with redundant resources. Monti and colleagues [23] presented a scalable algorithm for static energy-aware lightpath provisioning in WDM networks, with a specific focus on dedicated 1:1 path protection. In [24], Musumeci et al. compared four protection strategies, namely, shared-link, shared-path, dedicated-link, and dedicated-path protection. They provided mathematical models to support power-aware design in a sleep-mode scenario. Furthermore, in [25], the authors proposed a cognitive power management technique based on traffic prediction to efficiently activate or deactivate underutilized network elements. In [26], the authors introduced a hybrid architecture of the WDM network combining free space optics (FSO) and single-mode fiber (SMF)-based optics and achieved a significant reduction in energy consumption. Furthermore, in [27], the authors used a mixed-integer linear programming (MILP) model to compare different network topologies and optimize and minimize the embodied energy consumption of network equipment in the IP and optical layers. The authors of [28] presented a thorough examination of advancements in strategies aimed at enhancing the energy efficiency across various categories of networks. These encompass radio-and-fiber (R&F) networks, radio-over-fiber networks (RoF), hybrid fiber–wireless (FiWi) networks incorporating multi-access edge computing (MEC), and software-defined network (SDN)-based FiWi networks. Additionally, the paper explored potential future avenues for further enhancing energy efficiency within FiWi networks. In [6], the introduction of a new power-aware algorithm, which ensures energy efficiency by establishing the minimum number of backup links in the virtual topology to maintain tolerant connectivity, was presented. The protection scheme used was the 1 + 1 link protection scheme, where for every connection of two nodes, a backup connection is also provided that can be used in case of failure of the first one.

The network paths that may be present in the area that will suffer a catastrophic earthquake, as can be seen in Figure 2, are the A-B, B-A, A-B-E, and E-B-A paths. The appropriate optimal backup paths for this case are the A-D-C-B, B-C-D-A, A-D-C-E, and E-C-D-A paths.

2. Materials and Methods

2.1. Energy Contribution and Seismic Measurements

In this section, we analyze the energy contributions of individual network elements and introduce a new network redesign algorithm that significantly improves energy efficiency.

2.1.1. Energy Contribution

The main sources of power consumption in IP over WDM optical networks are IP router ports, WDM transponders, and EDFAs [29]. In detail, the energy consumption of each component is outlined below.

IP router port: an IP router port consumes about 1000 W [30] and is the most energy-consuming component of an optical network, processing all incoming and outgoing information. WDM transponder: a WDM transponder consumes about 73 W and is associated with each wavelength for data transmission and OEO conversion [31]. Erbium-doped fiber amplifier (EDFA): An EDFA consumes about 8 W and is deployed every 80 km of optical fiber installation [32]. In addition, there are always two EDFAs at the two ends of each link, to amplify the incoming and outgoing signals. The EDFAs have been chosen because they outperform other options in longer transmission distances, as can be seen in [33], and they can be effectively integrated into optical networks [34].

The total energy consumption can be estimated (in Watts) using the following Formula (1) [35]:

$$total energy consumption= \sum _{i\in N}{E}_r\times \left({\Delta }_i+\sum _{j\in N, i\ne j}{C}_{ij}\right)+\sum _{m\in N}\sum _{n\in N_m}{E}_t\times W_{mn}+\sum _{m\in N}\sum _{n\in N_m}{E}_e\times A_{mn}\times f_{mn}$$

(1)

The m and n symbols are the indexes of the nodes in the physical topology. The N_m symbol resembles a set of neighboring nodes of node m on the physical topology. The symbols i and j refer to indexes of the nodes in the virtual topology. The C_ij parameter refers to the number of wavelengths between nodes i and j. The W_mn symbol refers to the number of wavelengths between node m and node n. The parameter Amn means the number of EDFAs used on each physical link between nodes m and n. The f_mn symbol resembles the number of optical fibers between nodes m and n. The parameter E_r refers to the energy consumption at the IP layer, which accounts for the energy consumption of the IP router ports, while the parameters E_t and E_e refer to the power consumption of the WDM transponders and EDFAs, respectively. The L_mn parameter resembles the physical distance between nodes m and n. Furthermore, the parameter Δ_i is calculated as [(∑d∈N λid)/B], where B is the transmission capacity of each wavelength (40 Gbps), and A_mn is calculated as [L_mn/S − 1] + 2, where S is the distance between two adjacent optical amplifiers.

2.1.2. Richter and Gutenberg’s Law

Seismic activity is not distributed evenly across the surface of the Earth; rather, there are seismic zones that cover specific areas where seismic activity is notably higher. Figure 3 depicts the entire map of Greece, with each seismic zone distinguished by a different color, as provided by the Earthquake Planning and Protection Organization of the Ministry of Transport, Infrastructure, and Networks [36]. The zone with low seismic activity is marked in blue, the zone with medium seismic activity in green, and the zone with high seismic activity in orange. Since the regions of Greece encompass all these seismic zones, an alternative approach must be employed to calculate the probability of seismic activity in each region [6].

In general, most quantitative seismic measures are based on the Gutenberg–Richter (G-R) size distribution law. In seismology, the Gutenberg–Richter (G-R) law is used to express the relationship between the magnitude and the total number of earthquakes in any region and time period where earthquakes of at least that magnitude occur. It is defined mathematically as follows [37]:

$${log}_{10}N{\left(M\right)}_t=a_t-bM$$

(2)

where N(M)_t is the cumulative number of events with a size greater than or equal to M, in a period of t years, a_t is the duration, in years, of the research, and b is the slope of the above equation. The values of a_t and b can be estimated from an empirical distribution of earthquake frequencies, using the method of least squares (Equations (7)–(9)). The same equation can be written as:

$${log}_{10}N\left(M\right)=a-bM$$

(3)

where N(M) is the cumulative number of events of size greater than or equal to M in a year.

$$a=a_t-{log}_{10}t$$

(4)

$$T_m=\frac{{10}^{bM}}{{10}^a}$$

(5)

$$P_{t^{\prime }}=1-e^{\frac{\delta t^{\prime }}{T_m}}$$

(6)

$$a_t=\frac{{\sum }_{i=1}^n{x}_i^2{\sum }_{i=1}^n{y}_i-{\sum }_{i=1}^n{x}_i{\sum }_{i-1}^n{x}_i{y}_i}{D}$$

(7)

$$b=\frac{n\times {\sum }_{i=1}^n{x}_i{y}_i-{\sum }_{i=1}^n{x}_i{\sum }_{i-1}^n{y}_i}{D}$$

(8)

In Equation (4), a is the annual G-R constant. Equation (5) expresses the average return (repetition) period (arp) for earthquakes of magnitude M or greater, while Equation (6) calculates the probability of an earthquake of magnitude M or greater in the considered area for the next t years, making the standard assumption that earthquakes follow a random (Poisson) distribution. In Equations (7)–(9), x represents the magnitude of the earthquake in a region, starting from a minimum cutoff magnitude (e.g., 4.0) on the Richter scale, while y represents the logarithmic value of the cumulative number of earthquakes with this minimum magnitude. Finally, n is the total number of available earthquakes above the cutoff magnitude, in the considered area [6].

2.2. Operation of the Proposed Algorithm

Analysis reveals that the primary source of energy consumption is the IP routing ports, necessitating a reduction in their usage for significant energy savings. The total number of IP routing ports depends on the total number of paths, which, in turn, relies on the number of areas with a high seismic probability, the fibers they pass through, and the total number of new bypass paths. Based on these data, we conclude that reducing fibers passing through these areas would result in reduced energy consumption. Removing all these fibers would significantly reduce energy consumption but could also create a disconnected network, resulting in lost communication between nodes. Therefore, fiber removal from the network must be selective. Leveraging this knowledge, the proposed algorithm selectively removes specific fiber connections from the topology to reduce energy consumption while considering the seismic risk of the areas. Energy reduction will be calculated using the EAFFB algorithm [6].

The proposed algorithm aims to identify critical fibers, passing through seismically active areas, that can be removed without causing network disconnection. It selects combinations of links for removal, creating a new network that achieves two goals: prevents network disconnection and minimizes total energy consumption. The algorithm emphasizes complete links, assuming identical WDM channel sets. Link removal or deactivation is treated as a unified entity without considering the WDM level.

For example, when two neighboring regions are potential candidates for catastrophic earthquakes, and the only way to access a node in the network is through links passing through these regions, none of these links can be categorized as critical. Removing any of these links would render the node unreachable. This can be seen in Figure 4, where there are three affected regions: 35, 34, and 1, and the affected links are 270 and 341. Neither of them can be characterized as critical because removing any of those links immediately sets the RHO node as inaccessible.

The algorithm first identifies critical fibers in the physical topology and then determines the best combination of these fibers to exclude from the final topology. This ensures both full connectivity of the backbone network and significantly reduced energy consumption.

Below is a concise description of the proposed algorithmic approach, with the corresponding pseudocode in Algorithm 1. The input parameters in line 1 are a physical topology G (N, L), comprising a set of nodes N and a set of links L. In line 2, nodes (N) represent the network nodes, and in line 3, links (L) denote the physical fibers connecting pairs of nodes. In line 4, a traffic matrix [λ] specifies the precise traffic demand between two nodes. The [λ] is generated by a random function uniformly distributed within the range [10, 2X − 10] Gb/s, where X ∈ [20, 40, 60, 80, 100, 120]. A maximum of 80 wavelengths are multiplexed in each fiber, with a restriction on the total number of fibers on each physical link set at 48. The modulation format can be changed, as the presented algorithm is modulation-agnostic. Moreover, the presented algorithm can operate with varying link capacities, requiring minimal adjustments to its implementation. The link capacity of 40 Gbps was chosen in order to have a fairer comparison of the presented algorithm result with the results of the previous work presented in [6,37]. Additionally, the chosen modulation format is the Non-Return-to-Zero (NRZ). In optical communication, NRZ is a simple modulation format, where each bit is represented by a single pulse and the transmission capacity of each wavelength is 40 Gbps. There are no digital signal processing activities conducted in the channels in our WDM network that are being considered in the simulation. In line 5, the matrix [R] includes all 36 regions of the network map. For each region, the average repeat rate (arp) of earthquakes and the earthquake occurrence probability are presented in

Table 1. For each region, the average repeat rate (arp) of earthquakes and the earthquake occurrence probability are presented.

Regions	Average Repeat Rate (arp)	Earthquake Occurrence Probability (%)
1	9.16	42
2	32.97	14
3	52.01	9
4	21.84	20
5	39.17	12
6	30.80	15
7	16.68	26
8	44.13	11
9	48.13	10
10	33.91	14
11	20.13	22
12	31.18	15
13	53.10	9
14	31.58	15
15	16.35	26
16	18.49	24
17	107.94	5
18	14.90	29
19	27.78	16
20	57.79	8
21	13.97	30
22	36.25	13
23	51.20	9
24	30.44	15
25	21.22	21
26	28.88	16
27	23.71	19
28	71.80	7
29	98.20	5
30	28.17	16
31	41.64	11
32	27.07	17
33	46.58	10
34	5.38	60
35	13.80	30
36	33.34	14

. The region’s borders were set between each node and the links that connect each node pass through them. For each region, the collected past seismic activity data have helped the algorithm to calculate the probability of an occurrence of a future earthquake that could have damaged the links. Other inputs encompass the energy consumption values for a router port, a transponder, and an EDFA. In order for the optical signal to travel over long distances, EDFAs are used. A post-amplifier is provided after the transmitter, a pre-amplifier is provided before the receiver, and line-amplifiers are placed along the link every 80 km [32]. The total number of IP router ports, WDM transponders, and EDFAs that are being used varies for each case of average traffic and the lower threshold value of earthquake size. The EAFFB algorithm calculates them in order to output the total energy consumption of the network, and the calculated figures can be seen in

Table 2. For each earthquake occurrence probability threshold and all the average traffic cases, the number of IP router ports, WDM transponders, and EDFAs that are used by the network are depicted.

Earthquake Occurrence Probability Threshold	Average Traffic (Gb/s)	IP Router Ports	WDM Transponders	EDFAs
20%	20	2648	9004	30,613
	40	3897	13,218	30,613
	60	5191	17,656	30,613
	80	6575	22,348	30,613
	100	7925	26,994	30,613
	120	9200	31,428	30,613
30%	20	1258	2596	9356
	40	1876	3877	9356
	60	2498	5147	9356
	80	3122	6463	9356
	100	3730	7701	9356
	120	4423	9150	9356
40%	20	1104	2136	7348
	40	1646	3191	7348
	60	2195	4240	7348
	80	2726	5277	7348
	100	3290	6376	7348
	120	3842	7430	7348
50%	20	1104	2136	7348
	40	1639	3168	7348
	60	2178	4217	7348
	80	2754	5333	7348
	100	3306	6393	7348
	120	3835	7464	7348

. Initially, in lines 6 to 8, the algorithm identifies all critical regions using real seismic data and applying Richter and Gutenberg’s law to calculate the likelihood of a destructive magnitude earthquake in each region. Once critical regions are identified, in lines 9 to 11, the algorithm assesses whether each link passing through a critical region can be safely removed from the network.

Algorithm 1: Proposed Algorithm

Input:

G (N, L): Physical Topology

2. N: Set of nodes in the network

3. L: Set of links to the network

4. [λ]: Traffic demand per node pair

5. [R]: Regions

Output: bestOutput, originalOutputOfEAFFB

6. for each region ∈ [R] do

7.   find if critical region

8. end

9. for each link ∈ criticalRegions do

10.   filter links *

11. end

12. find all the combinations

13. for each Combination ∈ Combinations do

14.   implement EAFFB without the links in the combination

15. end

16. finds the combination with the best energy output on the EAFFB implementation

17. Return bestOutput, originalOutputOfEAFFB

* (Filter links that can be removed without creating a hole in the grid in case of an earthquake)

This is achieved by implementing the EAFFB algorithm on a new network, excluding only the one link that it checks every time. If the EAFFB algorithm runs successfully without creating a disconnected network, then the examined link could safely be removed. Then, in lines 12 to 15, the proposed algorithm finds out all the combinations between all the links that can be safely removed from the network. For each combination, it applies the EAFFB algorithm on a network where the links of each combination are excluded. Then, in line 16, the algorithm selects the combination of links whose removal or deactivation from the original network meets all the limitations of the original EAFFB algorithm and achieves the lowest energy consumption. At the end of line 17, the proposed algorithm outputs the calculated best energy consumption from the altered network and the original network’s energy consumption.

2.3. Simulation Specifications

The performance of the proposed approach was evaluated for a variety of simulation scenarios. With this in view, an optical network simulator has been implemented using Python 3.7 on PyCharm. The simulations were conducted on a PC running Windows 10 Pro with an Intel(R) Core(TM) i5-4590 CPU @ 3.30 GHz and 16 GB RAM. The time complexity of the EAFFB algorithm was calculated to be:

$$\left[EAFFB\right]=O\left(\right(N+R\left)\right(V+L)+2)$$

(9)

This complexity will be referred to as [EAFFB], where N represents the number of node pairs, R represents the number of links in a region, V represents the nodes, and L represents the links. The complexity arises from the utilization of the Breadth-First Search algorithm to compute the shortest paths, resulting in a complexity of:

$$O(V+L)$$

(10)

Therefore, the procedure of finding all the shortest paths at the start of the algorithm was estimated at:

$$O(N\times (V+L\left)\right)$$

(11)

while the complexity for calculating the probability of earthquake occurrence was O(1) due to the use of simple mathematical operations. The algorithmic analysis for determining the backup paths in the virtual topology was denoted as:

$$O(R\times (V+L\left)\right)$$

(12)

while the complexity of assessing the energy consumption was expressed, once again, as O(1), since it exclusively entails mathematical operations. In the context of the proposed algorithm, its efficiency was evaluated as:

$$O(R+2^R+\left(R+C\right)\times [EAFFB\left]\right)$$

(13)

where C encompasses all the combinations of filtered critical links. Finally, finding all critical links in all regions, filtering critical links, determining all combinations of filtered critical links, and calculating the energy output for the aforementioned combinations have, respectively, a computational complexity of:

$$O\left(R\right)$$

(14)

$$O(R\times [EAFFB\left]\right) \left[EAFFB\right]=O\left(\right(N+R\left)\right(V+L)+2)$$

(15)

$$O(C\times [EAFFB\left]\right)$$

(16)

2.4. Simulation Data

To estimate the overall power consumption of different design solutions, the network topology used in [6] was considered (Figure 5a). In detail, the network consisted of 24 nodes and 28 links, for each of which 2 directions will be considered, interconnecting the nodes, and forming a unified network. The network map was divided into 35 regions, calculating the probability of an occurrence of a future earthquake that could damage the links in each region.

On the map of Figure 5a, the letter code beside every node signifies the name of the town or island and is utilized to identify each individual node on the map. On the second map, depicted in Figure 5b, the numbers displayed next to each link represent the distance between two nodes that each link is spanning through. Additionally, Figure 5b shows the geographical regions used in the simulation, with each region specified with a unique number code in red.

It also offers clarity regarding which links pass through each of these geographical regions. Using real earthquake catalogs from the Geodynamic Institute of the National Observatory of Athens for the period from 1 January 1964 to 1 January 2023, all earthquakes with a magnitude greater than 4 on the Richter scale, deemed as strong, were included in the data considered by the simulation. For the purposes of this research, the country was divided into 36 distinct districts/regions. For each region, all earthquakes of magnitude 4 and above were studied. Then, the average recurrence period of a 5 Richter earthquake (T_m5) was calculated, as well as the probability that such an earthquake (5 Richter) would occur in the next five years (P_t). The areas considered dangerous, and taken into account, were those where the probability of a magnitude 5 earthquake in the next 5 years is greater than 20%, 30%, 40%, and 50%. The choice of a magnitude 5 earthquake was made based on the work in [38,39,40], which indicates that a 5 Richter earthquake can affect a network link that crosses this 5 km radius earthquake epicentral (damaging) area.

The methodology developed in this work is independent of the method or reliability of the seismicity quantities calculated and applied in this examination. That is, alternative zones, catalogs, and/or measures of seismicity could be used for the study area (mainland Greece), without changing the applicability of the proposed approach. This paper essentially provides a “proof of concept” on how seismicity measures, regardless of how they are evaluated, can be effectively used to design WDM networks to anticipate and take into account earthquake-induced problems.

3. Results

To assess the effectiveness of the proposed algorithm, a series of simulation experiments were conducted, and the detailed parameters are presented in Section 2.4.

Table 3. For each earthquake occurrence probability threshold, the affected areas, critical links, and chosen links that Algorithm 1 calculated are depicted.

Earthquake Occurrence Probability Threshold	Affected Areas	Critical Links	Chosen Links
20%	1	279	279
	4	125	125
	7	236	99
	11	147
	15	99
	16	62
	18	157
	21
	25
	34
	35
30%	1	62	62
	21
	34
	35
40%	1	341	341
	34
50%	34	341	341

provides a comprehensive view of affected areas, critical links, and links earmarked for removal or deactivation, calculated by the proposed algorithm across four scenarios (>20%, >30%, >40%, and >50% earthquake occurrence probability thresholds).

Affected areas encompass regions with a high probability of destructive earthquakes. Critical links are those traversing these areas, removable without disrupting network connectivity. Chosen links represent a judicious selection by the algorithm for removal or deactivation, strategically aimed at minimizing energy consumption. By removing or deactivating these chosen links, the algorithm eliminates the need to calculate backup paths for affected lightpaths, a crucial aspect significantly contributing to the total power consumption. This is especially pertinent in scenarios with numerous affected regions, necessitating a substantial number of backup paths to mitigate the disruption of lightpaths caused by damaged links.

In specific scenarios with earthquake occurrence probabilities exceeding 20% and 30% (magnitude 5 Richter or above), the total energy consumption of all backup paths constituted 66% and 20% of the network’s total energy consumption, respectively. Conversely, in scenarios exceeding 40% and 50%, the energy consumption contribution of all backup paths significantly reduced to 9% and 4%, respectively. The algorithm strategically removes links traversing regions deemed to have a high earthquake occurrence probability, resulting in a noteworthy decrease in power consumption. This reduction stems from the algorithm’s ability to avoid creating extra backup paths for those links.

Figure 6, Figure 7, Figure 8 and Figure 9 depict the network used in the simulation, showcasing a chart presenting the total power consumption of the EAFFB algorithm [6] alongside the comparative results of the proposed algorithm for each of the four cases (>20%, >30%, >40%, and >50% earthquake occurrence probability thresholds). Critical regions, calculated by the algorithm, are marked with an orange “x” sign on the network maps for each case.

Specifically, in the >20% case, the removal of three selected links (‘279’, ‘125’, and ‘99’) led to a 9% reduction, while in the >30% case, the removal of link ’62’ resulted in an 8% reduction in total energy consumption. Similarly, in the >40% and >50% cases, where only one link (‘341’) passed through affected areas, the calculated energy consumption for all backup paths exhibited a decrease of approximately 9% and 4%, correspondingly.

In the initial two cases of >20% and >30%, there was evident potential for a higher reduction in energy consumption, given that the total energy consumption of all backup paths was calculated to be 66% and 20%, respectively. However, due to the constraint of maintaining network connectivity, not all critical links could be removed, resulting in a lower total reduction of energy compared to the total energy consumption of all backup paths. In the >40% and >50% cases, the energy reduction calculated by the algorithm was maximized, as the total energy consumption of all backup paths was calculated to be 9% and 4%, respectively, aligning with the energy consumption reduction achieved by the proposed algorithm.

As the earthquake occurrence threshold increased, the reduction in energy consumption diminished, attributable to fewer areas being considered critical, resulting in a lower count of critical fibers and alternative paths. Consequently, fewer fibers can be removed from the network. The significant deviation in the algorithm’s results in the >50% case, presenting a 4% reduction in energy consumption compared to other cases, may be influenced by actual data retrieved from the National Observatory of Athens. In this specific case, only one area exceeded the >50% threshold, whereas in other cases, multiple regions surpassed the specified threshold. Consequently, alternative paths were calculated only once for the single link (link 341) passing through the affected region (region 34).

Upon a comprehensive review of the results, the algorithm emerges as effective in achieving a substantial reduction in energy consumption. It accomplishes this by identifying links passing through critical regions, subsequently removing or deactivating them from the network. This strategic relocation reroutes all traffic passing through those links, eliminating the need to create additional backup paths that would contribute to increased total energy consumption.

In summary, the outcomes of the proposed algorithm simulations underscore that improvements made to the backbone network can yield a significant 7.5% reduction in energy consumption, on average.

4. Conclusions

In this paper, we proposed a new algorithm that optimizes the energy consumption of a backbone WDM network while simultaneously achieving the key objectives of earth-quake resilience, network connectivity, and enhanced energy efficiency. The proposed algorithm accomplished its goals by removing or disabling less crucial links that contribute to higher energy consumption. With this innovative algorithm, it becomes possible to improve the design of new backbone networks and reduce the energy expenditures of existing ones. All the traffic that was previously passing through the removed or deactivated links changes path and uses the remaining links that are still active on the network. There is no need to introduce additional links to the network topology to compensate for these changes, as the number of removed or deactivated links constitutes only a small percentage of the total network topology. The proposed algorithm carefully assesses current seismic data, configuring the optimal network topology for the most efficient energy consumption results. In the event of seismic data changes in the future, the algorithm needs to be re-executed with the updated data as input. The backbone network remains fully functional and operational for all nodes, even in the scenario of removed or deactivated links. The algorithm primarily focuses on complete links rather than WDM channels. The assumption is that links consist of an identical set of WDM channels, and the deactivation or removal of links is treated as a single entity without considering the WDM level.

For future work, we are planning to study if it is possible to produce an even further reduction in energy consumption of backbone WDM networks by using ZR+ optics.