1 Introduction

Nearly two-thirds of the global population will have Internet access by the end of 2023 [1]. To accommodate this increasing user traffic, network operators need to ensure availability of adequate resources. Most Internet traffic today is carried using optical networks since they provide high capacity. Fiber-optic communication is conducted in the wavelength region where transmission loss is minimal. This low-loss region is divided into bands (O, E, S, C, L, and U bands) [2]. Among these bands, C band has been a prominent choice for optical communication systems due to its high resiliency to transmission losses. However, bandwidth in C band is finite (about 5 THz) [3]; and, with increasing traffic, this resource could soon be exhausted.

Hence, to meet the growing traffic demands, infrastructure upgrades in backbone networks are necessary. Optical-processing-enabled networks have emerged as a promising approach to achieve greater fiber capacity [4, 5]. This enhancement is enabled by the superpositioning of transitional lightpaths at intermediate nodes. Similarly, Space-Division Multiplexing (SDM) and Multi-band (MB) transmission, while differing in approach, are also well-known capacity-enhancement techniques. SDM uses transmissions over bundles of Multiple Fibers (MF), and/or over Multi-Core/Mode Fibers (MCF/MMF). Although MF technology is rewarding in terms of serving more traffic, the requirement of additional fibers and optical components such as Wavelength-Selective Switches (WSS), filters, and amplifiers makes it economically undesirable, while MCF/MMF require a complex infrastructure upgrade and are not commercially feasible at competitive prices. In this regard, MB transmission, which exploits the available spectrum in Single-Mode Fibers (SMFs) beyond the C band, could be a viable option to sustain traffic growth and could serve higher traffic [6] in optical backbone networks. With conventional networks likely reaching their physical limit (capacity crunch), MB transmission is a practical and promising direction. SMFs such as ITU G.652.D (which has a negligible water-absorption peak) are viable for MB expansion [7, 8], thus aiding in increased transmission capacity.

Expanding the spectral region of operation beyond the Conventional (C) band provides access to different bands. However, they require different amplifier technologies for signal transmission. For example, O, E, S, and U bands require Praseodymium-Doped Fiber Amplifier (PDFA) [9], Bismuth-Doped Fiber Amplifier (BDFA) [10], Thulium-Doped Fiber Amplifier (TDFA) [11], and Lumped Raman Amplifier (LRA) [12], respectively, which are still in their early stages of development, while the C band requires Erbium-Doped Fiber Amplifier (EDFA), which has reached technical maturity. Compared to O, E, S, and U bands, the L band is more favorable since it has only a negligible increase in the attenuation co-efficient compared to C band. In addition, the EDFA technology used for C band can also be used for L band. The activation of L band provides an additional 5 THz of bandwidth, thereby increasing the operational bandwidth to 10 THz per optical link [13]. Therefore, the use of C+L bands allows operators to work with an increased network capacity without additional fibers [14, 15]. To increase network capacity, current C-band-only infrastructure must be upgraded to adapt to MB transmission.

Adding L band to a C-band-only infrastructure is beneficial; however, L band exhibits more physical-layer impairments such as higher noise figure and chromatic dispersion compared to C band. These factors affect the Generalized Signal-to-Noise Ratio (GSNR) of lightpaths deployed in L band. Note that, while Optical Signal-to-Noise Ratio (OSNR), which typically considers Amplified Spontaneous Emission (ASE), is widely used, in this work, we also account for Non-Linear Interference (NLI), and hence use GSNR. Also, the effect of Inter-channel Stimulated Raman Scattering (ISRS) [16] becomes significant due to power transfer and affects the existing lightpaths in C band. The above factors can limit the GSNR, which is an important metric to consider during MB upgrade. A network can be upgraded either gradually or all once, depending on the network operators’ objective; but, generally speaking, upgrading all links of a topology at the same time might not be justified due to excessive Capital Expenditures (CapEx). In this regard, Ahmed et al. [17] showed that a network operator needs to wisely select a set/sequence of link(s) to upgrade from C to C+L which can delay future network upgrades, thereby achieving cost benefits.

A network upgrade can be further delayed by employing a mechanism called re-provisioning. We define re-provisioning as moving existing lightpaths in C band to L band. By moving more lightpaths to L band, availability of C-band spectrum increases, which allows an operator to continue operating in C band. This approach may be cost-effective because early upgrades can be expensive. Hence, re-provisioning is an important mechanism to delay network upgrades and efficiently use network resources. A distance-based re-provisioning strategy for C+L upgrade was proposed in Ahmed et al. [18]. Despite its effectiveness, re-provisioning lightpaths from one band to another may degrade the signal quality, i.e., GSNR of lightpaths, leading to increased service disruptions, which operators would like to avoid as much as possible.

To reduce disruption in the network, we propose new and improved re-provisioning strategies when upgrading a network to C+L bands. Also, although GSNR can be calculated analytically, we incorporate a synthetic, data-driven, Machine Learning (ML) model to estimate GSNR of lightpaths, which decreases computation times of lightpath-feasibility checks.

The two proposed GSNR-aware re-provisioning strategies, called Budget-Based (BB) and Margin-Aware (MA), aim at reducing lightpath disruption in the network, thereby improving spectrum utilization. In BB, a network operator is allowed to re-provision a fixed number of lightpaths from C band to L band after each batch upgrade, while in MA, existing C-band lightpaths are re-provisioned to L band based on their GSNR margin set by the network operator. We evaluate the performance of the proposed strategies with a baseline distance-based strategy in the BT-UK network. Results show that the BB and MA strategies significantly reduce disruption and blocking in the network, compared to the distance-based strategy in Ahmed et al. [18].

The remainder of this study is organized as follows: In Sect. 2, related works are reviewed. Section 3 describes the physical-layer model and the regression models used for Quality-of-Transmission (QoT) estimation. Section 4 describes the proposed re-provisioning strategies for C+L networks and also presents the algorithms. Section 5 introduces the simulation settings and traffic matrices, and shows the numerical results. Section 6 concludes the study.

2 Related works

How to deal with capacity crunch using MB transmission in optical networks is a topic of significant interest. Prior works, [8, 19,20,21], have considered different scenarios in MB to enhance transmission capacity. Uzunidis et al. [19] developed a planning tool that exploits physical-layer-aware Routing, Modulation, and Spectrum Assignment (RMSA) algorithm to activate optical bands based on incoming traffic. Sambo et al. [20] proposed a provisioning scheme considering C+L and C+L+S bands with the flexibility to assign preference to a specific transmission band. Their findings indicate that, despite the signal-strength degradation caused by neighboring bands in the C band, significant reduction in blocking probability can be achieved with MB transmission. Sambo et al. [8] considered a lightpath-provisioning scheme for different MB scenarios (C only, C+L, C+L+S, C+L+S+E, and C+L+S+E+O), showing a significant increase in transmission capacity. However, technical maturity and commercial availability of the necessary optical devices for different bands must be considered. Among the different bands, L-band technology has significantly matured, and previous studies [15, 22] provide a strong motivation for expanding to C+L. Also, network upgrades from C to C+L bands have been implemented in industry [23].

Considering these prior works, modeling the physical layer is an essential part to plan a practical MB expansion. Some major factors that need to be considered during MB operation are Stimulated Raman Scattering (SRS), NLI, noise figure, and type of optical amplifier required to operate in each band. Correia et al. [24] considered the above factors and showed that network traffic in MB might increase with an optimized power assignment. Ferrari et al. [7] discusses the potential challenges in MB by considering the effects of ASE noise (due to optical amplifiers) and non-linear effects such as SRS and NLI. Other works, such as [13, 25,26,27] have also modeled and evaluated the impact of ISRS in MB networks. Mitra et al. [28, 29] investigate MB scenarios limited to C+L systems by accounting for ASE due to in-line amplifiers and SRS.

The above factors add to signal impairments, thereby affecting the GSNR of lightpaths. Previous work [18] considered a worst-case scenario to calculate GSNR of lightpaths for incoming requests. In fact, determining GSNR using analytical calculations can be cumbersome, especially when a large number of lightpaths are provisioned in a network. Hence, to predict lightpaths’ QoT, in this study, we use ML-based QoT estimation for unestablished lightpaths based on the current network state. Multiple studies have demonstrated how to use ML-based QoT estimators to verify the feasibility of lightpaths for deployment. We review below some studies related to ML-based QoT estimation.

Sartzetakis et al. [30] proposed regression approaches which consider the effect of variations and uncertainties on fiber attenuation, non-linear coefficients, or amplifier noise figure per span, to estimate QoT. Thrane et al. [31] showed the benefits of using neural networks and Support Vector Machines (SVM) for modulation-format classification and GSNR estimation. In Morais and Pedro [32], effectiveness of various ML models such as k-nearest neighbors, logistic regression, and SVM for QoT estimation were described. Panayiotou et al. [33] investigated the performance of a data-driven QoT model on dynamic and unicast metro optical networks capable of supporting both unicast and multicast connections. The model predicts nearly-accurate QoT of lightpaths that need to be established. Other works, such as [34,35,36,37], show the application of ML to predict GSNR of lightpaths where real and synthetic data were used. Our work uses the predicted GSNR for lightpath provisioning and re-estimates GSNR using the ML model during migration to MB.

Operators choose to migrate to MB networks to sustain traffic growth. However, upgrading the entire network at once can incur large CapEx and Operational Expenditures (OpEx). Prior works, [6, 17, 38,39,40,41], have proposed cost models and upgrade strategies for MB expansion. Souza et al. [38] focused on a pay-as-you-grow order of band deployment in MB networks. Shariati al. [6] developed a cost model to assess migration scenarios from C band to C+L and C+L+S bands. Moniz et al. [39] emphasized the importance of link selection by proposing a framework in which fiber-capacity upgrade is geographically dependent. Ahmed et al. [17] modeled a multi-period batch upgrade from C to C+L networks by considering traffic demands and annual traffic growth, and discussed the significance of selecting appropriate links for C+L upgrade.

Our work focuses on C+L networks where all links initially operate in C band. Building on previous research, we use a link-selection technique from [17] that groups links into batches based on their spectrum utilization. This enables network upgrades from C to C+L with minimal cost. To further reduce upgrade cost, Ahmed et al. [17] extended their work to [18] and introduced a mechanism of distance-based re-provisioning, which delays upgrades by moving lightpaths, from C band to L band, based on their path length. For instance, upgrading the network in year 3, year 5, and year 10 may reduce the overall network upgrade cost. To show the effectiveness of our newly-proposed re-provisioning strategies, we use link-selection technique from [17] and upgrade times from [18]. Accordingly, Ahmed et al. [18] is significantly extended in this work by demonstrating that selectively moving lightpaths based on their QoT can reduce the number of disrupted connections in the network and hence limit the adverse impact of re-provisioning.

3 ML-based regression models for QoT estimation

The QoT of an optical lightpath is usually expressed using GSNR as in Eq. (1). Our study relies on known ML models to estimate GSNR of lightpaths. In this regard, Sect. 3.1 describes the physical-layer model used to generate data for training purposes. Note that, since the network is upgraded in batches, we need two estimators—a C-band estimator and a C+L-band estimator—which are described in Sect. 3.2.

3.1 Physical-layer model

Transmission in MB networks causes additional signal impairments. Our physical-layer model accounts for both ASE noise added by the in-line EDFA and for NLI. In C+L-band systems, the ISRS effect causes a phase-independent power transfer from higher frequencies to lower frequencies, which contributes to NLI. Additionally, the power profile of every active channel evolves over time, which also contributes to NLI. Our proposed estimation model considers the above factors while calculating GSNR of every lightpath in every span.

GSNR is calculated based on the actual load of the spectral bands (C and L). Parameters such as frequency, number of active channels, and GSNR are recorded for every lightpath. NLI interactions increase with number of active channels. Therefore, when a link is upgraded to include L band, the NLI and ISRS interactions will degrade the GSNR of existing lightpaths in C band. GSNR of a lightpath deployed on a frequency \(f_{z}\) and launch power \({P_{ch}^i}\) can be calculated as follows [42]:

$$\begin{aligned} \dfrac{1}{GSNR(f_z)} = \sum _{i=1}^{N_{L}} \bigg (\dfrac{P_{\textrm{ASE}}^{i} + P_{NLI}^{i}(f_z)}{P_{ch}^i} + \dfrac{P_{\textrm{ASE}}^{R_{i}} (f_z)}{P_{ch}^i} \bigg ), \end{aligned}$$
(1)

where \(P_{\textrm{ASE}}^i\) is total ASE noise from in-line EDFAs, \(P_{NLI}^i(f_z)\) is cumulative NLI due to ISRS in \(i^{th}\) optical link, \(P_{\textrm{ASE}}^{R_{i}}(f_z)\) is ASE noise generated by a ROADM (post amplification) in link i, and \(N_{L}\) is number of links traversed by the lightpath. The considered physical-layer model restores the signal loss due to fiber attenuation at every in-line amplifier. In addition, the power profile changes due to ISRS is compensated at every ROADM. Therefore, the received optical signal power for every lightpath matches the launch power. Hence, during GSNR calculations, we considered the same received optical power for every lightpath.

Our work assumes that NLI is accumulated incoherently across multiple spans. The following equation is used to calculate noise power \((P_{NLI})\) for all intermediate links based on their current state of spectral occupancy [29]:

$$\begin{aligned} P_{NLI}^i (f_z) = P_{ch}^3 N_{s}^i \eta _1 (f_z), \end{aligned}$$
(2)

where \(P_{ch}\) is channel launch power, \(N_{s}^i\) is number of spans in \(i^{th}\) link, \(\eta _1\) is NLI co-efficient for a single span, and \(P_{NLI}^i (f_z)\) is NLI power of \(i^{th}\) link for the channel of interest (COI) \(f_z\). \(\eta _1\) denotes total noise contribution across all the active interfering channels [29] which is given by:

$$\begin{aligned} \eta _1 (f_z) = \eta _{XPM}(f_z) + \eta _{SPM}(f_z), \end{aligned}$$
(3)

where \(\eta _{SPM}\) represents self-channel interference, and \(\eta _{XPM}\) represents cross-channel interference. Closed-form expressions for \(\eta _{SPM}\) and \(\eta _{XPM}\) are derived in [13], as follows:

$$\begin{aligned} \begin{aligned} \eta _{SPM}(f_z) \approx \dfrac{4}{9} \dfrac{\pi \gamma ^2}{B_{z}^{2} \phi \bar{\alpha } (2\alpha + \bar{\alpha })}\\ .\left[ \dfrac{T - \alpha ^2}{\alpha }{{\,\textrm{asinh}\,}}\left( \dfrac{\phi B_{z}^{2}}{\pi \alpha }\right) + \dfrac{A^2 - T}{A}{{\,\textrm{asinh}\,}}\left( \dfrac{\phi B_{z}^{2}}{\pi A}\right) \right] \end{aligned} \end{aligned}$$
(4)
$$\begin{aligned} \begin{aligned}&{\eta _{XPM}(f_z)} \approx \dfrac{32}{27} \sum _{k=1,k\ne z}^{N_{ch}} \left( \dfrac{P_k}{P_{ch}}\right) ^2 \dfrac{\gamma ^2}{B_{k} \phi _{z,k} \bar{\alpha } (2\alpha + \bar{\alpha })}\\&.\left[ \dfrac{T_{k} - \alpha ^2}{\alpha }{{\,\textrm{atan}\,}}\left( \dfrac{\phi _{z,k} B_{z}}{\alpha }\right) + \dfrac{A^2 - T_{k}}{A}{{\,\textrm{atan}\,}}\left( \dfrac{\phi _{z,k} B_{z}}{A}\right) \right] , \end{aligned} \end{aligned}$$
(5)

where \(N_{ch}\) symbolizes total number of active channels. The effect of \(\eta _{XPM}\) increases with higher values of \(N_{ch}\). \(P_{k}\) is power of \(k^{th}\) interfering channel, \(\gamma\) is fiber non-linear co-efficient, \(\phi _{z,k}\) is phase mismatch term between \(k^{th}\) interfering channel and COI, and \(T_k\) indicates the frequency-dependent constant of \(k^{th}\) channel for ISRS power transfer [13].

3.2 C and C+L-band QoT estimators

In previous work [18], GSNR calculation of a lightpath assumed that all channels in a route are occupied (fully-filled spectrum). Here, we observe that, it is important to calculate GSNR with growing traffic so that a network operator, given the state of the network, can assess the current QoT of a lightpath. Hence, in this work, we estimate the GSNR achieved for the actual current load in the network. Since repeating QoT estimations for a large number of lightpaths every time a network state changes could lead to unsustainable computational burden, we adopt a supervised ML model for QoT estimation, leveraging a well-known Random-Forest algorithm. The proposed model is fed with features that represent the state of the network: route, COI, number of intermediate links or hop counts, distance between source and destination, and number of active interfering channels in C or L band. To depict the route in which a lightpath operates, we encode all links of a route. ML algorithms require numerical inputs for data processing. Hence, we choose to encode a route in binary, i.e., if the lightpath traverses a link, we assign a binary value \('1'\) to the link variable, else \('0'\). Next, we discuss the necessity of using two estimators for GSNR estimation.

Since network upgrade occurs in batches [18], with each batch containing a set of links, the network will exist in a mixed state, where certain links will operate only in C band, while others are capable of operating in both C and L bands. Consequently, it becomes imperative to employ two distinct estimators to ensure necessary GSNR estimation, accounting for the impact of both C and L bands. We accomplish this by using the physical-layer model detailed in Sect. 3.1 to generate synthetic data for C and C+L band transmission, while considering the simulation parameters discussed in Sect. 5.1.

We now discuss an example on how different links are encoded during multi-period batch upgrade for model training. In Fig. 1a, blue links operate in C band and red links operate in C+L band. For each link, total number of channels and number of active channels are known. Consider lightpath \(\lambda _{1}\), which is provisioned over links AF, FE, and ED (named \(e_{6}\), \(e_{5}\), and \(e_{4}\), respectively). These links are assigned value \('1'\), while other links in the network are assigned with \('0'\). If the link variables (e) are arranged in a matrix as [\(e_{1}\), \(e_{2}\), \(e_{3}\), \(e_{4}\), \(e_{5}\), \(e_{6}\), \(e_{7}\), \(e_{8}\)], then the lightpath is encoded as [0, 0, 0, 1, 1, 1, 0, 0]. Since there are eight links in the network topology (Fig. 1a), a route can be expressed using eight binary variables. This encoding technique allows the model to effectively capture the presence or absence of a connection. The input to the estimator is an array composed of link variables and other parameters required to predict GSNR. If a route operates only in C band (e.g., \(\lambda _{1}\) in Fig. 1a), a C-band estimator is used. Similarly, if all links of the route are upgraded to C+L (e.g., \(\lambda _{2}\) in Fig. 1a), then a C+L-band estimator would be used.

Fig. 1
figure 1

Two scenarios of network operation

Full size image

Now, let us consider a scenario in which a lightpath traverses a route containing an upgraded link. For example, consider a lightpath \(\lambda _{3}\) going through links \(e_{1}\), \(e_{2}\), and \(e_{3}\). As shown in Fig. 1a, only link \(e_{2}\) is upgraded to C+L. In such case, we calculate the GSNR of the entire route on a per-link basis, i.e., links in C and C+L are fed into respective estimators. Using Eq. 1 presented in Sect. 3.1, GSNR of lightpath \(\lambda _{3}\) can be calculated as shown as follows:

$$\begin{aligned} GSNR_{\lambda _{3}}^{-1} = GSNR_{e_{1}}^{-1} + GSNR_{e_{2}}^{-1} + GSNR_{e_{3}}^{-1} \end{aligned}$$
(6)

By using historical data of relevant network features (for training and validation) and tuning the model for optimal performance, GSNR can be estimated. The predicted GSNR can be used to estimate the impact of new lightpaths in the network. These values, in turn, are used to determine lightpath capacity (as shown in Table 1). To improve model prediction, we conduct an exhaustive search to optimize the ML parameters that minimize the loss function of the algorithm. We evaluate the performance of the model according to the following metrics: R-squared (\(R^2\)), mean squared error (MSE), and mean absolute error (MAE). Both models have an \(R^2\) score higher than 96%, where \(R^2\) represents the proportion of variance in GSNR explained by the network features used to train the QoT estimator. The C-band estimator exhibits an MSE of 0.1725 and an MAE of 0.2808, while the C+L-band estimator yields an MSE of 0.5698 and an MAE of 0.5126.

4 GSNR-aware re-provisioning

4.1 Problem description

In this section, we describe the problem of re-provisioning in MB optical networks, then we propose two GSNR-aware re-provisioning strategies. These strategies move the lightpaths (from C to L band) based on the signal quality with the aim of reducing the overall disruption in the network. To implement the strategies, we adopt a multi-period upgrade strategy and upgrade times from [17] and [18], respectively.

Expansion to MB, which involves network upgrades, comes at a cost. Upgrading the entire network at once to address concerns of growing network traffic will lead to a high upgrade cost. Instead, by carefully selecting a set of links in a network, traffic growth could be sustained. In this regard, Ahmed et al. [17] proposed a multi-period, batch-upgrade strategy (where each batch contains a subset of links for upgrade), which reduces network upgrade cost over time. By sorting links in decreasing order of their spectrum utilization and grouping a set of links, network upgrades from C to C+L can be significantly delayed, thereby further reducing the upgrade cost. It was also established, for the parameter settings considered in Ahmed et al. [17], that upgrading the network in three batches would be most beneficial in terms of cost. To determine the timing of upgrade of each batch, extensive statistical analysis was conducted, guided by a target blocking probability set by the network operator.

While multi-period network upgrades lead to lower network upgrade cost, they cause the network to exist in a mix of C and C+L links. In doing so, lightpaths may exist on routes which contain upgraded links (e.g., \(\lambda _3\) in Fig. 1a). After each batch upgrade, the network operator will likely continue to serve most of the requests in C band, as only a subset of links can accommodate requests in L band. Hence, to maximize availability of C-band spectrum and delay future network upgrade, we choose to move some of the existing lightpaths in C band to L band, if possible.

In this regard, Ahmed et al. [18] proposed a re-provisioning strategy that relied on distance to delay network upgrades, thereby lowering network upgrade cost further. Although re-provisioning helps in lowering upgrade cost, it adds to an important practical problem of disruption. This so-called disruption (denoted as \(N_{Disruption}\)) is an effect occurring due to three factors, namely: Re-provisioning (denoted as \(N_{Re-provisioned}\)), Provisioning Overflow requests (denoted as \(N_{Overflow}\)), and Re-adjustment (denoted as \(N_{Re-adjusted}\)), where N is the number of lightpaths. Hence, disruption in a network can be computed as:

$$\begin{aligned} N_{Disruption} = N_{Re-provisioned} + N_{Overflow} + N_{Re-adjusted} \end{aligned}$$
(7)

In this study, re-provisioning, re-adjustment, and provisioning of Overflow requests are initiated after each batch upgrade in the network. To demonstrate how/when re-provisioning (the first factor in disruption) is triggered, we consider the following scenario: if a lightpath \(\lambda _3\) originates from node A and terminates at node D (in Fig. 1a), \(\lambda _3\) cannot be re-provisioned to L band, as not all links in the route have been upgraded. On the contrary, a lightpath \(\lambda _2\) starting at node B and terminating at node C could be moved to L band. However, moving a lightpath from one band to another comes at the cost of sacrificing its signal quality (GSNR).

Table 1 GSNR Classification for Modulation Assignment [28]
Full size table

GSNR of a lightpath decides the modulation format it supports. Usually, modulation format of a lightpath supports a range of GSNRs, as shown in Table 1. Growing network traffic and change in spectrum occupation (e.g., due to link upgrade to L band) can cause GSNR of lightpaths to degrade during their lifetime. A degraded lightpath needs to either be re-adjusted (i.e., modulation format should be down-shifted) or an additional overflow request must be provisioned on a new lightpath. Section 4.2 provides an example for overflow and re-adjustment, the second and third factors in disruption, respectively. As network traffic increases, it could impact existing lightpaths due to NLI effects, which leads to GSNR degradation. Hence, it is necessary to monitor lightpaths based on GSNR degradation.

4.2 Strategies for re-provisioning

We propose two GSNR-aware re-provisioning strategies, namely, Margin-Aware and Budget-Based. MA re-provisioning allows a network operator to move a lightpath to L band based on its proximity to the lower-bound GSNR value for the corresponding modulation format. Consider a lightpath \(\lambda _{4}\), as shown in Fig. 1b, that was provisioned in C band with an GSNR of 23.5 dB. Assume that the first batch of links was upgraded, and it contained all links on which \(\lambda _{4}\) is provisioned. We now re-estimate the GSNR of \(\lambda _{4}\) and find it to be 22 dB, which is close to the threshold (21.6 dB) as seen in Table 1. This lightpath is a good candidate to be re-provisioned, as lightpaths whose GSNR is close to the threshold are more likely to be affected due to NLI (with increasing traffic) and will anyway drop to a lower modulation format (and hence be disrupted) regardless of them being re-provisioned.

Alternatively, if a network operator has a budget based on the number of lightpaths that could be moved, BB re-provisioning may be employed. In this approach, like MA, we calculate the GSNR margin of lightpaths and select lightpaths whose margin is closest to the threshold. We continue to select and re-provision such lightpaths until a budget is reached.

After each batch upgrade, GSNR re-estimation is required for all existing lightpaths whose links have been upgraded. Existing degraded lightpaths may encounter the following scenarios: (a) Overflow requests can be provisioned on new lightpaths; and (b) C-band lightpaths can be re-adjusted.

Now, let us consider an example for overflow requests. Loss in signal quality can cause lightpaths to possibly drop modulation formats, which may lead to reduced capacity. This reduced capacity causes some requests to overflow and such requests need to be provisioned on new lightpaths. Consider the following example: suppose a lightpath \(\lambda _{5}\), as shown in Fig. 1b, has a GSNR of 25 dB when provisioned in C band and based on Table 1, has a corresponding data rate of 300 Gbps. Since we assume all lightpaths to have a uniform data rate of 100 Gbps, \(\lambda _{5}\) can serve at most three requests. Assume that subsequent lightpaths are provisioned thereafter, and we re-estimate the GSNR of \(\lambda _{5}\) to be 23 dB. This indicates that \(\lambda _{5}\) can now serve at most two requests. Hence, one of the three requests needs to be served by provisioning a new lightpath.

Now, let us consider an example for re-adjustment of lightpaths in C band. If a lightpath degrades such that it drops below its current modulation format but can still serve the existing requests, then such lightpaths are re-adjusted. Consider the following example: suppose a lightpath \(\lambda _{6}\), as shown in Fig. 1b, has a GSNR of 27 dB when provisioned in C band and from Table 1, has a capacity of 300 Gbps. Assume \(\lambda _{6}\) serves two requests (of 100 Gbps each). If the GSNR degrades to 23 dB, it indicates that the modulation format has changed (from Table 1). \(\lambda _{6}\) can continue to serve the existing requests with the new modulation format because of the data rate it supports. Hence, this lightpath would only be re-adjusted.

4.3 Algorithms for re-provisioning

We now describe the algorithms for our proposed re-provisioning strategies in MB networks.

Given parameters:

  • G(V, E): Network topology; V set of nodes, E set of links.

  • T: Traffic matrix.

  • \(E'\): Set of links sorted in descending order of spectrum utilization, where \(E' \subset E\).

  • \(E_{\textrm{C}}\): Set of links in C band, where \(E_{\textrm{C}} \subset E\).

  • \(E_{\mathrm {C+L}}\): Set of links in C+L bands, where \(E_{\mathrm {C+L}} \subset E\).

  • \(R_{p}\): Set of connection requests in a lightpath p.

  • \(q_{p}\): GSNR of lightpath p.

  • \(m_{p}\): Modulation format of a lightpath p.

  • \(P_{\textrm{C}}\): Set of lightpaths in C band.

  • \(P'_{\textrm{C}}\): Set of lightpaths in C band sorted based on GSNR proximity.

  • \(P_{\textrm{L}}\): Set of lightpaths in L band.

  • \(q'_{p}\): Lower-bound GSNR threshold of lightpath p.

  • N: Number of upgrade batches.

  • \(k_{N}\): Upgrade time of a batch N.

  • b(N): Set of un-upgraded links in batch number N.

  • B: Set of links upgraded in each batch b; where \(b \in B\).

  • \(X_{N}\): Number of lightpaths that can be moved (budget set by network operator) in each batch number N.

  • Q: GSNR margin set by network operator.

Our algorithms take as input the network topology and number of upgrade batches. We adopt a link-selection technique from [17] and fix the set of links that are upgraded per batch. These links are stored in \(E'\).

Here, we describe Algorithm 1. In this strategy, we assume that the network operator decides to re-provision a certain number (\(X_{N}\)) of existing lightpaths in C band. We obtain \(E'\) which is the set of links sorted in descending order of spectrum utilization, and we upgrade the links in \(E'\) in N batches. When N is greater than 0 and at a fixed upgrade time \(k_{N}\), a set of un-upgraded links, b(N), from \(E'\) is upgraded and is added to \(E_{\mathrm {C+L}}\) (line 3). For each lightpath p in \(P_{\textrm{C}}\), the algorithm extracts the corresponding features to recompute GSNR (\(q_{p}\)), corresponding modulation format (\(m_{p}\)) (lines 5–6), and proximity to the lower GSNR window of the current modulation format (line 7). Lightpaths in \(P_{\textrm{C}}\) are then sorted in ascending order of their GSNR proximity and are stored in \(P'_{\textrm{C}}\) (line 8). For lightpaths in \(P'_{\textrm{C}}\), re-provision (if possible) the ones whose links are upgraded to L band (lines 9–16); and if a request in the re-provisioned lightpath overflows in L band, it is served by a new lightpath (lines 17–19). We count the number of lightpaths that were re-provisioned (line 20) and check if it exceeds the budget, \(X_{N}\) (line 21). We continue to re-provision lightpaths as long as the number is less than the budget decided by the network operator. After the re-provisioning phase, GSNR of the remaining lightpaths in C band, whose links are upgraded to L band, are re-calculated (lines 22–24), and the modulation format is updated accordingly. If a request in a path overflows the lightpath capacity due to the updated GSNR, it is served by a newly-provisioned lightpath (lines 25–27). If the GSNR of the lightpath changes such that its modulation format remains unaltered, the request remains in the same lightpath with the updated GSNR. After the first batch upgrade, new requests are allocated in L band first. We store the set of upgraded links from each batch in B (line 28). The algorithm checks for any remaining batches to upgrade (line 29); if so, it continues to upgrade until all links in the network are upgraded (line 1).

figure i

Algorithm 1 Budget-Based re-provisioning

Now, we describe Algorithm 2. This algorithm works in a similar way to Algorithm 1, except that the network operator provides a GSNR margin (Q) instead of a budget (\(X_{N}\)). Then, we check if each lightpath p in \(P_{\textrm{C}}\) is eligible to be re-provisioned (lines 4–5) and if its GSNR (\(q_{p}\)) lies within the GSNR margin (lines 9–10). All such lightpaths would be re-provisioned to L band (lines 11–14). Overflow requests of re-provisioned lightpath p will be served by a new lightpath in L band (lines 15–17). After the re-provisioning phase, GSNR of all remaining lightpaths in C band will be updated and the overflow requests will be served by newly-provisioned lightpaths in C band (lines 18–23). The upgraded links from each batch are stored in B (line 24). The algorithm checks for remaining batches (line 25), and continues to upgrade until the entire network is upgraded (line 1).

figure j

Algorithm 2 Margin-Aware re-provisioning

Time complexities of both Algorithms 1 and 2 are: \(O(N. |P_{\textrm{C}}|. T. log(n))\), where N is the number of batches, T is the number of decision trees in the Random-Forest model, and n is the number of samples in the dataset.

Fig. 2
figure 2

BT-UK network: link lengths in kilometer (km)

Full size image

5 Results and discussion

5.1 Simulation setup

An event-driven, custom-built Java simulator is used to emulate an upgrade environment from C to C+L bands while incorporating physical-layer modeling. For our simulation, the BT-UK network (Fig. 2) is considered, which consists of 22 nodes and 35 links that are bi-directional. The average link distance in the network is about 147 km. A uniform channel launch power of 0 dBm and ROADM loss of 18 dB are assumed [29]. To build the QoT Estimator, synthetic data were generated using the physical-layer model in Sect. 3.1, while considering the system parameters from Table 2. Using these parameters, we generate 1000 datapoints for C and C+L bands separately. These datapoints were subsequently partitioned, with 70% allocated for training and 30% for testing. Routing and spectrum selection are carried out using k-shortest path and first-fit methods, respectively. Modulation format of each lightpath is selected according to the GSNR window shown in Table 1. We run the simulation for 20 seeds, each with 3000 demands.

Table 2 System Parameters
Full size table

The network topology in Fig. 2 along with a traffic matrix are provided as inputs. Incoming connection requests are allocated with available modulation format based on the physical-layer modeling of spectrum bands. Initially, the network operates exclusively in C band, where all connection requests are provisioned. We adopt a multi-period upgrade strategy from [17] to support transmission in C+L. After each batch upgrade, new requests are allocated (if possible) in L band first.

Traffic in backbone networks is typically quasi-static. To resemble traffic flow, a biased traffic matrix of the BT-UK network is used (an incrementally-growing traffic with a growth factor of 30% per year [18]). Source-Destination pairs are selected according to a gravity model consisting of the traffic generation probability of each node [17]. Data rate of all requests is assumed to be uniform, and 3000 connection requests of 100 Gbps are considered for simulation [17].

5.2 Baseline strategies

To evaluate the effectiveness of our proposed GSNR-aware re-provisioning strategies, we compare them with a set of distance-based re-provisioning strategies introduced in [18]. In these distance-based strategies, re-provisioning of existing C-band lightpaths to L band is guided by the evaluation of their path lengths. By calculating the median path length of all allocated ligthpaths, various versions of the distance-based strategy presented in [18] are listed as follows:

  • R: In this strategy, all existing lightpaths whose links are upgraded to L band are re-provisioned.

  • \(R^{long}\): In this strategy, we identify and re-provision all lightpaths whose path length is longer than the median path length of existing lightpaths.

  • \(R^{short}\): In this strategy, we identify and re-provision all lightpaths whose path length is shorter than the median path length of existing lightpaths.

5.3 Total disruption in the network

In this subsection, we assess the impact of the proposed GSNR-aware re-provisioning strategies compared to the distance-based re-provisioning strategies by evaluating the disruption metric in the network. It is calculated using Eq. 7 (a detailed description of the factors involved in disruption is provided in Sects. 4.1 and 4.2).

To represent the variations of the Budget-Based and Margin-Aware re-provisioning strategies, we use notations \(BB_{x}\) and \(MA_{y}\), respectively. Here, x indicates the budget or the percentage of the existing C-band lightpaths (whose GSNR is closest to the lower limit of their GSNR window as per Table 1) that can be moved to the L band; and y indicates the GSNR margin set by the network operator such that the lightpaths within y dB of their GSNR threshold (as per Table 1) can be moved to L band.

With BB re-provisioning, we show in Fig. 3 that \(BB_{5\%}\) yields the least disruption in the network by re-provisioning 5% of the lightpaths that are close to the GSNR threshold. In comparison to \(R^{short}\), \(R^{long}\), and R, \(BB_{5\%}\) results in about 22, 19, and 29% lower disruption, respectively. As the budget (i.e., the number of lightpaths that can be moved) increases (e.g., from \(BB_{5\%}\) to \(BB_{15\%}\)), more lightpaths are re-provisioned, causing higher disruption in the network; however, the disruption still remains lower compared to the distance-based re-provisioning strategies. Unlike the distance-based strategies, BB takes into account the QoT of lightpaths and restricts the number of lightpaths that may be re-provisioned after every batch upgrade. Hence, BB is an effective strategy to minimize disruption in the network.

With MA re-provisioning, we observe that disruption in the network is least when lightpaths whose GSNR is within 0.1 dB of the GSNR threshold (\(MA_{0.1}\)) are re-provisioned. As shown in Fig. 3, compared to \(R^{short}\), \(R^{long}\), and R, \(MA_{0.1}\) results in about 27, 24, and 34% lower disruption, respectively. As GSNR margin increases (e.g., from \(MA_{0.1}\) to \(MA_{0.5}\)), more lightpaths become candidates for re-provisioning, which leads to higher disruption in the network, but it still remains lower than the disruption caused by distance-based re-provisioning. Unlike distance-based strategies, MA preemptively moves lightpaths that are likely to drop to lower modulation formats and thus avoids those lightpaths from contributing to disruption. Hence, MA is an effective strategy to minimize disruption in the network.

Among the distance-based re-provisioning strategies, R causes the highest disruption as it re-provisions all candidate lightpaths. \(R^{long}\), which re-provisions only the longer lightpaths to the L band, results in the least disruption. However, to re-provision longer lightpaths, additional links must be upgraded to ensure sufficient bandwidth availability, resulting in higher upgrade cost. On the other hand, \(R^{short}\) re-provisions lightpaths with shorter path lengths, causing higher disruption than \(R^{long}\) but lower disruption than R. By re-provisioning only shorter lightpaths, network operations can continue in the C band, which delays future batch upgrades and reduces overall upgrade cost. Thus, \(R^{short}\) is the most cost-effective option [18]. In this context, it is most relevant to compare our proposed GSNR-aware re-provisioning strategies to \(R^{short}\) to evaluate their effectiveness in mitigating disruptions.

Besides disruption, we also evaluate the number of requests that were blocked in the network. As shown in Fig. 4, \(BB_{5\%}\) blocks about 11% fewer requests compared to \(R^{short}\), and \(MA_{0.1}\) blocks 17% fewer requests compared to \(R^{short}\). Note that increasing the budget in BB or the GSNR margin in MA results in higher disruption, which leads to more blocked requests. Also, we observe that \(MA_{0.1}\) blocks fewer requests compared to \(BB_{5\%}\), making it a better strategy.

Fig. 3
figure 3

Total lightpath disruption in the network due to different re-provisioning strategies

Full size image
Fig. 4
figure 4

Total lightpath disruption and number of blocked requests in the network due to different re-provisioning strategies

Full size image

5.4 Evaluation of different factors of disruption

This section evaluates the potential impact of the proposed GSNR-aware re-provisioning strategies on the different factors involved in disruption.

5.4.1 Impact of re-provisioning on disruption

Table 3 highlights the effectiveness of BB and MA strategies in terms of cumulative lightpaths re-provisioned in the network. With BB strategy, we observe that \(BB_{5\%}\), compared to \(R^{short}\), significantly reduces the number of re-provisioned lightpaths by approximately 54% after the first batch upgrade, by 58% after the second batch upgrade, and by 74% after upgrading all links in the network. In addition, we see that, as the budget increases (e.g., from \(BB_{5\%}\) to \(BB_{15\%}\)), more lightpaths are re-provisioned to L band in the network. Although re-provisioning more lightpaths is desirable to delay future upgrades and lower the upgrade cost, a network operator must consider the consequences of disturbing a large number of existing lightpaths as they can increase disruption. Hence, given a certain network upgrade cost, a network operator must aim to minimize the total disruption in the network.

Table 3 Cumulative lightpaths re-provisioned with \(R^{short}\), BB, and MA
Full size table
Table 4 Cumulative lightpaths re-adjusted with \(R^{short}\), BB, and MA
Full size table
Table 5 Cumulative overflow requests provisioned with \(R^{short}\), BB, and MA
Full size table

With MA strategy, we show that, compared to \(R^{short}\), \(MA_{0.1}\) yields significant reduction of almost 95% and 94% in the number of re-provisioned lightpaths after the first and second batch, respectively. Furthermore, upgrading all links in the network resulted in 89% decrease in the number of re-provisioned lightpaths. Increasing the GSNR margin (e.g., from \(MA_{0.1}\) to \(MA_{0.5}\)) results in higher number of re-provisioned lightpaths in every batch. Therefore, a network operator must carefully select the GSNR margin to minimize disruptions when moving a certain volume of lightpaths.

As more lightpaths are added to accommodate traffic growth, degradation of GSNR in these lightpaths due to NLI may become increasingly significant. This trend is demonstrated for MA re-provisioning in Table 3. For instance, in \(MA_{0.1}\), only three lightpaths could be re-provisioned after the first batch upgrade. However, with subsequent batch upgrades, more lightpaths are affected and need to be re-provisioned (eight in the second and 35 in the third batch). This could also be attributed to the fact that only few links are upgraded after the first batch, resulting in fewer eligible lightpaths for re-provisioning. Note that this trend, which is consistent with MA with increasing GSNR margin (e.g., from 0.1 dB to 0.5 dB), contributes to the increasing disruption in the network (as shown in Fig. 3).

5.4.2 Impact of re-adjustment and overflow requests on disruption

With increasing network traffic, lightpaths may experience degradation in GSNR, which may necessitate their re-adjustment or the provisioning of overflow requests on new C-band lightpaths. Tables 4 and 5 show the number of lightpaths re-adjusted and overflow requests that were provisioned on new lightpaths after every batch upgrade, respectively. As more lightpaths are re-provisioned (in \(R^{short}\) and \(BB_{x}\)), we see that the number of lightpaths that are re-adjusted or new lightpaths that were provisioned to support overflow requests are lower. However, employing MA re-provisioning with low GSNR margins may still result in significant re-adjustment and overflow, particularly during the first and second batches due to the large number of lightpaths remaining in the C band. Increasing the GSNR margin, e.g., to 1 dB, 1.5 dB, or higher, follows a pattern which is similar to BB. Although re-provisioning is a major factor that contributes to disruption, re-adjustment and provisioning of overflow requests are by-products of GSNR degradation and cannot be ignored.

6 Conclusion

We investigated different re-provisioning strategies to be employed during the upgrade of a C-band-only optical backbone network to a C+L network. We adopted a multi-batch upgrade strategy and leveraged Machine Learning techniques for QoT estimation of lightpaths. We proposed two GSNR-aware re-provisioning strategies, namely, Budget-Based and Margin-Aware, to minimize disruption in the network. In Budget-Based re-provisioning, a network operator sets a budget on the number of lightpaths to be re-provisioned while in Margin-Aware re-provisioning, GSNR margin is used as a parameter to re-provision lightpaths. We compared the proposed strategies with a baseline distance-based strategy to evaluate disruptions inflicted in the network. Numerical results show that disruptions are reduced by almost 22% with Budget-Based re-provisioning and by almost 27% with Margin-Aware. Furthermore, the proposed strategies are capable of accommodating more requests in the network. Results show decrement of about 11 and 17% in the number of blocked requests with Budget-Based and Margin-Aware re-provisioning, respectively. Hence, we showed how a network operator can reduce disruptions in the network while keeping the upgrade cost to a minimum.