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Saddle dynamics is a time continuous dynamics to efficiently compute the any-index saddle points and construct the solution landscape. In practice, the saddle dynamics needs to be discretized for numerical computations, while the corresponding numerical analysis are rarely studied in the literature, especially for the high-index cases. In this paper we propose the convergence analysis of discrete high-index saddle dynamics. To be specific, we prove the local linear convergence rates of numerical schemes of high-index saddle dynamics, which indicates that the local curvature in the neighborhood of the saddle point and the accuracy of computing the eigenfunctions are main factors that affect the convergence of discrete saddle dynamics. The proved results serve as compensations for the convergence analysis of high-index saddle dynamics and are substantiated by numerical experiments.

Current trends in networking propose the use of Machine Learning (ML) for a wide variety of network optimization tasks. As such, many efforts have been made to produce ML-based solutions for Traffic Engineering (TE), which is a fundamental problem in ISP networks. Nowadays, state-of-the-art TE optimizers rely on traditional optimization techniques, such as Local search, Constraint Programming, or Linear programming. In this paper, we present MAGNNETO, a distributed ML-based framework that leverages Multi-Agent Reinforcement Learning and Graph Neural Networks for distributed TE optimization. MAGNNETO deploys a set of agents across the network that learn and communicate in a distributed fashion via message exchanges between neighboring agents. Particularly, we apply this framework to optimize link weights in OSPF, with the goal of minimizing network congestion. In our evaluation, we compare MAGNNETO against several state-of-the-art TE optimizers in more than 75 topologies (up to 153 nodes and 354 links), including realistic traffic loads. Our experimental results show that, thanks to its distributed nature, MAGNNETO achieves comparable performance to state-of-the-art TE optimizers with significantly lower execution times. Moreover, our ML-based solution demonstrates a strong generalization capability to successfully operate in new networks unseen during training., IEEE Transactions on Cognitive Communications and Networking (2023). arXiv admin note: text overlap with arXiv:2109.01445

Graph neural networks (GNN) have shown outstanding applications in fields where data is essentially represented as graphs (e.g., chemistry, biology, recommendation systems). In this vein, communication networks comprise many fundamental components that are naturally represented in a graph-structured manner (e.g., topology, routing, signal interference). This position article presents GNNs as a fundamental tool for modeling, control and management of communication networks. GNNs represent a new generation of data-driven models that can accurately learn and reproduce the complex behaviors behind real-world networks. As a result, these models can be applied to a wide variety of networking use cases, such as planning, online optimization, or troubleshooting. The main advantage of GNNs over traditional neural networks lies in their unprecedented generalization capabilities when applied to other networks and configurations unseen during training. This is a critical feature for achieving practical data-driven solutions for networking. This article starts with a brief tutorial on GNNs and some potential applications to communication networks. Then, it presents two state-of-the-art GNN models respectively applied to wired and wireless networks. Lastly, it delves into the key open challenges and opportunities yet to be explored in this novel research area. This publication is part of the Spanish I+D+i project TRAINER-A (ref. PID2020-118011GB-C21), funded by MCIN/AEI/10.13039/501100011033. This work is also partially funded by the Catalan Institution for Research and Advanced Studies (ICREA) and the Secretariat for Universities and Research of the Ministry of Business and Knowledge of the Government of Catalonia and the European Social Fund.

Network slicing, as a key 5G enabling technology, is promising to support with more flexibility, agility, and intelligence towards the provisioned services and infrastructure management. Fulfilling these tasks is challenging, as nowadays networks are increasingly heterogeneous, dynamic and large-dimensioned. This contradicts the dominant network slicing solutions that only customize immediate performance over one snapshot of the system in the literature. Instead, this paper first presents a two-stage slicing optimization model with time-averaged metrics to safeguard the network slicing in the dynamical networks, where prior environmental knowledge is absent but can be partially observed at runtime. Directly solving an off-line solution to this problem is intractable since the future system realizations are unknown before decisions. Therefore, we propose a learning augmented optimization approach with deep learning and Lyapunov stability theories. This enables the system to learn a safe slicing solution from both historical records and run-time observations. We prove that the proposed solution is always feasible and nearly optimal, up to a constant additive factor. Finally, we demonstrate up to $2.6\times $ improvement in the simulation when compared with three state-of-the-art algorithms.

Network modeling is a fundamental tool in network research, design, and operation. Arguably the most popular method for modeling is Queuing Theory (QT). Its main limitation is that it imposes strong assumptions on the packet arrival process, which typically do not hold in real networks. In the field of Deep Learning, Graph Neural Networks (GNN) have emerged as a new technique to build data-driven models that can learn complex and non-linear behavior. In this paper, we present RouteNet-Erlang, a pioneering GNN architecture designed to model computer networks. RouteNet-Erlang supports complex traffic models, multi-queue scheduling policies, routing policies and can provide accurate estimates in networks not seen in the training phase. We benchmark RouteNet-Erlang against a state-of-the-art QT model, and our results show that it outperforms QT in all the network scenarios. This publication is part of the Spanish I+D+i project TRAINER-A (ref.PID2020-118011GB-C21), funded by MCIN/ AEI/10.13039/501100011033. This work is also partially funded by the Catalan Institution for Research and Advanced Studies (ICREA) and the Secretariat for Universities and Research of the Ministry of Business and Knowledge of the Government of Catalonia and the European Social Fund.

Network models are an essential block of modern networks. For example, they are widely used in network planning and optimization. However, as networks increase in scale and complexity, some models present limitations, such as the assumption of Markovian traffic in queuing theory models, or the high computational cost of network simulators. Recent advances in machine learning, such as Graph Neural Networks (GNN), are enabling a new generation of network models that are data-driven and can learn complex non-linear behaviors. In this paper, we present RouteNet-Fermi, a custom GNN model that shares the same goals as Queuing Theory, while being considerably more accurate in the presence of realistic traffic models. The proposed model predicts accurately the delay, jitter, and packet loss of a network. We have tested RouteNet-Fermi in networks of increasing size (up to 300 nodes), including samples with mixed traffic profiles — e.g., with complex non-Markovian models — and arbitrary routing and queue scheduling configurations. Our experimental results show that RouteNet-Fermi achieves similar accuracy as computationally-expensive packet-level simulators and scales accurately to larger networks. Our model produces delay estimates with a mean relative error of 6.24% when applied to a test dataset of 1,000 samples, including network topologies one order of magnitude larger than those seen during training. Finally, we have also evaluated RouteNet-Fermi with measurements from a physical testbed and packet traces from a real-life network. This work was supported in part by the Spanish I+D+i Project TRAINER-A funded by the Ministry of Science and Innovation (MCIN)/State Investigation Agency (AEI)/10.13039/501100011033 under Grant PID2020-118011GB-C21, in part by the Catalan Institution for Research and Advanced Studies (ICREA), and in part by the Secretariat for Universities and Research of the Ministry of Business and Knowledge of the Government of Catalonia and the European Social Fund.

Wide Area Networks (WAN) are a key infrastructure in today's society. During the last years, WANs have seen a considerable increase in network's traffic and network applications, imposing new requirements on existing network technologies (e.g., low latency and high throughput). Consequently, Internet Service Providers (ISP) are under pressure to ensure the customer's Quality of Service and fulfill Service Level Agreements. Network operators leverage Traffic Engineering (TE) techniques to efficiently manage network's resources. However, WAN's traffic can drastically change during time and the connectivity can be affected due to external factors (e.g., link failures). Therefore, TE solutions must be able to adapt to dynamic scenarios in real-time. In this paper we propose Enero, an efficient real-time TE solution based on a two-stage optimization process. In the first one, Enero leverages Deep Reinforcement Learning (DRL) to optimize the routing configuration by generating a long-term TE strategy. To enable efficient operation over dynamic network scenarios (e.g., when link failures occur), we integrated a Graph Neural Network into the DRL agent. In the second stage, Enero uses a Local Search algorithm to improve DRL's solution without adding computational overhead to the optimization process. The experimental results indicate that Enero is able to operate in real-world dynamic network topologies in 4.5 seconds on average for topologies up to 100 edges., 12 pages, 9 figures

We analytically and numerically examine the dynamic behavior of an undamped, linear, uniform and homogeneous Euler-Bernoulli beam of finite length, partially supported in its interior by local, grounded, linear spring-dashpot pairs and subjected to a harmonic displacement at its pinned left boundary or at both its ends. The Euler-Bernoulli beam is known to be dispersive and, thus, to exhibit a non-constant relationship between frequency and wave number. Local dissipation due to the interior support results in a non-classically damped system and, consequently, mode complexity. An analytical framework is developed to examine the coexistence of propagating and standing harmonic waves in complementary regions of the beam for four distinct boundary conditions at the right end: pinned, fixed, free and linear elastic. We show that the system can be designed so that, for a particular input frequency and interior support location, nearly perfect spatial separation of traveling and standing waves can be achieved; the imperfection is shown to be caused by the non-oscillatory evanescent components in the solution. We further demonstrate that vibration localization is achieved by satisfying necessary and sufficient wave separation conditions, which correspond to frequency- and position-dependent support stiffness and damping values, and that linear viscous damping in the interior support, but not necessarily linear stiffness, is required to achieve the separation phenomenon and vibration localization.

Graph Neural Networks (GNN) have recently exploded in the Machine Learning area as a novel technique for modeling graph-structured data. This makes them especially suitable for applications in the networking field, as communication networks inherently comprise graphs at many levels (e.g., topology, routing, user connections). In this demo, we will present IGNNITION, an open-source framework for fast prototyping of GNNs applied to communication networks. This framework is especially designed for network engineers and/or researchers with limited background on neural network programming. IGNNITION comprises a set of tools and functionalities that eases and accelerates the whole implementation process, from the design of a GNN model, to its training, evaluation, debugging, and integration into larger network applications. In the demo, we will show how a user can implement a complex GNN model applied to network performance modeling (RouteNet), following three simple steps. This open-source project has received funding from the European Union’s Horizon 2020 research and innovation programme within the framework of the NGI-POINTER Project funded under grant agreement No. 871528. This article reflects only the authors’ view; the EC is not responsible for any use that may be made of the information it contains. The work was also supported by the Spanish MINECO under contract TEC2017-90034-C2-1-R (ALLIANCE) and the Catalan Institution for Research and Advanced Studies (ICREA).

Border Gateway Protocol (BGP) is the standard inter-domain routing protocol that is used to exchange reachability information among Wide Area Networks (WANs). BGP is a policy-based routing protocol that introduces a lot of flexibility. However, this flexibility increases the configuration complexity. In this research, we introduce DeepBGP as a neural network-based system that synthesizes network configuration given a high-level operator intent. We adopt Graph Neural Network (GNN) to represent network topology and generate partial network configuration. A validation unit is then used to calculate a reward based on which an Evolution Strategies (ES) optimizer updates neural network parameters. Since ES does not require backpropagation, they provide a significant reduction in calculation time. Further, the recent advances in deep learning with strong hardware acceleration and the parallelization capabilities offered by ES provide great potential in scaling the proposed solution to larger topologies. We demonstrate experimentally that DeepBGP can generate a network-wide configuration for both Huawei and Cisco devices while fulfilling operator requirements. We also show how Deep-BGP scales when the network size increases, and how hardware acceleration could improve the scalability of the system.

As a key enabling technology for 5G network softwarization, network function virtualization (NFV) provides an efficient paradigm to optimize network resource utility for the benefits of both network providers and users. However, the inherent network dynamics and uncertainties from 5G infrastructure, resources, and applications are slowing down the further adoption of NFV in many emerging networking applications. Motivated by this, in this paper, we investigate the issues of network utility degradation when implementing NFV in dynamic networks, and design a proactive NFV solution from a fully stochastic perspective. Unlike existing deterministic NFV solutions, which assume given network capacities and/or static service quality demands, this paper explicitly integrates the knowledge of influential network variations into a two-stage stochastic resource utilization model. By exploiting the hierarchical decision structures in this problem, a distributed computing framework with two-level decomposition is designed to facilitate a distributed implementation of the proposed model in large-scale networks. The experimental results demonstrate that the proposed solution not only improves 3~5 folds of network performance, but also effectively reduces the risk of service quality violation.

This paper presents a method for reconstructing transient waves traveling in a discrete granular chain from acoustic pressure measurements made in the resulting sound field. A transient vibro-acoustic model is developed, based on the acoustic impulse response of an accelerating sphere, which superposes acoustic radiation from each bead of a granular chain using a convolution integral. We assume straight-line radiation of the acoustic pressure and constant position of the granular chain during propagation of a primary traveling wave. The continuous convolution integral is discretized to obtain the transfer matrix of the acoustic field response that correlates to vibrational motion of a discrete granular chain. To overcome ill-posedness in inverse processing, Tikhonov regularization with appropriate parameter-choice methods is applied. Acoustic field pressures are sampled with a linear microphone array conformal to the geometry of a granular chain at various standoff distances. It is found that the amplitude and speed of the primary traveling wave in a discrete granular chain can be reconstructed from acoustic field responses. The accuracy of reconstruction and the parameter sensitivity are examined with finite element analysis results as benchmarks. For acoustic field pressures contaminated by white noise, root-mean-square error analysis demonstrates that reasonably good reconstruction accuracy can still be achieved when the ill-conditioning of the convolution matrix and the matching of acoustic field pressures are balanced well. This study provides a useful approach to measure and visualize pulse transmission through a discrete granular medium in a time-efficient and cost-effective manner.

The free and forced vibrations of a linear string with a local spring-damper on a partial elastic foundation, as well as a linear string on a viscoelastic foundation conceptualized as a continuous distribution of springs and dampers, are studied in this paper. Exact, analytical results are obtained for the free and forced response to a harmonic excitation applied at one end of the string. Relations between mode complexity and energy confinement with the dispersion in the string system are examined for the steady-state forced vibration, and numerical methods are applied to simulate the transient evolution of energy propagation. Eigenvalue loci veering and normal mode localization are observed for weakly coupled subsystems, when the foundation stiffness is sufficiently large, for both the spatially symmetric and asymmetric systems. The forced vibration results show that nonproportional damping-induced mode complexity, for which there are co-existing regions of purely traveling waves and standing waves, is attainable for the dispersive string system. However, this wave transition phenomenon depends strongly on the location of the attached discrete spring-damper relative to the foundation and whether the excitation frequency Ω is above or below the cutoff frequency ωc. When Ω

Previously, we have proposed a C/U-plane (Control/User plane) decoupled railway wireless network in which higher frequency bands are adopted by small cells to provide wider available spectra for the U-plane of passengers’ services. In order to guarantee reliable connectivity to wayside eNodeBs (eNBs), an onboard mobile relay (MR), consisting of two components, namely, MR-UE (User Equipment) and MR-AP (Access Point), is employed to forward passengers’ services over backhaul links between MR-UE and wayside eNBs. The remaining problem here is how to utilize spectra effectively and efficiently under this new configuration. Since a given wayside eNB hosts only one single accessed user most of the time, we design an additional uplink scheduler for the MR-UE to self-manage the usage of uplink resources, avoiding the complicated uplink grant procedure commonly used in the conventional cellular systems. Moreover, we develop eNB schedulers to coordinate the spectra in small cells. To deal with occasional multi-user scenarios, we propose an uplink scheduler switcher for the macro cell to judge which uplink scheduler should be activated. Furthermore, an uplink resource allocation scheme with high spectrum efficiency is deliberately designed for the new dual-scheduler configuration. Finally, we carry out theoretical analysis and numerical simulations to demonstrate the effectiveness of our proposed scheme.

A new kind of expanded graphite-based composites (EGC) was prepared by sucrose–phosphoric acid solution impregnation, solidification, carbonization and activation. It involves expanded graphite (EG), sucrose and phosphoric acid as starting materials. X-ray diffraction (XRD), scanning electron microscopy (SEM), nitrogen adsorption and mercury porosimetry were selected to analyze the microstructure of the EGC. The results showed that the EGC were made up of graphite and activated carbon. The EGC was not the simply mechanical mixture of the EG and the activated carbon, but coating the activated carbon on the surface of interior and external pores of the EG in the form of thin carbon layer. The thickness of the activated carbon layer was nearly 100 nm by calculation. So the prepared EGC consisted of both macropores from EG and micropores from activated carbon.

In order to enable reliable spatial multiplexing transmission, an environment with rich scatterers is often required, which is not equipped in most railway running environment. So the MIMO channel with sparse scatterer and dominant LOS component in high-speed railway scenario is usually strongly spatial correlated and often fails to support a multiplexing transmission link. While it is actually not a pure LOS environment even in open plain or on a viaduct according to the existing engineering measurements. Hence, in high-speed railway environment, it is still highly possible to support partial multiplexing transmission if configuring a reasonable antenna placement structure with adequate antennas along the train body in the future. To target this problem, this paper investigates the solution of reconstructing the highly correlated railway channel into an equivalent channel with less correlation using the method of principal component analysis and thereon proposes an optimal partial multiplexing transmission solution to improve the link performance. With the proposed solution, the capacity in the distant area from the base station is verified to be significantly improved and that in close distance area is maintained meanwhile the condition number is reduced to be less than 10 to meet the required link quality.