Design of Filterless Metro-Aggregation Networks Resilient to Frequent Local Power Outages

Design of Filterless Metro-Aggregation Networks Resilient to Frequent Local Power Outages Jo˜ ao Pedro(1,2), Mohammad M. Hosseini(3), Antonio Napoli(3), Johan B¨ ack(4), Ronald Moorcroft(5) (1) Nokia, Optical Networks, Carnaxide, Portugal, [email protected] (2) Instituto de Telecomunicac¸ ˜ oes, Instituto Superior T´ ecnico, Lisboa, Portugal (3) Nokia, Optical Networks, Munich, Germany, [email protected] (4) Nokia, Optical Networks, Sweden; (5) WIOCC, Johannesburg, South Africa Abstract—Metro-aggregation networks have unique requirements: capacity and cost targets in between those of the access and metro-core networks they interconnect, and survivability to (at least) single failures. Meeting these requirements can be achieved via low-cost pluggable transceivers and cost-effective optical nodes, deployed over a horseshoe topology. By maintaining connectivity between each (leaf) node and the hub nodes at the extremes of the horseshoe, survivability to single link or node failures is guaranteed. However, in certain countries/regions, frequent power outages or enforcement of load shedding can make these networks temporarily vulnerable to single failures. Recently, it has been shown that resiliency against these events can be improved by adopting a filterless node architecture and minimizing the utilization of active devices in the express path of the optical signals. This paper extends the seminal work by proposing extensions to the original design framework that allow it to cover a larger number of network scenarios. Moreover, it reports the outcome of a comprehensive set of network simulations that provide insight into the impact that the coupler types used to realize the optical nodes have on both the number of required optical amplifiers and the vulnerability to local power outages and load shedding. Index Terms—coherent pluggable transceivers, failure survivability, optical networks, amplifier placement, power budget. I. INTRODUCTION In the landscape of (fixed) telecommunications networks, metro-aggregation networks have the key role of distributing/aggregating traffic to/from multiple access networks. The relevance of this role justifies the adoption of a network architecture that guarantees survivability to the most common failure scenarios (i.e. single link or node failure). This can be achieved by adopting a horseshoe physical topology, having a replica of the router/switch at the end nodes of the horseshoe – hereafter designated as hub nodes – and setting up a connection between each transit horseshoe node – hereafter designated as leaf nodes – and each hub node [1], [2]. The resulting pair of connections is disjoint and, hence, the service to each leaf node is protected against any of these events: single link failure, single hub node failure, and single failure at one of the other transit nodes. This work received funding from the EU Horizon 2020 project SEASON under grant agreement No. 101096120, FCT/MECI through national funds and when applicable co-funded EU funds under UID/50008: Instituto de Telecomunicac¸ ˜ oes. Although the volume of traffic in metro-aggregation networks is relatively small (i.e. compared to fiber capacity), the traffic growth being predicted [3] will impact them and drive the use of high-capacity coherent pluggable transceivers, instead of legacy intensity modulation-direct detection (IMDD) transceivers [4]. Noteworthy, since the traffic pattern in these networks is hub-and-spoke, recently proposed coherent point-to-multipoint (P2MP) transceivers, enabled by digital subcarrier multiplexing (DSCM) [5], can support this pattern more efficiently than the traditional point-to-point (P2P) transceivers. With DSCM, it becomes possible to transmit from the leaf nodes multiple low-rate traffic flows and receive them at an hub node with a single high-capacity device, leading to significant improvements in cost, power consumption, and space utilization [6]. Hence, future-proofing the architecture of metro-aggregation networks should consider the utilization of P2P and P2MP coherent transceivers. The filterless architecture, which differs from traditional wavelength division multiplexing (WDM) networks by employing passive optical splitters and combiners and a limited number of fixed filters instead of reconfigurable add/drop multiplexers (ROADMs) [7], is a promising candidate to realize metro-aggregation networks based on coherent transceivers. Firstly, the low nodal degree of horseshoe topologies is ideal for filterless networks, which tend to scale poorly with nodal degree. Secondly, since a filterless architecture leads to higher accumulation of amplified spontaneous emission (ASE) noise – each added (unfiltered) signal contributes with noise to existing ones – the relatively small number of nodes and low spectral usage that characterize metro-aggregation networks [8] mitigates the performance degradation due to this effect. Thirdly, the simplicity and low cost of passive splitters/combiners (when compared to filters) contributes to meeting the stringent cost targets set for these networks [6]. Finally, the filterless architecture is well-suited to optically aggregate multiple subcarriers (SCs) from the leaf nodes to hub nodes when using P2MP transceivers, since the narrow spectral width of SCs and the need to have them packed tightly together is not supported by state-of-the-art optical filters [9]. In typical conditions, the redundancy offered by the horseshoe topology is enough to assure high service availability, since the likelihood of two simultaneous and independent failures is expected to be almost negligible [10], [11]. This is because the probability that a fiber is cut or a network element fails is very low [12] and the power grid that serves the network is assumed to be reliable. However, in certain countries/regions, the latter assumption may not hold. For instance, stabilizing South Africa’s power grid is currently being achieved at the expense of load shedding, which consists of selectively cutting off power to certain areas, forcefully reducing demand to match limited supply. These events occur on a pre-defined schedule and last a few hours (e.g., 2-4 hours), albeit sometimes the schedule changes with short or even no notice [13]. Keeping the network infrastructure available in these conditions requires substantial investments in backup generators, battery banks, and solar panels. An industry report highlighted that, in 2023, addressing the unreliability of the power grid consumed around 12% of South Africa’s network operators’ capital expenditures (CapEX) [14]. Still, the value and visibility of the backup power equipment coupled with the fact that the community in the vicinity of these sites does not benefit from backup power sources during load shedding has led to rampant theft and vandalism [15], resulting in significant losses and additional investments to secure the sites. Another region where frequent local power outages occur is Ukraine. Although the deployment of backup systems has been critical to address power outages [16], adopting architectures that confine the impact of these outages would be beneficial to the overall resilience of critical communication services. Given the geographical footprint of metro-aggregation networks, the impact of a load shedding instance, or a localized power outage, may involve one or a few leaf nodes depending on the level of load shedding and the network nodes’ location. Besides the inevitable impact on local residential and business users who cannot power their devices anyhow (e.g., halt of fixed access services), in the absence of backup power sources, the express signals in the horseshoe network are also disrupted. This means that leaf nodes downstream of the directly impacted node(s) cannot communicate with one of the hub nodes, becoming vulnerable to single-failure events. Our seminal work [17] addressed this problem by combining the passive coupler devices used to realize a filterless architecture with a parsimonious utilization of optical amplifiers in the express path of the optical signals, allowing to mitigate the number of instances where load shedding/power outage disrupts the connectivity to downstream nodes. In this paper, we extend our previous work [17] by: (1) proposing a design framework that covers a wider set of network scenarios, namely the use of P2P and P2MP transceivers while optimizing amplifiers placement and couplers deployment considering three different coupler type strategies: flexible, semi-flexible, and fixed (the original work only considers P2MP transceivers and flexible coupler type selection); and (2) reporting a comprehensive set of network simulations that provides insight on the impact of the transceiver type and coupler type selection strategy on the total number of required optical amplifiers and the number of sites that provide express path resiliency to frequent local power outages. The remainder of the paper is organized as follows. Section II details the architecture proposed to increase the resiliency of metro-aggregation networks in the presence of frequent local power outages. Section III describes the ILP-based optimization framework, which can be configured for different network scenarios. The simulation results, obtained by applying the design framework to a set of metro-aggregation networks, are presented and discussed in Section IV. Finally, Section V highlights the main conclusions of this work. II. METRO-AGGREGATION NETWORK ARCHITECTURE The horseshoe topology can inherently provide singlelink and single-hub protection due to hub redundancy and transceiver duplication at the leaf nodes to communicate with the hubs via two disjoint paths [2]. By avoiding active devices, such as wavelength selective switches (WSSs), and using passive splitter/combiners instead, the filterless architecture reduces the number of leaf node devices that must be powered. However, optical signals must reach the transceiver at the destination node with a power level above the device’s sensitivity, which requires using optical amplifiers, e.g., Erbium-doped fiber amplifiers (EDFAs), along the transmission path. Figure 1(a) illustrates a 5-leaf node filterless horseshoe network based on a passive 2-by-2 coupler node architecture. Amplifiers can be located before each leaf node (express amplifiers), at the ingress and egress of hub nodes and at the add and drop ports of leaf nodes. Note that each fiber direction carries downstream traffic from one hub and upstream traffic towards the other hub. Given their relevance and larger footprint, hub nodes are assumed to be protected against power outages (e.g., via backup generators or batteries). However, leaf nodes may be deployed in small street cabinets and other locations without access to backup power sources and, therefore, a power outage (deliberate or not) disables the amplifiers of the leaf node. In this circumstance, express amplifiers are more critical than add/drop amplifiers because they amplify signals directed to/generated at multiple leaf nodes, which are outside the area impacted by the power outage. Fig. 1(a) depicts the impact of a fiber cut between leaf nodes 4 and 5 at the time when the area where leaf 2 is located is affected by a power outage. In this case, besides leaf node 2 being without power, leaf nodes 3 and 4 lose connectivity to both hubs. As can be seen from inspecting Fig. 1(a), similar events will occur if the power outage impacts leaf node 1 – leaf nodes 2, 3 and 4 become disconnected – or leaf node 3 – leaf node 4 becomes disconnected. Unfortunately, offering survivability to double failures [18] is cost-prohibitive in this network segment. However, assuming a filterless architecture and in case it is possible to avoid deploying express amplifiers at a sub-set of the leaf nodes, the described vulnerability can be significantly mitigated. For example, consider the case depicted in Fig. 1(b), which assumes that the same metro- aggregation network instance can be realized with express amplifiers only at leaf node 3. In this case, even in the presence of a fiber cut between leaf nodes 4 and 5, a power outage at leaf node 1, 2, 4 or 5, only impacts that leaf node, since the optical signals do not traverse any active device when being expressed at these nodes. Only a power outage at leaf node 3 would have an impact on leaf node 4, which would be disconnected from both hubs. Despite the simplicity of the concept to enhance network resiliency against frequent local power outages by ensuring that express optical signals are not blocked (i.e., only service that start/end at the leaf nodes directly affected by the power outage are impacted), designing a filterless metro-aggregation network based on this principle is not trivial. This is because the feasibility of end-to-end channels set up in the network must be considered to determine the leaf nodes where express amplifier deployment can be avoided and the ones where this is not possible [17]. Given the relatively small number of nodes and short span distances in these networks, previous works focused on minimizing the total number of amplifiers required, by optimizing their location and the coupler type utilized at each leaf node (which can be set to reduce express losses or add/drop losses) [4]. Our recent work [17] described a framework that prioritizes minimizing the number of sites with express amplifiers to improve resiliency against load shedding and local power outages, even though this may be attained at the expense of increasing the total number of amplifiers required to ensure the feasibility of the design. However, the original framework is limited to deployments with P2MP transceivers and assuming full flexibility in terms of selecting the coupler type per leaf node and transmission direction. This work proposes a more general design framework that also supports traditional P2P transceivers and scenarios where, for simplicity of deployment and spare part management, the same type of coupler is imposed at every leaf node or the same sequence of coupler types is imposed for both transmission directions. III. NETWORK DESIGN FRAMEWORK The design framework for load-shedding resilient filterless horseshoe networks is an evolution of the one proposed in [17], fitted with the required modifications to cover the additional use cases mentioned above. The framework comprises an ILP model to ensure that the optimal solution is found (if exists). The objective function of the ILP model includes three terms: •Number of express amplification sites: number of leaf nodes hosting at least one express amplifier, which is representative of the vulnerability to load shedding / local power outages. •Total number of amplifiers: total number of amplifiers deployed at the express and add/drop locations, which is representative of optical signal amplification costs. •Maximum subcarriers (SCs) power difference: this objective is specific to P2MP transceivers. If upstream SCs from different leaf nodes reach the hub’s receiver Hub 1 Hub 2 1 234 5 OUTAGE 2x2 coupler optical amplifier Out-of-service leaf nodes Hub 1 Hub 2 1 234 5 OUTAGE Out-of-service leaf node (a) (b) Fig. 1. Fiber cut during power outage in a filterless horseshoe network with: (a) express amplifiers at every leaf node and (b) minimum number of express amplifiers (only present at leaf node 3). with significantly different power levels, performance can be degraded. This low-priority objective complements a constraint on the maximum SCs power difference and is used to further reduce this difference, when possible. While minimizing all the goals mentioned above would be ideal, in most problem instances they conflict. By using appropriate weights for the terms in the objective function it is possible to set different priorities. Particularly, two scenarios are considered. In the first one, minimizing the number of express amplification sites has a higher priority. This means that the model is set to find a feasible solution that requires the least number of express amplification sites, even if at the expense of demanding a higher total number of amplifiers. Conversely, in the second scenario, minimizing the total number of amplifiers takes precedence, that is, the model will seek to minimize amplification costs. In the following, we present the model’s main input parameters and decision variables. Input Parameters The input parameters of the ILP model are listed below. •Network Topology: –L: Set of leaf nodes. –A: Set of fiber links. •Device Placement parameters: –Gg: EDFA gain range (0 indicates no amplifier). –Hp s: Add/drop and express losses of coupler s. •Path Matrices: –Ml,a d: Binary link-path matrix (|L|×|A|) from Hub1 to leaf nodes; 1if the path from Hub1 to Leaf l contains link a, and 0otherwise. –Ml,a u: Binary link-path matrix (|L|×|A|) from leaf nodes to Hub2; 1if the path from Leaf lto Hub2 contains link a, and 0otherwise. –Nl,lx d: Binary node-path matrix (|L|×|L|) from Hub1 to leaf nodes; 1if the path from Hub1 to Leaf l passes through Leaf lx, and 0otherwise. –Nl,lx u: Binary node-path matrix (|L|×|L|) from leaf nodes to Hub2; 1if the path from Leaf lto Hub2 passes through Leaf lx, and 0otherwise. •Power Levels: –Pl: Launch power per SC (P2MP) or per channel (P2P). –Pn: Nonlinearity power threshold per SC (P2MP) or per channel (P2P). –Ps: Receiver sensitivity (minimum power level at the receiver input). –Px: Maximum power difference tolerance between SCs (only for P2MP). Decision Variables The following decision variables are used in the ILP model: •Variables for Couplers Selection: –∆: Binary variable; for different coupler optimization scenarios ∗Flexible and Semi-flexible: all couplers can be freely optimized for both directions or couplers deployed at each leaf node must be the same for each transmission direction; Binary variable ∆s l,t; 1if coupler sis selected for Leaf lat direction t, and 0otherwise. ∗Fixed: a single coupler must be used for all leaf nodes; Binary variable ∆s;1if coupler sis selected, and 0otherwise. –γp l,t: Loss of port pof the selected coupler in Leaf l at direction t. •Variables for Amplifiers Placement: –µ12 a,g: Binary variable; 1if the express amplifier on link atakes gain gfor the fiber direction Hub1 to Hub2, and 0otherwise. –µ21 a,g: Binary variable; 1if the express amplifier on link atakes gain gfor the fiber direction Hub2 to Hub1, and 0otherwise. –µd1 l,g,µd2 l,g: Binary variables; 1if the drop amplifier at Leaf ltakes gain g(for each of the two possible drop directions), and 0otherwise. –µu1 l,g,µu2 l,g: Binary variables; 1if the add amplifier at Leaf ltakes gain g(for each of the two possible add directions), and 0otherwise. –µb1 g,µb2 g: Binary variables; 1if the booster amplifier at Hub1/Hub2 takes gain g, and 0otherwise. –µp1 g,µp2 g: Binary variables; 1if the pre-amplifier at Hub1/Hub2 takes gain g, and 0otherwise. •Quality of Transmission Variables: –ϕ12d l: Received power per SC (P2MP)/per channel (P2P) at Leaf lcoming from Hub1. –ϕ12u l: Received power per SC (P2MP)/per channel (P2P) at Hub2 coming from Leaf l. –ϕ21d l: Received power per SC (P2MP)/per channel (P2P) at Leaf lcoming from Hub2. –ϕ21u l: Received power per SC (P2MP)/per channel (P2P) at Hub1 coming from Leaf l. •SCs Power Bounds (only for P2MP): –ϵ11,ϵ12: Lower and upper bounds, respectively, for the received power ϕ12u l. –ϵ21,ϵ22: Lower and upper bounds, respectively, for the received power ϕ21u l. •Express Amplification Site Variable: –nl: Binary variable; 1if Leaf lhas at least one express amplifier, and 0otherwise. Equation (1) expresses the objective function of the ILP model. z=w1Ns+Nt+w2[ϵ12 −ϵ11 +ϵ22 −ϵ21](1) where w1and w2are weight factors controlling the priority of each goal. Ns=Plnlrepresents the total number of amplification sites, while Nt=X a X g=1 (µ12 a,g +µ21 a,g)Gg+X l X g X g=1 (µd1 l,g +µd2 l,g +µu1 l,g +µu2 l,g +µp1 g+µp2 g+µb1 g+µb2 g)Gg is the total number of amplifiers. The third term of the objective function represents the sum of the maximum power difference between SCs at the hubs’ receivers. The ILP model comprises the following constraints. X g µY Y XX = 1,∀a∈A or l ∈L(2) X s ∆s l,t = 1 ∀l∈L, t ∈ {12,21}(3a) X s ∆s= 1 (3b) γp l,t =X s ∆s l,t ×Hp s∀l, t, p ∈ {add/drop,exp}(4a) γp l,t =X s ∆s×Hp s∀l, t, p ∈ {add/drop,exp}(4b) ∆s l,′12′= ∆s L+1−l,′21′∀l, s (5) Constraints (2) ensure that a single gain index is selected for each amplifier in the network (where XX and Y Y represent the appropriate index sets for each class of amplifiers). Constraints (3) are used to choose the coupler types as per the coupler scenario. For flexible and semi-flexible scenarios, only constraints (3a) are active while for the fixed coupler scenario, only constraints (3b) are present. Accordingly, constraints (4a) or (4b) assign the resulting loss to each port of the couplers. Constraints (5) are only active when the semi-flexible coupler scenario is being simulated. ϕ12d l=−γadd/drop l,12 −X a AaMl,a d−X lx γexp lx,12Nl,lx d+Pl +X g (µd1 l,g +µb1 g)Gg+X a X g µ12 a,gGgMl,a d∀l∈L (6) ϕ12u l=−γadd/drop l,12 −X a AaMl,a u−X lx γexp lx,12Nl,lx u+Pl +X g (µu1 l,g +µp2 g)Gg+X a X g µ12 a,gGgMl,a u∀l∈L (7) ϕ21d l=−γadd/drop l,21 −X a AaMl,a u−X lx γexp lx,21Nl,lx u+Pl +X g (µd2 l,g +µb2 g)Gg+X a X g µ21 a,gGgMl,a u∀l∈L (8) ϕ21u l=−γadd/drop l,21 −X a AaMl,a d−X lx γexp lx,21Nl,lx d+Pl +X g (µu2 l,g +µp1 g)Gg+X a X g µ21 a,gGgMl,a d∀l∈L (9) Constraints (6) to (9) calculate the power received by the leaf nodes originating from Hub1, by Hub2, by the leaf nodes originating from Hub2, and by Hub1, respectively. ϕXX l≥Ps,∀l∈L, (10) The series of constraints listed in (10) ensure that the received power is greater than the transceiver’s sensitivity. ϵ11 ≥ϕ12u l, ϵ12 ≤ϕ12u l, ϵ21 ≥ϕ21u l, ϵ22 ≤ϕ21u l,(11) ϵ11 −ϵ12 ≤Px, ϵ21 −ϵ22 ≤Px,(12) Constraints (11) and (12) are only activated when optimizing for the P2MP scenario. The lower and upper bounds of the power levels received by transceivers in Hub1 and Hub2 are determined by constraints (11). Constraints (12) ensures that the difference between the highest and lowest SCs power levels (this value is called SCs power difference in the rest of the paper) does not exceed the threshold defined for each transceiver located at the hub nodes. −X a AaMl,a d−X lx γexp lx,12Nl,lx d−γexp l,12 +Pl+ X g µb1 gGg+X a X g µ12 a,gGgMl,a d≤Pn∀l∈L(13) −X a AaMl,a u−X lx γexp lx,21Nl,lx u−γexp l,21 +Pl+ X g µb2 gGg+X a X g µ21 a,gGgMl,a u≤Pn∀l∈L(14) To prevent the launch power at the beginning of the fiber links from exceeding the nonlinearity threshold for downstream signals, constraints (13) and (14) are implemented. Pl+X g µu1 ln,gGg+X a,g µ12 a,gGg(Mln,a u−Mlm,a u) −X a Aa(Mln,a u−Mlm,a u)−X lx γexp lx,12(Nln,lx u−Nlm,lx u)− −γadd/drop l,12 ≤Pn∀lm∈L, ln∈L, lm≥ln (15) Pl+X g µu2 ln,gGg+X a,g µ21 a,gGg(Mln,a d−Mlm,a d) −X a Aa(Mln,a d−Mlm,a d)−X lx γexp lx,21(Nln,lx d−Nlm,lx d)− −γadd/drop l,21 ≤Pn∀lm∈L, ln∈L, lm≥ln (16) Constraints (15) and (16) ensure that the output power of each SC (P2MP) / channel (P2P) after each leaf node on the horseshoe remains within the limits established by the nonlinearity power threshold for upstream signals. X g µb1 gGg+Pl≤PnX g µb2 gGg+Pl≤Pn(17) Constraints (17) make sure that the output power booster amplifiers remain within the linear regime. Mnl≥ |L| X l=1 X g µ12 l,gGg+ |L|+1 X l=2 X g µ21 l,gGg∀l∈L(18) Constraint (18) calculates the number of express amplification sites using binary variables nland a large number M. As referred, the ILP model can be applied to both P2MP and P2P scenarios. For P2P cases, input power levels must be per channel, and constraints (11) and (12) have to be deactivated in the optimization framework. Moreover, the value of weight w1can be used to prioritize minimizing either the number of express amplification sites or the total number of amplifiers. IV. RESULTS AND DISCUSSION The described optimization framework was used to design a set of 25 synthetic 8-leaf node horseshoe topologies generated based on the statistical properties of real horseshoe topologies from [1]. The network designs assume that every leaf node communicates with both hubs. For reference, dualpolarization 16-QAM modulation format and 4 Gbaud per SC are assumed [5], resulting in a data rate of 25 Gb/s per SC. The minimum receiver input power is set to -22 dBm per SC, whereas the transmitter output power is -12 dBm per SC. To minimize the impact of nonlinear interference, the launch power into any fiber span is upper bounded to -8 dBm per SC. In the case of P2MP transceivers, the SCs power difference at the hubs’ receivers must not exceed Px= 8 dB. The parameterization for P2P transceivers is obtained from the one described by setting the number of SCs per optical channel (e.g., 100 Gb/s channels correspond to 4 SCs). Fiber spans are assumed to consist of standard single-mode fiber with a loss coefficient of 0.25 dB/km. The minimum and maximum amplifier gain values are 10 dB and 20 dB, respectively, with 1 dB increments. The coupler types available for use at the leaf nodes have a splitting ratio of: 50/50, 60/40, 70/30, 80/20, and 90/10. The last four coupler types have an unbalanced splitting ratio that can favor, in terms of reduced attenuation, the express path or the add/drop path, depending on how it is placed at the leaf node. Hereafter, it is defined that 70/30 denotes the case where a coupler with a 70/30 splitting ratio is placed to favor the express path, whereas 30/70 denotes the case where that coupler type is placed to favor the add/drop path. A 0.7 dB excess loss is considered on top of the splitting loss for the considered couplers. The optimization framework described in Section III was implemented using the JuMP package and the problem instances were solved using the CPLEX solver. While individual connection OSNR was not explicitly verified, the short link distances and low amplifier count, combined with the high OSNR performance observed in comparable networks [4], suggest that OSNR-related performance limitations are unlikely. Figure 2 depicts the average value and the 90% confidence interval for the number of express amplifier sites, express amplifiers, and total amplifiers considering P2P or P2MP transceivers and setting the optimization framework to minimize the number of express amplification sites or the total number of amplifiers. The three plots cover the (a) flexible, (b) semi-flexible, and (c) fixed scenarios, which correspond to the cases where the coupler type at each leaf node/transmission direction is individually optimized, the same sequence of coupler types must be selected for both transmission directions, and a single coupler type is selected for all leaf nodes, respectively. Several trends can be observed from the plots. Firstly, it becomes clear that the optimization framework can effectively minimize the number of sites that have express amplifiers – average value between 1.4 and 1.6 – which means that the resulting metro-aggregation networks have an improved resilience to load shedding and local power outages. Secondly, as expected, these load-shedding resilient designs are attained at the expense of increasing the total number of amplifiers deployed. Particularly, it is possible to halve the average number of express amplification sites when compared to the case of prioritizing the minimization of the total number of amplifiers (e.g., 1.4 vs. 2.8 in the flexible case with P2P transceivers) although this requires a significant increase of 1.4 1.4 2.8 3.0 2.8 2.9 5.7 5.9 10.9 13.5 6.4 6.6 0 2 4 6 8 10 12 14 16 18 20 22 P2P P2MP P2P P2MP Min. express amplification sites Min. total amplifiers Site / amplifier count 1.4 1.5 3.1 3.4 2.8 3.0 6.0 6.5 12.2 13.4 6.8 7.0 0 2 4 6 8 10 12 14 16 18 20 22 P2P P2MP P2P P2MP Min. express amplification sites Min. total amplifiers Site / amplifier count 1.4 1.6 3.0 4.0 2.8 3.3 6.0 7.2 15.2 20.4 8.3 9.0 0 2 4 6 8 10 12 14 16 18 20 22 P2P P2MP P2P P2MP Min. express amplification sites Min. total amplifiers Site / amplifier count Express amplification sites Express amplifiers Total amplifiers (a) (b) (c) Fig. 2. Average number of amplification sites and total number of amplifiers in the: (a) flexible scenario; (b) semi-flexible scenario; (c) fixed scenario. the total number of amplifiers (e.g., 10.9 vs. 6.4). The reason for this increase is that reducing the number of express amplification sites demands using fewer express amplifiers, but each of these amplifies all connections present at the egress of the leaf node, whereas add/drop amplifiers only amplify the signals that are added/dropped locally. Evidence of this benefit is visible in the fact that when the design prioritizes minimizing the total number of amplifiers, between 72 and 93% of the devices are placed as express amplifiers. Thirdly, when comparing the flexible, semi-flexible, and fixed scenarios, two main observations are due: (i) flexible and semi-flexible lead to very similar results, suggesting that the constraint of using the same sequence of coupler types in both transmission directions have only a minor impact on the metrics being minimized; (ii) although the constraint of using a single coupler type in all leaf nodes introduced in the fixed scenario has a noticeable impact on the number of amplifiers required (between 30 and 50% additional amplifiers compared to the flexible scenario), the optimization framework still manages to find design solutions with very few express amplification sites. Finally, comparing the results with P2P and P2MP transceivers, it can be seen that the utilization of P2MP instead of P2P transceivers can increase the metrics being minimized: average increase of 13% and 15% in the number of express amplification sites and total number of amplifiers, respectively. This increase is due to the need to meet the constraint of maximum SCs power difference at the hubs’ receivers. Importantly, despite the increase in the number of amplifiers, it should be highlighted that P2MP transceivers allow more efficient utilization of transceiver devices in huband-spoke traffic patterns. For instance, if 100 Gb/s are required for each leaf node, a total of 32 100 Gb/s-capable P2P transceivers are required in these networks, whereas a total of 16 100 Gb/s-capable plus 4 400 Gb/s-capable P2MP transceivers would provide the same connectivity. To gain insight into the types of couplers selected and their positioning (i.e., favoring express or add/drop paths), Fig. 3 depicts the share of each coupler type when designing the network for P2MP transceivers. In general, coupler types with more asymmetric splitting ratios and placed to reduce express losses have a higher share. Moreover, this trend is more pronounced when minimizing the number of express amplification sites. Note that, the coupler type distribution when considering P2P transceivers follows similar trends to the ones observed for P2MP transceivers. 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50/50 60/40 70/30 80/20 90/10 40/60 30/70 20/80 10/90 Coupler share 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50/50 60/40 70/30 80/20 90/10 40/60 30/70 20/80 10/90 Coupler share 0% 10% 20% 30% 40% 50% 60% 70% 80% 50/50 60/40 70/30 80/20 90/10 40/60 30/70 20/80 10/90 Coupler share Min. express amplification sites Min. total amplifiers (a) (b) (c) Fig. 3. Coupler type distribution in the: (a) flexible scenario; (b) semi-flexible scenario; (c) fixed scenario. V. CONCLUSIONS This work proposed a comprehensive framework to optimize filterless horseshoe metro-aggregation networks, which can be configured to improve the network’s resilience against frequent local power outages or to minimize the total amplification costs. 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