Shuangyi Yan
email: shuangyi.yan@bristol.ac.uk

Zhengguang Gao

Rui Wang

Alex Mavromatis

Reza Nejabati

Dimitra Simeonidou

Dynamic Abstraction of Optical Networks with Machine Learning Technologies

Keywords: Machine Learning, Network Abstraction, Low-Margin Networks

The emerging 5G network will bring a huge amount of network traffic with big variations to optical transport networks. Softwaredefined optical networks and network function virtualization contribute to the vision for future programmable, disaggregated, and dynamic optical networks. Future optical networks will be more dynamic in network functions and network services, with high-frequency network reconfigurations. Optical connections will last shorter than that of the static optical networks. It's straightforward that Programmable optical hardware will require a reduced link margin to improve the hardware utilization. To configure network dynamically, real-time network abstractions are required for both current links and available-for-deploy links. The former abstraction guarantees the established links not be interfered by the newly established link while the latter abstraction provides information for intelligent network planning. In this talk, we use machine-learning technologies to process the collected monitoring data in a field-trial testbed to abstract performances of multiple optical channels. Based on the abstract information, a new channel can be established with maximum performance and minimized interference on the current signals. We demonstrated the dynamic network abstraction over a 563.4-km field-trial testbed for 8 dynamic optical channels with 32 Gbaud Nyquist PM-16QAM signals. The work can be further extended to support complex optical networks.

Introduction

Optical networks have becoming the essential infrastructure for the future fifth generation (5G) networks. 5G transport networks, including fronthaul, middlehaul and backhual networks, rely on optical network infrastructure [START_REF] Tzanakaki | Optical networking interconnecting disaggregated compute resources: An enabler of the 5G vision[END_REF]. Optical and wireless converged network architecture was proposed to support operational network and end-user services [START_REF] Tzanakaki | Wireless-Optical Network Convergence: Enabling the 5G Architecture to Support Operational and End-User Services[END_REF]. In addition, the emerging 5G applications, such as augmented reality applications, require more interactions with computing resource that located either in the cloud or in the edge. Compared to the previous mobile networks, an increased proportion of mobile traffic will be sent to metro and core networks. The successful deployments of 5G networks require lot of innovations to be made in optical networks. In 5G networks, a peak data rate up to 20 Gbit/s is provided for per user [START_REF] Hattachi | Machine-learning method for quality of transmission prediction of unestablished lightpaths 10[END_REF], which is comparable to optical channel capacities in optical networks providing 100G Ethernet standard still dominates the market [START_REF] Houtsma | Recent Progress on Standardization of Next-Generation 25, 50, and 100G EPON[END_REF]. Therefore, dynamic network traffic with big variations in 5G networks need to be supported by a flexible and dynamic optical network.

On the other side, optical networks are continuously evolving to be more flexible and dynamic. Software-defined optical networks (SDN) decouple the control plane and data plane, allowing the independent developments of both technologies [START_REF] Channegowda | Software-Defined Optical Networks Technology and Infrastructure: Enabling Software-Defined Optical Network Operations[END_REF]. Network function virtualization (NFV) brings flexibility of network functions to be configured, migrated or terminated in optical networks. End-to-end network service orchestration can deploy network services over multiple network domains [START_REF] Bonafiglia | End-to-end service orchestration across SDN and cloud computing domains[END_REF]22]. In the perspective of optical hardware, hardwareprogrammable network functions have been developed to deliver node functions in an on-demand way [START_REF] Shuangyi | Hardware-programmable Optical Networks[END_REF].

In dynamic optical networks, network services or connections will serve in a short time and high-frequency network re-configurations will be expected in optical networks. From the perspective of network operators or network controllers, it is straightforward that optical networks should be planned at short timescales rather than the end of life (EoL) of network facilities. Network margins part of which were reserved for aging can be eliminated by considering the service life period [START_REF] Soumplis | Network Planning With Actual Margins[END_REF].

Dynamic optical networks with reduced network margins raise many challenges for network operations. One of the key challenges is that network controllers need up-to-date information about dynamic networks to dynamic configure optical networks with a reduced margin. Network abstraction that abstracts information of network states assists network controllers to deploy services according to the current network states. In addition, the abstract process needs to evaluate the impact of the new established services or links on the previous services or links. The latter abstraction function guarantees the established links not be interfered by the newly established link. In margin-reduced networks, the dynamic abstraction becomes more critical. Due to the fast-frequency network re-configurations, the dynamic abstraction need to be continually updated after each reconfiguration with a fast response time.

In optical networks, one of the key information regarding per link is the link impairment, which is affected by operation parameters of network facility and network configurations. Static network abstraction can be achieved by testing link performance in advance [START_REF] Ives | A Comparison of Impairment Abstractions by Multiple Users of an Installed Fiber Infrastructure[END_REF]. However, the static network abstraction neglects the dynamics in network payloads and other physical parameters. In marginreduced dynamic optical networks, it is of vital importance to abstract optical network impairments dynamically. Therefore, time-consuming link optimization can be eliminated to support high-frequency network reconfigurations.

In this paper, we explored machine-learning technologies to process the collected optical performance monitoring data and operation data of the key equipment in a field-trial testbed to dynamically abstract qualities of transmission (QoTs) of multiple optical channels. For the first time, we developed machinelearning (ML) based dynamic network abstraction using Random forest regression. The developed ML-based dynamic network abstraction is able to predict the transmission quality, i.e., BERs of the un-established optical channels and to evaluate the impact on the previously established channels. The ML-based predictor can predict the link performance up to 8 channels simultaneously. The evaluation of the current link is essential for a low-margin network. In the demonstration, a field-trial link between Bristol and London is setup with 24 optical channels transmitting over 564 km. A network-scale cloud network configuration and monitoring database (CMDB) is implemented over the field-trial link based on [START_REF] Shuangyi Yan | Field trial of Machine-Learning-assisted and SDN-based Optical Network Planning with Network-Scale Monitoring Database[END_REF], with extensions to include parameters of EDFA pump lasers, such as pump laser current and temperature. The central 8-channel signals, generated by eight real-time PM-16QAM transponders, are configured dynamically with real-time BER (Bit Error Rate) measurements. Random forest regression based network abstraction algorithm is developed to abstract all the eight channels by the transmission performance. With 4324 training data sets, the developed net-work abstraction algorithm can predict the performance of the un-established channels based on the current network states. The algorithm can also evaluate the impacts on the previous established channels. The experimental results show the developed network abstraction algorithm could abstract network performance with a high precision. The dynamic network abstraction can assist network controller to deploy new services based on link performance while minimize the disturbance on current services. The work will be one of the potential enabling technologies for a reliable margin-reduced network.

Literature review of network abstraction with machine learning technologies

To abstract optical network impairments, multiple technologies have been explored. Gaussian-noise (GN) model has been developed extensively to provide a relatively simple and sufficiently-reliable tool for performance predictions [9,[START_REF] Poggiolini | The GN-Model of Fiber Non-Linear Propagation and its Applications[END_REF]. Considering the complexity in dynamic optical networks, the complex calculation in GN-model prohibits its deployment in practical networks for network planning. Some simplified analytical models have been developed to reduce the complexity in [START_REF] Bosco | Analytical results on channel capacity in uncompensated optical links with coherent detection 19[END_REF][START_REF] Poggiolini | Analytical Modeling of Nonlinear Propagation in Uncompensated Optical Transmission[END_REF]. Such analytical models could be used for general analysis to support network design. Nokia bell labs also reported a similar system design tool to facilitate the design of the terrestrial transmission systems with high-order modulation formats and coherent detection technologies [START_REF] Lavigne | System Design Tool for High Bit Rate Terrestrial Transmission Systems With Coherent[END_REF]. In [START_REF] Filer | Multi-Vendor Experimental Validation of an Open Source QoT Estimator for Optical[END_REF], an open source QoT estimator was developed with the capability to predict performance with an accuracy of ±0.75db. This kind of analytical models can't provide precision predictions to reflect the impairments, especially the dynamic impairments in optical networks. Therefore, these tools were mainly used at the network design phase. In margin-reduced networks, more precise QoT estimation with a short computation time is required. The QoT prediction needs to be done for each operation. Thanks to the advance of machine learning technologies, many researchers started to explore network dynamics in optical networks with advanced machine learning technologies. Artificial neural network based QoT prediction algorithms have been developed to predict the performance of the un-established optical channels [START_REF] Mo | ANN-Based Transfer Learning for QoT Prediction in Real-Time Mixed Line-Rate Systems[END_REF]13,[START_REF] Shuangyi Yan | Field trial of Machine-Learning-assisted and SDN-based Optical Network Planning with Network-Scale Monitoring Database[END_REF]. Most of the previous works use network configurations, such as modulation formats, link distance, fiber parameters, to predict the QoT of the unestablished channels. In such case, the QoT-prediction actually neglects the dynamics in optical devices, especially the active devices, whose operation parameters affect the transmission performance significantly. The developed QoT prediction algorithm worked well in the collected data in a short time. However, failure to handle dynamics in optical device will lead to inaccuracy of QoT estimations in long term. In [START_REF] Shuangyi Yan | Field trial of Machine-Learning-assisted and SDN-based Optical Network Planning with Network-Scale Monitoring Database[END_REF][START_REF] Yan | Dimitra Simeonidou: Data-driven network analytics and network optimisation in SDN-based programmable optical networks[END_REF][START_REF] Yan | Field Trial of Machine-Learning-Assisted and SDN-Based Optical Network Management[END_REF], we built a cloud network configuration and optical performance monitoring database to collect the physical parameters over the whole network. ANN-based QoT prediction was developed to predict a single channel. Combining with network configurations, the developed ANN-based QoT prediction algorithm is able to handle the dynamics in optical networks, which could be reflected in the operation parameters in optical devices. In this paper, we further developed the concept to dynamic optical network with multiple channels.

Field-trial demonstration of dynamic network abstraction

Figure 1 shows experimental setup of the field-trial testbed. Selective Switches (WSSs). After auto equalization, the combined 24-channel signal is launched to the 563.4-km fiber link between Bristol and London. The optical spectrum of the 24-channel optical signal is shown in Fig. 2. In this paper, the developed dynamic network abstraction will focus on the dynamic channels as indicated in Fig. 2. The node controller and scenario generator controls the three transmitter sets and WSSs. It can generate any combination with different channel slot "on". By configuring the three transmitter sets, various network scenarios with different channel distribution can be configured.

The used link which is part of the national dark fiber infrastructure (NDFIS) includes five intermediate nodes. Each intermediate node includes EDFA, DCM and a Polatis fiber switch to allow remote reconfiguration and monitoring of the fibers and amplifiers. The fiber switch monitors the launch power of each span. The operation parameters of the EDFAs are sent back to the cloud monitoring database. The launch power for each span was estimated using incoherent GN model. After transmission over the field-trial link, the signals are demultiplexed by another 4 × 20 WSS. Then the BER measurements will be carried out for each channel. The BER measurements of the 8-channel PM-16QAM signals are also collected and sent to the cloud monitoring database.

Cloud Monitoring Database

To dynamic configure a margin-reduced network, network controller requires upto-date network state information. In addition to the dynamic network payloads (spectrum allocations), operation states of the key infrastructure in the link can provide in-depth information to abstract link impairments. The EDFAs in the link contribute to the most OSNR penalties. On the other hand, optical powers play a significant role for nonlinear effects, which limit the maximum transmission distance. Thus, a cloud monitoring database (CMDB) is implemented to collect network configuration information, operation information of key infrastructure, and the quality of transmission per links. The database creates the relationship between network configurations and the corresponding transmission performance. The design of the cloud monitoring database enables reusing of the local monitoring data. The separation of database from the SDN controller allows the possibility to deploy high-performance computing resource to analysis collected data and implement powerful machine-learning algorithms to serve the SDN controller as a network abstraction service.

The proposed CMDB is implemented over the field-trial testbed as shown in Fig. 1. The CMDB collects network configuration information from the SDN controller, such as channel configurations, wavelength, modulations, link lengths. The optical link monitoring information in the CMDB includes optical launch power monitored at each span, operation parameters of all EDFAs, and optical spectrum information at the transmitters and receivers. Regarding EDFAs, the CMDB collects operation information from each EDFA, include temperature and bias of the pump laser, optical power of the input and output ports, and the noise figure. Considering that the data contains a lot of features, Random Forest Regression is chosen as a Machine Learning algorithm to predict link performance and evaluate the impact on the current channels. Random Forest is one of the most effective ensemble learning algorithms, which includes N random decision Trees. Its final prediction result is combined from a set of base models, which improve its performance compared with a single model [START_REF] Tin | The random subspace method for constructing decision forests[END_REF]. Furthermore, it handles thousands of features efficiently and runs on big data bases. Figure 3 shows the structure of BER prediction algorithm based on monitoring data from the CMDB. Monitoring data include three parts: network configuration information, optical link monitoring information and the BER measurements from the 8-channel real-time transponders. In order to improve the accuracy of prediction, the interrelationship of established channels is characterized by One-Hot coding.

Machine learning based network abstraction

In order to generalize the network state, the node controller and scenario generator as shown in Fig. 1 configures the transmitter sets to generate different scenarios of the 8 dynamic channels. We collected 4324 data to train the model. Each data include information about the transmitters, optical links, and receiverside BER measurements. To verify proposed network abstraction algorithm, one scenario with only channel 2 "on" is considered. To deploy new link, the network abstraction algorithm will predict the BER performance of all the available channel slots and evaluate the corresponding impact on the Channel 2. Figure 4 shows the comparison of the predicted and actual BERs for un-established channel when only channel 2 is established. The developed network abstraction algorithm predicted the BER of all the available channels (Channel 1,3,4,5,6,7,8). As show in the Fig. 4, the implemented network abstraction algorithm predicted the link BERs of the un-established channel with a high precision. The maximum error occurs at Channel 5. The different performances for channel 5 and other channels contribute to the difference. The predicted performance for all the available channel slots can help network controller to deploy optical links intelligently. In the future work, the transmitter performance will be also included in the prediction model.

Results of dynamic network abstraction

In the margin-reduced dynamic network, another challenge is to ensure the established channels not to be disturbed by the new deploy channels. Therefore, in the phase of network planning, the proposed network abstraction algorithm can evaluate the impact of the establishing links on the current channels. The evaluation will prohibit the failure of current channels. In the same scenario, the network abstraction algorithm predicts BERs of the channel 2 when the new established channel is deployed in the available channl slots, such as Channel 1, 3, 4, 5, 6, 7, 8. Figure 5 shows the comparison of predicted BERs and the actual BER for existed channel 2 when channel 1,3,4,5,6,7,8 is switched on respectively. We can see the prediction is very accurate, and the performance of existed optical path almost remains unchanged as the experiment platform is very stable. By adding another channel, the impact on the current channel is very limited.

Scalabilities of the cloud monitoring database and

Machine-learning based QoT predictor

In this paper, we extended the previous work to dynamically abstract the QoTs of multiple channels. The experimental demonstration shows the ML-based QoT prediction can help the SDN controller plan the network efficiently, i.e., to maximize the link capacity by reducing link margins with precise QoT predictions and minimize the interference on the current established channels. The QoT prediction relies on the collected massive network operation data from both the SDN controller and the optical performance monitoring. In current demonstration, the OSNR penalties of the multiple paths connected several optical nodes can be predicted with the implemented cloud monitoring database. To deploy the ML-based QoT predictor in the future optical networks, scalabilities of both cloud monitoring database and the ML-based QoT predictor need to be considered.

Regarding the cloud monitoring database, i.e.,NCMDB, each physical transmitter is used with the event time together to generate the record ID. All the other information is linked to the record ID. In such approach, the whole network activities can be recorded and linked to each transmitter. Therefore, the scale of the NCMDB depends on the deployed transmitters in the link. Especially in core networks, there are limited numbers of nodes and links. The NCMDB can be easily scaled up to store more network information. The centralized monitoring data hub collects the monitoring information through dedicated links. The dedicated link could provide enough bandwidth to allow the NCMDB to collect raw data. Therefore, the data can be re-used by multiple network analytic applications. The network analytic applications that run on top of the NCMDB also provides an interface for the SDN controller to access the processed monitoring information. Therefore, the developed network abstraction application is deployed as a service. In such way, the centralized network information hub simplifies the work-flow of SDN controller to use the monitoring information. The design of the NCMDB provides good scalability for future big networks.

As far as the scalability of the ML-based QoT prediction technique is concerned, an increase in network size will definitely result in an increase in the number of links parameters (e.g. number of EDFAs' parameters) which are in fact used by our ML model for OSNR monitoring. This implies that the computational resources/time required for the training of ML will also increase significantly in this case. However, we would like to emphasize that the training procedure of ML model is conducted completely offline and prior to actual deployment in an SDN. Once the parameters of an ML are optimized offline, the actual OSNR monitoring process in SDNs employing trained ML model involves few simple matrix multiplications. Therefore, we believe that the computational complexity and processing time will keep at a low level and possible provide real-time network abstractions.

Conclusion

In this paper, random forest regression based network impairment abstraction algorithm is developed to analyze the implemented cloud monitoring and configuration database (CMDB). The network abstraction algorithm predicts the performance of all the available channel slots and also evaluate the impact on the current links when any available slot is selected to deploy new links. We demonstrated the network impairment abstraction up to 8-channels over a 564-km field-trial link . The implemented algorithm could predict the channel perfor-mance with a high precision to support margin-reduced optical network. The dynamic network abstraction could be integrated with the SDN controller to achieve low-margin dynamic optical networks. The introduced CMDB and the network analytic applications open new possibilities for future dynamic optical networks.

Fig. 1 .

 1 Fig. 1. Field-trial demonstration over a 560-km link between Bristol and London.

Fig. 2 .

 2 Fig. 2. Optical Spectrum of the 24-channel optical signal. The dynamic abstraction focuses on the 8×32 Gbaud PM-16QAM signals.

Fig. 3 .

 3 Fig. 3. Structure of BER prediction algorithm based on random forest regression.

Fig. 4 .

 4 Fig. 4. Predicted BERs vs. Real BERs for all the available channel slots in the chosed scenario.

Fig. 5 .

 5 Fig. 5. Evaluation of the impacts on the current link by choosing different wavelength slots to establish a new link. The channel number is the choosed wavelength slot. The corresponding BER is the predicted BER performance of the previous link when the new link is established.

  Total 24-channel optical signals are generated with three sets of transmitters in our lab. Eight external cavity lasers (ECLs) are combined together and then modulated with a dual-polarization IQ modulator to generate 8 × 28 Gbaud PM-QPSK signals. The IQ modulator is driven by four 28 Gbaud electrical signals, which are generated by a high-performance FPGA. In a similar way, another eight ECLs are modulated by another IQ modulator driven by a 32 Gbaud pulse pattern generator (PPG), to generate 32 Gbaud PM-QPSK signals. Another 8-channel real-time Nyquist PM-16QAM signals are generated by two Facebook Voyager transponders, which also provide BER measurements of per channels. The total 24 channel optical signals are multiplexed together by a 4 × 20 Wavelength

This work is supported by the UK EPSRC through the TOUCAN project (EP/L020009/1) and the INSIGHT project (EP/L026155/2), the EU-H2020 Metro-Haul project (761727).


Kostas Katsalis
email: kostas.katsalis@huawei.com

Rixin Li
email: lirixin@huawei.com

Programmable Flex-E and X-Ethernet Networks for Traffic Isolation in Multi-Tenant Environments

Keywords: Flex-Ethernet, X-Ethernet, Network Slicing, Service differentiation, Throughput guarantees

In this work we investigate the coupling of Flex-E and X-Ethernet technologies as a means to realize interface slicing and fast switching respectively. Flex-E is investigated as a key technology that is able to split a physical interface into isolated sub-channels, decouple MAC rate from PHY rate and achieve hard bandwidth isolation. X-Ethernet technology introduces Ethernet PCS switching, eliminates table lookup and buffer queuing and will be investigated as a fast switching mechanism that is exploiting the PCS layer relay. We present evaluation results from implementation activities that showcase the ability of an integrated Flex-E/X-Ethernet solution to enable network slicing features in transport networks. Furthermore we present a technical approach on the way the control plane of Flex-E/X-Ethernet network can be integrated with an orchestration and management solution.

Introduction

In order to couple with the strain raised and satisfy the strict requirements of 5G systems, significant changes have been undergoing in transport networking. Under the umbrella of 3GPP-based mobile cellular networks, transport networks support connectivity services between the various Disaggregated Radio Access Networks (DA-RAN) network components (3GPP TR38.816, TR38.801).

With respect to the terminology used by 3GPP (3GPP TR23.799, TR38.803) as transport network we consider the Fronthaul (FH), Midhaul (MH) and Backhaul (BH) type of communication networks that are used to interconnect Network Functions (NFs). Note that NFs can be either Physical (PNFs) or Virtual Network Functions (VNFs). In the case where the DA-RAN paradigm is adopted, NFs reside in the Radio Unit(RU), Centralized Unit (CU), Distributed Unit (DU) and in the Core Network (CN) [START_REF] Chang | Slice orchestration for multi-service disaggregated ultra-dense rans[END_REF]. Furthermore, in 3GPP TS23.501 where the 5G Architecture is described, future network designs also consider network operations in the light of Network Slicing [START_REF] Katsalis | Network Slices toward 5G Communications: Slicing the LTE Network[END_REF].

In this paper we investigate Flex-E and X-Ethernet technologies as a means to realize transport network slicing with the support of fast switching. Flex-E will be investigated as a key technology that is able to split a physical interface into isolated sub-channels, decouple MAC rate from PHY rate and achieve "hard" bandwidth isolation. X-Ethernet technology introduces Ethernet PCS switching, eliminates table lookup and buffer queuing and will be investigated as a fast switching mechanism that is exploiting PCS layer relay.

Traditional deployments where relying on fiber technologies and PDH T1/E1 connections, ATM , SONET/SDH, like also MPLS to support transport network connectivity services. However, the last decade we witness a spiraling adoption of Ethernet technology as a means to implement transport networking for the mobile network. A flat Ethernet solution simplifies provisioning and planning, while also helps to radically reduce OPEX. Solutions like Ethernet over MPLS, Ethernet over SONET/SDH, Packet over SONET (PoS), Ethernet over DWDM Ethernet over OTN and so on, are inexorably driving the Ethernet technology as the de facto standard to support mobile network connectivity. Open Internet working Forum (OIF), a global industry forum for advanced inter-operable optical networking solutions, devised Flex-E in OIF-FLEXE-01.0 -Flex Ethernet Implementation Agreement (IA). The key features of Flex-E are the ability to create larger links out of multiple slower links, multiplex lower speed traffic from different clients in higher speed links, while also utilize a specific portion of some PHY link. As we will analyze in the following Flex-E can serve as an ideal technology to realize the concept of Network Slicing in transport networks and offer guaranteed performance and services per tenant even in scenarios of extreme flow multiplexing.

The main contributions of this paper are the following:

-We present the primitives of operation of Flex-E and X-Ethernet technologies as key enabling technologies towards slicing the transport network. -We present evaluation results from real testbed experimentation. As we will analyze Flex-E is able to provide strict throughput guarantees, while X-Ethernet is able to bring switching time cost up to level of few nanoseconds. -Our demonstrator considers the case of channelization where several lowerspeed links are created for different ethernet clients. -We provide insight information on the way a SDN solution could be incorporated in an integrated platform and how an overall orchestration and management solution could be designed.

This paper is organized as follows. In section 2 we present the related work. In section 3, we present the primitives of operation of Flex-E and X-Ethernet technologies. In section 4, we present evaluation results. In section 5 we elaborate on the way programmability can be enabled in Flex-E, X-Ethernet networks and the way they can be integrated with orchestration and management systems. We conclude our study and present future research directions in section 6.

Flex-E enables Ethernet-based services to be mapped over a next-generation optical transport network with the most efficient utilization of capacity possible. It was originally conceived to meet the challenges of Internet Content Providers (ICPs) for higher capacities and dynamicity, and as a new mechanism for the data center interconnect (DCI). It was originally proposed by OIF in Interoperability Agreement (IA) OIF-FLEXE-01.0 on March 2016. A detailed description of the technology can be found by OIF in IA OIF-FLEXE-02.0 (2018), IA OIF-FLEXE-01.1 (2017), IA OIF-FLEXE-01.0 (2016) and [START_REF] Katsalis | Towards Slicing for Transport Networks: The Case of Flex-Ethernet in 5G[END_REF]. The forthcoming Flex-E 2.1 project is about prototyping Flex-E over 50Gbps PHY applications and extending the recently released Flex-E 2.0. Flex-E 2.1 will further specify a new Flex-E frame and multiplexing format and address applications with lower bandwidth needs. Flex-E neighbor discovery is discussed in IA OIF-FLEXE-ND-01.0 (2018). Potential use cases were considered within other organizations such as the Ethernet Alliance and described by certain industrial players like Google in [START_REF] Hofmeister | How can flexibility on the line side best be exploited on the client side? In Optical Fiber Communication Conference[END_REF]. Proprietary deployments considering an integrated approach of the control and management plane of Flex-E over OTN were also contributed by Huawei [START_REF] Vilalta | Network slicing using dynamic flex ethernet over transport networks[END_REF]. Regarding Flex-E implementation landscape Huawei incorporates Flex-E in PTN990 router series, IXIA presented a demo in OFC 2016 with Altera/Intel, with Flex-E 2x100GbE and Ciena provides the Flex-E Liquid Spectrum solution. A 400 Gbps of Flex-E traffic was sent over four bonded 100 GbE interfaces on network demonstration in OFC 2018 by OIF and Ethernet Alliance.

In [START_REF] Tipmongkolsilp | The evolution of cellular backhaul technologies: Current issues and future trends[END_REF] a survey on backhaul network technologies is presented with an analysis on the relevant synchronization issues. A detailed analysis on the topic of transport network slicing is presented in [START_REF] Kaloxylos | Network slicing. 5G System Design: Architectural and Functional Considerations and Long Term Research[END_REF]. Virtualization techniques for different types of optical networks and technologies where granularities may vary, according to the node and link characteristics. For example, in a wavelength switched network with optical cross connects (OXCs) and Reconfigurable Optical Add-Drop Multiplexing (ROADMs) virtualization approaches are different from networks with sub-wavelength granularity of switching and control [START_REF] Nejabati | Optical network virtualization[END_REF]. In [START_REF] Jinno | Virtualization in optical networks from network level to hardware level[END_REF] hardware and spectrum resource virtualization techniques for the optical network are investigated. An adaptive transponder design is analyzed for WXC/WDM, while also multiflow transponder mechanisms for right-sized superchannels with the necessary number of subtransponders. Flex-O is described in ITU-T G. 3 Transport Network Slicing with Flex-E and X-Ethernet

Flex-E Basic Operation & Concepts

In principle, in the OSI stack in the Data Link Layer Logical Link Control (LLC) is performing multiplexing network protocols over the same Media Access Control Sublayer (MAC), which is used for addressing and channel access control mechanisms. Reconciliation Sublayer (RS) processes PHY local/remote fault messages, while in the PHY Layer Physical Coding Sublayer (PCS) performs auto-negotiation and coding. Flex-E technology is introduced as a thin layer, known as Flex-Shim, and being able to support data rates out of the conventional range offered by current Ethernet standards. In more detail, the Flex-E Shim layer (Fig. 1) is responsible for the mapping of Flex-E clients (Ethernet flows) to groups of PHYs. From a layering perspective Flex-E Shim is introduced between the Ethernet MAC and the PCS sublayers. The main idea behind Flex-E is to decouple the actual PHY layer speed from the MAC layer speed of a client. Flex-E is based on a time-division multiplexing mechanism that is able to drive the asynchronous Ethernet flows over a synchronous schedule over multiple PHY layers. The main operational components of Flex-E are depicted in Table 3.1.

Currently there are three operational scenarios supported by Flex-E, which describe different ways the MAC layer speed is related with the corresponding PHY speed, allowing a distinct manner for multiplexing clients in time:

-Bonding: allows a MAC layer speed higher than a single PHY by grouping multiple PHYs to serve a flow (e.g. support a 200G MAC over two bonded 100GBASE-R PHYs). -Sub-rating: MAC layer speed is less than the actual PHY. Allows the MAC layer to use a portion of a PHY to serve a flow (e.g. support 50Gbps MAC over a 100GBASE-R PHY). -Channelization: enables multiple Flex-E clients over a shared single PHY or bounded PHY via the means of time division multiplexing in the Flex-Shim (e.g. support 150Gbps and a 50Gbps MAC over two bonded 100GBASE-R). Hybrids of these scenarios are also possible, for instance a sub-rate of a bonded PHY supporting 250Gbps MAC over three bonded 100GBASE-R PHYs. These options allow increased resource flexibility for 5G and fine-tuning the offered rate depending on the usage.

X-Ethernet technology

X-Ethernet is a Huawei proprietary technology, where X stands for extended distance, expanded granularity and extremely low latency. X-Ethernet introduces Ethernet PCS switching based on the interface offered by Flexible-Ethernet.

The basic switching unit is FlexE Client. The switch device will redirect FlexE Clients (64B/66B block streams) from its inbound port to its outbound port without waiting for the arrival of the whole Ethernet frame for FCS checksum and forwarding decision with table lookup. Therefore, all the time consuming procedure, such as encapsulation/decapsulation, queuing and table lookup, can be removed. We give another name to the PCS switching that is PCS Non-Stop Switch (NSS). What's more, the remaining procedure processing time is predictable, which results in deterministic device latency. Idle insertion or deletion according to IEEE 802.3 may be performed to rate-adapt FlexE Client to the Flex Group. Details of the technology can be found in [START_REF] Li | X-ethemet: Enabling integrated fronthaul/backhaul architecture in 5g networks[END_REF].

4 Performance Evaluation

Flex-E testbed, experiment description and evaluation results

We demonstrate and evaluate Flex-E technology, while verifying the theoretical framework proposed by OIF. The system demonstrator under test, is depicted in Fig. 2 where for the implementation of the testbed two Huawei Optix PTN 990 are used. A software patch on VRP V100R008C10, supports the necessary Flex-E functionality. PTN devices are primarily used on bearer networks that carry various services, such as mobile communication and enterprise users' services. It transports packet services on the network and converges them to an IP/MPLS backbone network. In this demonstrator one 100G link between the two routers is "splitted" using the Flex-E technology. The splitting is made by creating Flex-E channels. The Flex-E clients are identified using VLAN technology and each VLAN is mapped to a specific Flex-E channel. As presented in Fig. 3 for the demonstrator we allocate different time slots for two Flex-E channels, namely Channel 0 and Channel 2. The mapping of channels in Flex-E flows is made on a VLAN basis where for the current implementation the lower two bits of the channel ID and VLAN ID correspond to each other (e.g., VLAN 4 maps to channel 0 and VLAN 5 to channel 1 and VLAN 6 in channel 2 and so on). In Fig. 3 a sample channel configuration is presented for router 1 (R1 prompt) while a similar configuration also exists for router 2. In the example depicted, slots 5 to 9 are allocated in channel 2, while all the other slots (1-4 and 6-20) are allocated in channel 0. With this allocation channel 0 receives 15/20=3/4 capacity (translated to scheduling opportunities) from the 100G interface, channel 2 receives 1/4 from the link capacity, while channels 1

Rx Line (bps) and 3 are blocked. Because of the specific flow mapping implementation, channel 0 will support not only VLAN 4 but also all VLAN-ids where the ending bits are 00 (like 0b000, which is VLAN 8) and so on. Different Flex-E client mapping mechanisms are under consideration and development.

To create multiple Ethernet flows with the necessary VLAN identification, traffic has been generated by using a Huawei 100GE traffic generator, which was controlled using Tesegine 2.0 V300R006C10B410 software. Using the Tesegine 2.0 traffic generator software, we were able to generate multiple concurrent flows with different configuration options of all the frames/packets fields (like src/dst MAC address, VLAN-id, src/dst IP address etc.). As a baseline experiment, we created two flows: Flow-1 (VLAN-id 4) that could be critical traffic and Flow-2 (VLAN-id 6) being the background traffic. The goal of the demonstrator was to showcase the ability of Flex-E channelisation to provide precise capacity shares between the two competing channels/flows. Channel statistics were obtained using interface counters that were updated to report per channel reports.

From all the experiments performed, perfect isolation was achieved; not only the capacity ratios were respected but also channels 1 and 3 that could block the traffic are not mapped to "open" Flex-E channels and thus had no effect on performance. Even though we only present here a representative subset of results, our conclusions apply to a wide range of experiments with the adjustment of different network parameters. In Fig. 4 and Fig. 5 we present the evaluation results of the experiment described above with two Flex-e channels serving to Ethernet flows that are identified using their VLAN-id. As we can see, the 100G link is precisely sliced exploiting time scheduling on the Flex-Calendar. Flex-E channel 0 throughput is 75 Gb/s on average while channel 2 throughput is 25 Gb/s on average (5 slots out of 25) Fig. 4. An important observation however is that although Flex-e technology is able to provide precise throughput guarantees per flow using very low level slicing, is not able to differentiate delay and jitter per channel for each Flex-E client. This phenomenon was however expected and is depicted in Fig. 5(a) and Fig. 5(b) where, as we can observe, both flows experience similar delay and jitter performance.

X-Ethernet testbed, experiment description and evaluation results

A X-Ethernet testbed was used to carry demonstration activities, where for each X-Ethernet switch the solution is based on a FPGA board, six 100G CFP2 optical module slots, two 10G SFP+ optical module slots, one Ethernet interface slot. The FPGA board is mainly composed by one Virtex UltraScale chip, one ZYNQ chip, two DDR3 SDRAM chips, one DDR4 SODIMM, two Quad-SPI flashes and one Micro SD.

In the following, we provide experimentation results from the execution of three test scenarios that were carried out and showcase the ability of X-Ethernet technology to satisfy challenging switching requirements for a Flex-E network. Three X-Ethernet prototypes are connected to each other and formed a network. A controller (PC) configures each of the devices via the RS232 port on each device. A CPRI tester is used to generate CPRI option 7 traffic. A network performance tester is used to generate Ethernet traffic with 100 Gb/s maximum bit rate. CPRI is injected into the X-Ethernet node device 1 (XE1) and transport to XE2, then loop back to the CPRI tester. The Ethernet traffic pass through three XE devices one by one and loop back to the network performance tester. It should be noted that the connection between XE devices is though 100G links. Particularly, CPRI and Ethernet traffic share the same 100G link between XE No.1 and XE2. Moreover, the connection between Network performance tester and XE devices are also 100G link. Network performance tester generate an Ethernet traffic that has an effective data rate ranges from 0 to 100 Gb/s.

Experiment T1: Setup the test environment as shown in Fig. 6(a). We configured end-to-end Ethernet traffic flow between XE nodes in two scenarios: Flex-E tunnel allocated 2 and 10 slots respectively. The TestCenter generated and send packets of length 128 bytes.

Experiment T2: Setup the test environment as shown in Fig. 6(b). We configured end-to-end Ethernet traffic flows between three XE nodes. The Test-Center generate and send packets of length 128 bytes. In both experiments we For the packet streams of different packet length at different rates, X-Ethernet exhibits its ultra-low latency forwarding capability at around 0.5 use. Compared to the classic router/switch performance (30 us to 200 ms), X-Ethernet has a huge advantage in carrying latency sensitive services. Thanks to its L1.5 Non Stop Switching mechanism, all the time consuming procedures like table lookup, queuing, buffering, etc., are removed. What's more, due to its TDM like mechanism, it provides end-to-end hard isolation pipe, which guarantees a nanosecond level jitter in the transmission.

XE1 XE2 Traffic Generator Flex-E X-Ethernet X-Ethernet Topology 1 (a) XE1 Traffic Generator XE3 XE2 Flex-E Flex-E X-Ethernet X-Ethernet X-Ethernet
5 Enabling programmability on Flex-E, X-Ethernet networks an integration with 5G-OS Software Defined Networking (SDN) is a technology paradigm that drives innovation on the network segment but mainly inside the data center, it has just recently applied also in the wireless access but also in the transport network.

Although there is a proposal to adopt GMPLS as the Flex-E control plane, is not yet standardized [START_REF] Hussain | Gmpls routing and signaling framework for flexible ethernet (flexe). draft-izh-camp-fiexe-fwk-05[END_REF]. To enable programmability on the Flex-E/X-Ethernet solution a NETCONF protocol-based solution with out-of-band signaling could be also adopted. In the case of NETCONF protocol, a NETCONF server should operate on the switching device to interpret messages send from a remote SDN controller implementing the NETCONF client. NETCONF is connected oriented using TCP while messages are encoded in XML and encrypted by SSH. An SDN controller like ODL or RYU could be used to implement this functionality and be directly connected to an orchestration and management solution like the 5G Operating System (5G-OS) proposed and designed in the context of the 5G-PICTURE project [START_REF] Dräxler | 5g os: Control and orchestration of services on multi-domain heterogeneous 5g infrastructures[END_REF]. A 5G-OS instance can be used to manage services and slices on top of the infrastructure provided by multiple Infrastructure Provider(s). A 5G-OS is composed of different orchestration, management and control components that are tightly integrated to control the operational and business aspects of multiple technological and administrative domains. A simplified version of the 5G-OS integrated with a NETCONF based solution for the programmability of the X-Ethernet solution is depicted in Fig. 8. In 5G-OS a controller within a single domain is referred to as a Domain Controller(DC), similarly an orchestrator within a single domain is called a Domain Orchestrator(DO). An orchestrator that spans multiple DOsand is responsible for full service instantiation is called a Multi-Domain Orchestrator(MDO). Depending on the NETCONF approach with the appropriate YANG models RESTCONF API can also be exploited. RESTCONF is a REST like protocol running over HTTP for accessing data defined in YANG using datastores defined in NETCONF. In both GMPLS and NETCONF cases, new data models need to be devised expose the Flex-E information and functionalities to the control plane. Although the design of YANG models is possible over RSVP, new YANG models are expected to emerge for Flex-E. As in all control plane models, the design primitives for the Flex-E control plane are security, scalability and fast convergence. To on-board on 5G-OS a possible service descriptor should include:

-Flex-E Group provisioning, configuration and instantiation operations: Routers must advertise the type of Flex-E support that they offer, the current calendar allocation and information like link delay and node delay. Regarding capabilities exposure auto-negotiation procedures also need to be defined. -Flex-E calendar scheduling: The control plane must be able to provide an efficient mechanism for the optimal assignment of PHYs to a specific group, while also consider for the optimal slot allocation in the group calendar for each Flex-E client. -Establishment of Flex-E multi-hop paths: Existing solutions consider a preconfigured Command-Line Interface (CLI) based Flex-E group configuration and client assignment. Note that the most important functionality in order to have a functional Flex-E setup is that for each PHY the mux and demux share the same sub-calendar. Otherwise, it would be impossible to decode the slot information to a specific Flex-E client. In a multi-hop setup this information sharing can be challenging. -Dynamic calendar switching configurations: Control plane must support dynamic switching between calendar configurations (A or B) and allow modifying the configuration of Flex-E clients into calendar slots, based on SLAs and performance criteria.

Regarding X-Ethernet, note that it is a Huawei proprietary experimental solution and the focus in the current development phase is on the dataplane operations. No YANG models are currently available or under development. However, these are planned to be implemented the following period, exploiting NETCONF protocol and enabling integration with the 5G-OS. For an orchestration and management system like 5G-OS a possible X-Ethernet service descriptor should include: VLAN ID, Flex-E client bandwidth, Flex-E group ID, PHY ID, Flex-E calendar slot number, performance monitoring information, system-type. data mode, client signal type.

Conclusions and future work

In this work we investigated the coupling of Flex-E and X-Ethernet technologies as a means to realize interface slicing and fast switching respectively. Flex-E is a key technology that is able to split a physical interface into isolated subchannels, decouple MAC rate from PHY rate and achieve "hard" bandwidth isolation. X-Ethernet technology introduces Ethernet PCS switching, eliminates table lookup and buffer queuing and will be investigated as a fast switching mechanism that is exploiting PCS layer relay. We presented evaluation results from implementation activities that showcase the ability of an integrated Flex-E/X-Ethernet solution to enable programmability and network slicing features for future transport networks. As Flex-E is a living standard, we are following all the recent amendments that we are willing to incorporate into our testing infrastructure. Furthermore, we are also investigating solutions where on the top of the end-to-end pipe that Flex-E is able to construct, virtual networks (like VLAN or enhanced VPN solutions based) can be constructed and operate depending on network slice requirements.

  709.1/Y.1331.1 recommendation. Flex-O provides OTN interfaces with comparable functionality as to what was introduced in Flex-E for Ethernet interfaces. It provides an interoperable system interface for OTUCn transport signals; while it enables higher capacity ODUflex and OTUCn, by means of bonding m standard-rate interfaces (see ITU-T G.709.1/Y.1331).

100G9Fig. 2 .

 2 Fig. 2. Flex-E operational scenarios

Fig. 3 .

 3 Fig. 3. Flex-E allocated slots per channel (4 channels supported)

Fig. 4 .Fig. 5 .

 45 Fig. 4. Flex-E throughput guarantees per flow

Fig. 6 .

 6 Fig. 6. X-Ethernet experiment topology.

Fig. 7 .

 7 Fig. 7. X-Ethernet experimentation results.

Fig. 8 .

 8 Fig. 8. NETCONF-based programmability of Flex-E/X-Ethernet switches

Table I :

 I Flex-E main operational componentsFlex-E Client is an Ethernet flow based on a MAC data rate that may or may not correspond to any Ethernet PHY rate. The MAC rates currently supported are 10, 40, and m x 25 Gb/s. FlexE 2.0 augments FlexE 1.0 by providing support for FlexE Groups composed of m x 200 Gb/s Ehernet PHYs and m x 400 Gb/s Ethernet PHYs, and several other features.Flex-E Group is a group of Ethernet PHYs that are bonded together. OIF supports Flex-E groups composed of one or more bonded 100GBASE-R PHYs. Higher rates like 400GbE are under development in IEEE P802.3bs and will be supported in future Flex-E releases.Flex-E Shim is the layer that maps or de-maps the Flex-E clients over a Flex-E group. This procedure relies on a calendar-based slot scheduling. Essentially a set of slots are assigned to each client, according to the MAC layer speed.

Acknowledgements

This work has received funding from the EU H2020 5G-PICTURE project under grant agreement no 762057.


Marcia H M Paiva
email: marcia.paiva@ufes.br

Gilles Caporossi
email: gilles.caporossi@hec.ca

Moises R N Ribeiro
email: moises@ele.ufes.br

Marcelo E V Segatto
email: segatto@ele.ufes.br

Intrinsically Resilient Optical Backbones: An Efficient Ring-Based Interconnection Paradigm

Keywords: Network physical topology design, optical backbone networks, resilience, twin graphs

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The provisioning of uninterrupted connectivity services is an indispensable feature of optical backbones. Considerable amounts of tangible and intangible losses, i.e., legal and reputation damages, can result from mere cable cuts as high aggregates of traffic are nowadays transported over a fiber strand [START_REF] Wu | Fiber Network Service Survivability[END_REF]. Therefore, in order to properly serve new demands from an information-dependent society, networks must be designed using architectures not only with intrinsic abilities to survive, but they also must be resilient in face of a reasonable set of fault events.

Survivability is defined in [START_REF] Al-Kuwaiti | Towards a standardized terminology for network performance[END_REF][START_REF] Kerivin | Design of survivable networks: A survey[END_REF] as the ability of networks to fulfill their mission in a timely manner in the presence of attacks, failures or accidents. Raising the bar for network architects, resilience is defined in [START_REF] Ramirez | Managing resilience in carrier grade networks: Survey, open issues and trends[END_REF] as the capability of a network to minimize link or node failures effects, by assuming the sustainability of the provided services. For instance, a 16-node ring network survives to any single node or link failure, but this network is not resilient. When any link fails in this network, the distance between the corresponding neighbor nodes increases from 1 to 15 hops, and a 2-hop path must be replaced by a 14-hop path after any node failure. Therefore, considerable side effects can be felt on higher network layers and, as a result, implications to the service delivered to end users.

Modern optical backbones encompass complex multilayer mechanisms. Wavelength division multiplexing (WDM) transparently provides end-to-end interconnects over the physical topology. The coarse bandwidth granularity and rigid spectrum allocation of WDM have motivated recent developments in elastic networks and flexible transmission technologies. They aim at better grooming and transmitting heterogeneous traffic demands [START_REF] Papanikolaou | joint multi-layer survivability techniques for ip-over-elastic-optical-networks[END_REF]. Indeed, these new spectral and bit-rate manageable solutions provide extra degrees of freedom (i.e., elastic and tuneable transponders) in accommodating extra demands arising from restoring impacted traffic demands, over sub and super-wavelength services, for improving the overall network resilience [START_REF] Miladić-Tešić | Traffic grooming technique for elastic optical networks: A survey[END_REF].

Nevertheless, re-grooming, re-routing or just switching traffic demands around faulty elements, with the least impact on both working and protected/restored demands, still is a huge challenge for backbone network architects. The intrinsic complexity of this multilayer problem turns exact optimization approaches unlikely to be solved in polynomial time. But there is a fundamental aspect that has been overlooked when trying to improve network resiliency. Regardless of the overlay grooming and transmission technologies, the outcomes of traffic engineering optimization tools will always be constrained by the connectivity diversity of the underlay graph at physical layer.

Nowadays, survivability is a necessary but not a sufficient condition. It is no longer acceptable to design networks for just providing means of service continuity. For instance, there is the challenge for designing optical backbones for supporting the emerging services from the 5th Generation (5G) mobile communications network. The Ultra-reliable and low-latency communications (URLLC) assume that there will be latency-bound and highly dependable underlayer connectivity across distributed datacenters [START_REF] Liberato | RDNA: Residue-Defined Networking Architecture Enabling Ultra-Reliable Low-Latency Datacenters[END_REF]. Thus, optical backbones, operating under either normal or faulty conditions, should meet stringent requirements far beyond mere survivability metrics.

Unfortunately, the topological design of backbones is a complex task in its own right; and that is why the literature already addresses them using heuristic, rule-of-thumb based, and demographic methods, e.g., [START_REF] Kamiyama | Network topology design using analytic hierarchy process[END_REF], [START_REF] Baroni | Wavelength requirements in arbitrarily connected wavelength-routed optical networks[END_REF], and [START_REF] Grey | Towards a model for global-scale backbone networks[END_REF]. Lately, graph theory has joined forces in this front. By abstracting physical aspects and demand parameters, graph theory focus simply on identifying potentially good templates for network topologies, rather than chasing them in extremely large multidimensional search spaces from multi-parameter models. Previous works al-ready investigated Harary graphs tacking survivability in optical backbones [20], twin graphs in datacenter networks [START_REF] Vassoler | Twin datacenter interconnection topology[END_REF], and graph invariant optimization for optical backhaul networks [START_REF] Frascolla | Optimizing C-RAN backhaul topologies: A resilience-oriented approach using graph invariants[END_REF].

The contribution of this paper is to propose to the network community an interconnection paradigm that is able to systematically tackle resiliency (and survivability as a consequence) when designing or evolving backbone networks. Grounded on graph theory, our solution exploits a particular 2-geodetically connected (2-GC) graph family called twin graphs. A key point is that such graphs are already optimal in providing 2-GC with the least number of links. They can also be adapted over the classical ring-based legacy solutions, which were originally designed only having survivability in mind. Thus, backbones designed under this new paradigm can gracefully evolve networks from survivable rings into intrinsically resilient meshes.

The remainder of the paper is organized as follows. Section 2 discusses the evolution of backbone networks toward resilient and affordable architectures in face of growing demands from dependable services. We then present in Section 3 a formal definition of twin graphs, and a constructive method to generate them [START_REF] Chang | The characterizations of hinge-free networks[END_REF]. In order to demonstrate the practical relevance of twin graphs, we perform comparisons with a set of real-world backbone topologies (and rings) with the same number of nodes in Section 4. Finally, Section 5 brings a use case for direct comparison of a geographically mapped twin topology with a real-world topology. Section 6 presents our concluding remarks and future works.

2 Why rings are no longer good enough for our networks?

Survivability in ring topologies is due to their 2-connectivity property, whereas resilience refers to 2-geodetically connectivity that rings are unable to provide. The difference is that any 2-geodetically connected topology intrinsically provides at least two node disjoint (working and backup) paths of minimal length (i.e., geodesics) connecting each node pair of the network, whereas a 2-connected topology provides at least two node disjoint paths connecting each node pair of the network, no matter their lengths. Thus, besides the survivability assured by the simple existence of backup paths, backbone networks should ensure the existence of backup paths not much longer than the working ones in order to provide service resilience either through protection or restoration strategies. Protection refers to techniques in which backup paths are defined prior to the occurrence of any failure, whereas in restoration techniques the backup paths are only defined when failures occur.

On the other hand, ring topology is a prototype traditionally used to address the survivability issue with the least number of extra links. The transition from survivable to resilient topologies should take this legacy architecture into account and upgrade it as inexpensively as possible. Service providers cannot afford to abundantly deploy spare resources for protecting network elements in face of their ever diminishing revenues.

Evolving rings into meshes

Ring topologies have scalability limitation. Big rings, i.e., many nodes spread across large geographical areas, are not economically nor technically viable. For instance, SONET/SDH and Resilient Ethernet Protocol limit their rings to 16 nodes [START_REF]Ethernet ring protection switching[END_REF]. Currently, interconnected rings is still believed to be the appropriate architectural arrangement for larger networks. Hierarchical structures composing collector and core rings can be built [START_REF] Wu | Fiber Network Service Survivability[END_REF]. But note that a single node failure can isolate parts of the network. Therefore, the dual-homed ring is the most appropriate approach to follow when building interconnected rings, in spite of its higher deployment cost. Standardization bodies also support the multi-ring/ladder network prototype as a way of building a mesh through interconnected rings, e.g., [START_REF]Ethernet ring protection switching[END_REF]. Note that such an arrangement also makes network topologies to gradually depart from the simple and cost effective ring-based approach, demanding also more complex and less effective protection schemes [START_REF] Resendo | Optimal multilayer groomingoriented design for inter-ring traffic protection in DNI multiring WDM networks[END_REF].

As a result, network architects are already arguing against a rigid (dualhomed) ring hierarchy and advocating for a flexible mesh hierarchy [START_REF] Alexander | Intelligent infrastructure provides new broadband opportunities, slides from Ciena CTO Steve Alexander[END_REF]. Note that there is still an evident inclination in those modern proposals of following classic rules of thumb, such as building meshes with concentric and interconnected rings [START_REF] Wu | Fiber Network Service Survivability[END_REF], to ensure survivability. There are initiatives such as the use of bounded rings in [START_REF] Fortz | Two-connected networks with rings of bounded cardinality[END_REF], which provides an integer linear program model to design such a topology; and some heuristic algorithms are also presented in [START_REF] Fortz | A tabu search heuristic for the design of two-connected networks with bounded rings[END_REF][START_REF] Ventresca | A genetic algorithm for the design of minimum-cost two-connected networks with bounded rings[END_REF][START_REF] Foxwell | Particle swarm optimisation for the design of two-connected networks with bounded rings[END_REF]. Unfortunately, so far no systematic and scalable topology model has been proposed to grow survivable ring networks into resilient meshes.

How can graph theory help?

We argue in this paper that the principle of network resilience has been neglected at network topology design phase. Usually resilience has been left to be resolved by protection and restoration techniques, after a survivable network topology has been put in place.

It is usually assumed that survivability and resiliency are different instances of the network design problem; or at least a far too complicated problem to be solved at once. Not only inefficient solutions are being proposed for protecting traffic, but also complex and slow mechanisms for traffic restoration can be the result of an underlying constrained physical topology. Note that a consistent study of graph properties can address resiliency (and survivability as a consequence) and also unlock features to be used by overlay networks embedded in this physical topology.

But to be practical, this topology design coming from graph theory must prove to be geographically viable. Network architects should be also able to expand their network in a pay-as-you grow style, without being constrained by modular, "exotic", or inflexible node interconnection architectures. It is also highly desirable that these graphs could resemble (or be compatible) with legacy solutions, such as multi-ring topologies. This may ease its adaptation to existing operator's control and management frameworks.

3 Background: Twin Graphs Twin graphs are particular 2-connected graphs that have at least 2 node-disjoint geodesics between every two non-adjacent nodes, and require for that the minimum number of links [START_REF] Farley | Minimum self-repairing graphs[END_REF]. In graph theory literature, they are called minimumsize 2-geodetically-connected graphs. Each twin graph has order n ≥ 4 nodes and size m = 2n -4 links [START_REF] Farley | Minimum self-repairing graphs[END_REF].

Twin graphs are recursively defined as follows [START_REF] Farley | Minimum self-repairing graphs[END_REF]: (i) the cycle of order 4 (C 4 ) is a twin graph; (ii) if G is a twin graph of order n and (u, v) is a twin pair in G (i.e., a pair of nodes that have the same node neighbors), then the addition of a new node v by using two new links uv and vv produces a twin graph G of order n + 1. Thus, in order to grow a twin graph G, only two steps are needed:

1. Identify a twin pair (u, v) in G; 2. Build G , where V (G ) = V (G) ∪ {v } and E(G ) = E(G) ∪ {uv , vv }.
Notice that this scaling up process can also be used to add to a twin graph more than one node at the time. Indeed, one can add a new node in each of the twin pairs of interest in order to build larger twin graphs. Moreover, there are other graph operations, such as the merging process proposed in [START_REF] Chang | The characterizations of hinge-free networks[END_REF], that can be used to build larger twin graphs.

When recursively generating a twin graph from the C 4 , whenever a node is added, it creates new cycles of order 4, thus all nodes and links of each twin graph belong to cycles of order 4 (see Fig. 1 in Section 4).

In summary, twin graphs can be easily generated by a recursive method, which consists of adding nodes by means of twin pairs. One can always grow a twin graph by adding a node to a twin pair, and in general it can be done in several ways, since twin pairs are not unique [START_REF] Farley | Minimum self-repairing graphs[END_REF].

Results

In this Section practical issues are objectively investigated before suggesting twin topologies to network architects. Although it is not an exhaustive list of practical points to be considered, we expect to provide preliminary and yet solid results supporting twin graphs as a reference model for optical backbone topological design. Cable cuts caused by construction work is the more frequent disruption to optical backbones [START_REF] Habib | Disaster survivability in optical communication networks[END_REF]. Therefore, this paper only focus on link failure analysis when testing resiliency and survivability.

Scalability and flexibility

To illustrate the twin topologies scalability discussed in Section 3, Figure 1 presents the growing process (from n to n + 1) for all (non-isomorphic) twin topologies from 4 up to 7 nodes. Let n denote a twin topology on n nodes. Starting from the C 4 = 4 (first row, first column), by adding an extra node, only one twin topology 5 can be built (second row, first column). Now starting from the 5 (first row, second column), two different twin topologies 1 6 and 2 6 can be built (second row, second column). They, in turn, can generate only two different twin topologies 1 7 and 2 7 (second row, third column) on 7 nodes. Finally, starting from 1 7 and 2 7 (first row, fourth column), one can generate four different twin topologies on 8 nodes (second row, fourth column).

Topology diversity

An optical backbone is a complex physical system and a graph is merely a very simplified abstraction meant just to represent node adjacency. Physical distance, link capacity and other aspects are not represented. Perhaps a given graph is not feasible due to geographical obstacles, so topology diversity provides designers options to pick and choose from a set of equivalent and yet different solutions. The importance of topology diversity and graph weighting will be latter illustrated in an use case.

Expanding results previously illustrated in Fig. 1 beyond n = 7, Table 1 brings the number of twin topologies with n ≤ 17 nodes. As expected, the number of twin topologies increases with n, since all twin topologies of order n + 1 can be generated from a twin topology of order n. For each n there is a twin topology of diameter 2, namely, the complete bipartite graph K 2,n-2 [START_REF] Farley | Minimum self-repairing graphs[END_REF]. This particular instance is also known as dual hub architecture [START_REF] Narula-Tam | Physical topology design for survivable routing of logical rings in WDM-based networks[END_REF]. Besides this, for each n ≤ 17, we have found at least one twin topology for each diameter in the range from 2 to n/2 .

Another important feature of twin topologies is that, given the network order, the number of possible topologies is bounded. For instance, for n = 17 there are 310 twin topologies to be investigated. This diversity also helps solving the physical topology design problem by finding topologies with a good trade-off between diameter and maximum degree depending on the specificity interconnect problems, e.g., [START_REF] Vassoler | Twin datacenter interconnection topology[END_REF].

Neighbor nodes resiliency to link failures

Every twin topology survives single link failures, as well as every 2-connected topology. However, a cut between neighbouring nodes in any topology always comes with a negative impact on routing. In this particular case, a working path of length one would necessarily be replaced by a longer backup path. We propose the link removal impact, denoted as ∆ h , to measure the extent of that impact on routing, by summing up the differences in length of backup and working paths for each pair of nodes. More formally, the link removal impact is written as:

∆ h = n-1 u=1 n v=u+1 (h b uv -h w uv ), (1)
where h b uv and h w uv are, respectively, the length of the backup and working paths, in number of hops, from node u to node v.

Results of the link removal impact can be seen in Figure 2 for all twin topologies with 4 ≤ n ≤ 17 nodes, rings with up to 20 nodes, and real-world optical backbone topologies (reported on [START_REF] Morais | Estimating extra capacity for dedicated protection in mesh optical transport networks[END_REF]) of order up to 20. It is noteworthy the fact that in Figure 2 all twin topologies with a given number of nodes have the same link removal impact. Moreover, compared to the rings and the realworld networks under study, the twin topologies present the lowest link removal impact. Thus, among these sets of networks, the twin topologies are the most resilient regarding cuts between neighbouring nodes.

It is important, however, to remind that any pair of non-adjacent nodes in a twin graph will have at least one backup path exactly with the same number of hops as the working path since twins are 2-GC topologies. So the removal of links, other than neighboring ones, in twin nodes has absolutely no impact on routing in terms of hop count. Fig. 2. Impact of all possible cuts between neigbouring nodes, for twin graphs with up to 17 nodes, rings with up to 20 nodes, and real-world optical backbone topologies (reported on [START_REF] Morais | Estimating extra capacity for dedicated protection in mesh optical transport networks[END_REF]) of order up to 20.

Suvivability to multiple link failures

Any twin topology will survive a single failure but its 2-GC feature can not guarantee that it will survive multiple failures. Following the procedure described in [20], we computed the relative number of link cut sets of sizes 2, 3 and 4 for the three sets of topologies. That procedure allow us to analyze twin topologies stressed with multiple failures.

The number of link cut sets of size i, denoted as S i , gives the number of ways a network becomes disconnected after removing i links. When normalizing S i with respect to the total number of sets of i links, we get the relative number of cut sets of size i, which is denoted as S i (%). We can formally present it as:

S i (%) = S i m i 100, (2)
where m i it the combination of m links taken i at a time without repetition. Figure 3 shows S i (%) for i = 2, 3 and 4. For instance, when S 2 (%) = 25% it means that a quarter of all possible simultaneous failures in two links will disconnect the network. Thus, the higher this number, the more likely is the network to be disconnected.

Results in Figure 3 show, as expected, that ring topologies become disconnected after removing 2 or more links. The larger is the cut set, the better twin-graph families perform in comparison to the group of real-world topologies. There is a clear and consistent trend: A lower probability of disconnecting the network when larger cut sets are considered for twin graph topologies in comparison to real-world topologies. This is highlighted by S 4 (%) in Fig. 3(c) when n ≥ 9. Results for real-world networks is highly topology depended and therefore are scattered in contrast with twin topologies outcomes clustered in a narrow range despite their topology diversity seen in Table 1. This result shows that the overall vulnerability to simultaneous failure events can be significantly reduced by designing physical topologies with twin topologies.

Number of additional links to provide intrinsic resilience

We must test if twin topologies produce networks that would be compatible with current optical backbone networks. For that, we present in Figure 4 the number of links versus the number of nodes for all twin topologies, rings and real-world backbones under study. Evidently, the ring topology provides the lower bound and it can be seen that twin topologies in general require few more links than real-world optical backbones.

The literature shows that real-world optical backbones typically have average degree (that is twice the number of links over the number of nodes) ranging from 2 to 4 [START_REF] Pavan | Generating realistic optical transport network topologies[END_REF]. For twin graphs, the average degree d is given by:

d = 2m n = 4n -8 n = 4 - 8 n . (3)
Thus, it is noteworthy to see that the average node degree is bounded to the interval 2 ≤ d < 4 for twin topologies of any order. In other words, the number of links of twin and real-world topologies with n nodes is between n and 2n. We can conclude that, for a given n node topology, we can provide intrinsic resiliency with almost the same number of links used by real-world topologies. Thus, all the aforementioned advantages of twin topologies may come at a very reasonable cost. nodes, and real-world optical backbone topologies (reported on [START_REF] Morais | Estimating extra capacity for dedicated protection in mesh optical transport networks[END_REF]) of order up to 20.

Use case: A resilient CESNET redesign

In order to illustrate how our paradigm can be used in practice, we have chosen to redesign the 12-node CESNET network shown in Figure 5(a) to improve its resilience. Out of the set of real-world networks, this is the one with the closest average degree to a twin graph.

For mapping nodes from a twin topology to cities in their geographical positions, we have exhaustively analyzed twin topologies with 12 nodes looking for the minimal total fiber length. The result of CESNET redesigned as a twin expending the least accumulated fiber length is shown in Figure 5 Note that in this paper, we have initially chosen to consider only unweighted links because we focus on topological features of twin graphs. However, there is no constraint in considering, a posteriori, links weighted by geographical distances between nodes to optimally map a twin graph to geographical positions. Note that one may also use link capacities or any other link weighting parameter.

The total fiber length of the original CESNET topology and the corresponding twin topology are about 1842km, and 2137km, respectively. This 16% increase is somewhat expected since the original CESNET topology has 19 links, whereas any twin topology with 12 nodes has 20 links. Nevertheless, the benefits for resilience is clear as the link removal impact, ∆ h , which is originally at 106, reduces to 40 (62% smaller) for our twin-graph-based redesign. In addition, a significant improvement is achieved on the survivability to multiple link failures, measured by the relative number of cut sets of sizes 2, 3, and 4 shown in Table 2. For instance, 23.3% of all possible simultaneous failures in four links will disconnect the original CESNET topology, compared to only 15.3% for its twin version shown in Fig. 5(b). Table 2. of resilience and survivability for topologies shown in Figure 5.

Concluding remarks

We proposed the twin topology as a new reference model to design (or redesign) physical topologies for next generation optical backbone networks. Twin graphs have an average degree in agreement with the average degree of real-world optical backbone topologies. Besides its intrinsic resilience given by their 2-GC, we found out improved survivability to multiple failures, fine granularity for scalability, and topology diversity for better matching graphs to the real problem. We noticed also that the twin graph on n nodes minimizing the diameter, i.e, the complete bipartite graph K 2,n-2 , corresponds to the solution presented by [START_REF] Narula-Tam | Physical topology design for survivable routing of logical rings in WDM-based networks[END_REF] to the problem of designing physical topologies that ensure logical rings of size n -2 can be embedded in a survivable manner. Since solutions of this problem must have at least 2n -4 links ([18], Theorem 2.5), it is interesting to investigate which twin graphs on n nodes also satisfy it.

Twin topologies solve, for κ = 4, the problem stated in [START_REF] Fortz | Two-connected networks with rings of bounded cardinality[END_REF], i.e., the problem of finding a 2-connected network such that each link belongs to a cycle of length at most κ. For future work, it is interesting to investigate topologies based on cycles of different order (e.g., 3, 5, and 6) in the context of the design of optical backbone networks.

The implications for this new topology design on WDM systems are yet to be investigated. An exhaustive analysis over all 7-node networks have shown that throughput and blocking ratio strongly depends on physical interconnection topology [START_REF] Tessinari | On the impact of the physical topology on the optical network performance[END_REF]. These results suggest that wavelength requirements will be also affected by physical interconnection topology. It is expected that intrinsic 2-GC features of twin topologies can facilitate wavelength routing and therefore reduce wavelength counting. Future work will also involve the impact of our underlay twin topology on the multi-layer resilience mechanisms considering elastic and flexible optical transmission technologies.

Fig. 1 .

 1 Fig.1. Growing twin topologies from the C4. Blank nodes and dashed lines represent all possible (non-isomorphic) ways for growing twin topologies of order 4 ≤ n ≤ 7 (on the top) by means of twin pairs, which are highlighted in colors, in order to build new twin topologies of order n + 1 (on the bottom).

Fig. 3 .

 3 Fig. 3. Relative number of cut sets of sizes (a) 2, (b) 3, and (c) 4 versus the number of nodes, for ring topologies, twin topologies, and real-world backbone topologies.

Fig. 4 .

 4 Fig.[START_REF] Chang | The characterizations of hinge-free networks[END_REF]. Number of links required by twin graphs with up to 17 nodes, rings up to 20 nodes, and real-world optical backbone topologies (reported on[START_REF] Morais | Estimating extra capacity for dedicated protection in mesh optical transport networks[END_REF]) of order up to 20.

  (b). It is noteworthy that 11 out of 19 links of the original network remain unchanged (solid lines) in its Twin version.

Fig. 5 .

 5 Fig. 5. (a) The original CESNET topology; (b) A twin topology labelled according to CESNET nodes in order to minimize the total fiber length. Solid lines represent links that exist in both network versions. Dashed lines represent removed links in (a) and added links in (b), respectively.

Table 1 .

 1 Number of twin topologies with n ≤ 17 nodes.

	n 4 5 6 7 8 9 10 11 12 13 14 15 16 17
	# 1 1 2 2 4 5 9 13 23 35 63 102 182 310

This work was partially supported by FAPES, CAPES, and CNPq (Brazil), and NSERC (Canada). It is also part of the FUTEBOL project, which has received funding from the European Union's Horizon 2020 (grant no. 688941), as well from the Brazilian Ministry of Science, Technology and Innovation (MCTI) through RNP and CTIC.