Greedy routing and virtual coordinates for future networks

At the core of the Internet, routers are continuously struggling with ever-growing routing and forwarding tables. Although hardware advances do accommodate such a growth, we anticipate new requirements e.g. in data-oriented networking where each content piece has to be referenced instead of hosts, such that current approaches relying on global information will not be viable anymore, no matter the hardware progress. In this thesis, we investigate greedy routing methods that can achieve similar routing performance as today but use much less resources and which rely on local information only. To this end, we add specially crafted name spaces to the network in which virtual coordinates represent the addressable entities. Our scheme enables participating routers to make forwarding decisions using only neighbourhood information, as the overarching pseudo-geometric name space structure already organizes and incorporates "vicinity" at a global level. A first challenge to the application of greedy routing on virtual coordinates to future networks is that of "routing dead-ends" that are local minima due to the difficulty of consistent coordinates attribution. In this context, we propose a routing recovery scheme based on a multi-resolution embedding of the network in low-dimensional Euclidean spaces. The recovery is performed by routing greedily on a blurrier view of the network. The different network detail-levels are obtained though the embedding of clustering-levels of the graph. When compared with higher-dimensional embeddings of a given network, our method shows a significant diminution of routing failures for similar header and control-state sizes. A second challenge to the application of virtual coordinates and greedy routing to future networks is the support of "customer-provider" as well as "peering" relationships between participants, resulting in a differentiated services environment. Although an application of greedy routing within such a setting would combine two very common fields of today's networking literature, such a scenario has, surprisingly, not been studied so far. In this context we propose two approaches to address this scenario. In a first approach we implement a path-vector protocol similar to that of BGP on top of a greedy embedding of the network. This allows each node to build a spatial map associated with each of its neighbours indicating the accessible regions. Routing is then performed through the use of a decision-tree classifier taking the destination coordinates as input. When applied on a real-world dataset (the CAIDA 2004 AS graph) we demonstrate an up to 40% compression ratio of the routing control information at the network's core as well as a computationally efficient decision process comparable to methods such as binary trees and tries. In a second approach, we take inspiration from consensus-finding in social sciences and transform the three-dimensional distance data structure (where the third dimension encodes the service differentiation) into a two-dimensional matrix on which classical embedding tools can be used. This transformation is achieved by agreeing on a set of constraints on the inter-node distances guaranteeing an administratively-correct greedy routing. The computed distances are also enhanced to encode multipath support. We demonstrate a good greedy routing performance as well as an above 90% satisfaction of multipath constraints when relying on the non-embedded obtained distances on synthetic datasets. As various embeddings of the consensus distances do not fully exploit their multipath potential, the use of compression techniques such as transform coding to approximate the obtained distance allows for better routing performances

Incremental Grid-like Layout Using Soft and Hard Constraints

We explore various techniques to incorporate grid-like layout conventions into a force-directed, constraint-based graph layout framework. In doing so we are able to provide high-quality layout---with predominantly axis-aligned edges---that is more flexible than previous grid-like layout methods and which can capture layout conventions in notations such as SBGN (Systems Biology Graphical Notation). Furthermore, the layout is easily able to respect user-defined constraints and adapt to interaction in online systems and diagram editors such as Dunnart.Comment: Accepted to Graph Drawing 201

A policy-based architecture for virtual network embedding

Network virtualization is a technology that enables multiple virtual instances to coexist on a common physical network infrastructure. This paradigm fostered new business models, allowing infrastructure providers to lease or share their physical resources. Each virtual network is isolated and can be customized to support a new class of customers and applications. To this end, infrastructure providers need to embed virtual networks on their infrastructure. The virtual network embedding is the (NP-hard) problem of matching constrained virtual networks onto a physical network. Heuristics to solve the embedding problem have exploited several policies under different settings. For example, centralized solutions have been devised for small enterprise physical networks, while distributed solutions have been proposed over larger federated wide-area networks. In this thesis we present a policy-based architecture for the virtual network embedding problem. By policy, we mean a variant aspect of any of the three (invariant) embedding mechanisms: physical resource discovery, virtual network mapping, and allocation on the physical infrastructure. Our architecture adapts to different scenarios by instantiating appropriate policies, and has bounds on embedding efficiency, and on convergence embedding time, over a single provider, or across multiple federated providers. The performance of representative novel and existing policy configurations are compared via extensive simulations, and over a prototype implementation. We also present an object model as a foundation for a protocol specification, and we release a testbed to enable users to test their own embedding policies, and to run applications within their virtual networks. The testbed uses a Linux system architecture to reserve virtual node and link capacities

Optimal and probabilistic resource and capability analysis for network slice as a service

Network Slice as a Service is one of the key concepts of the fifth generation of mobile networks (5G). 5G supports new use cases, like the Internet of Things (IoT), massive Machine Type Communication (mMTC) and Ultra-Reliable and Low Latency Communication (URLLC) as well as significant improvements of the conventional Mobile Broadband (MBB) use case. In addition, safety and security critical use cases move into focus. These use cases involve diverging requirements, e.g. network reliability, latency and throughput. Network virtualization and end-to-end mobile network slicing are seen as key enablers to handle those differing requirements and providing mobile network services for the various 5G use cases and between different tenants. Network slices are isolated, virtualized, end-to-end networks optimized for specific use cases. But still they share a common physical network infrastructure. Through logical separation of the network slices on a common end-to-end mobile network infrastructure, an efficient usage of the underlying physical network infrastructure provided by multiple Mobile Service Providers (MSPs) in enabled. Due to the dynamic lifecycle of network slices there is a strong demand for efficient algorithms for the so-called Network Slice Embedding (NSE) problem. Efficient and reliable resource provisioning for Network Slicing as a Service, requires resource allocation based on a mapping of virtual network slice elements on the serving physical mobile network infrastructure. In this thesis, first of all, a formal Network Slice Instance Admission (NSIA) process is presented, based on the 3GPP standardization. This process allows to give fast feedback to a network operator or tenant on the feasibility of embedding incoming Network Slice Instance Requests (NSI-Rs). In addition, corresponding services for NSIA and feasibility checking services are defined in the context of the ETSI ZSM Reference Architecture Framework. In the main part of this work, a mathematical model for solving the NSE Problem formalized as a standardized Linear Program (LP) is presented. The presented solution provides a nearly optimal embedding. This includes the optimal subset of Network Slice Instances (NSIs) to be selected for embedding, in terms of network slice revenue and costs, and the optimal allocation of associated network slice applications, functions, services and communication links on the 5G end-to-end mobile network infrastructure. It can be used to solve the online as well as the offline NSIA problem automatically in different variants. In particular, low latency network slices require deployment of their services and applications, including Network Functions (NFs) close to the user, i.e., at the edge of the mobile network. Since the users of those services might be widely distributed and mobile, multiple instances of the same application are required to be available on numerous distributed edge clouds. A holistic approach for tackling the problem of NSE with edge computing is provided by our so-called Multiple Application Instantiation (MAI) variant of the NSE LP solution. It is capable of determining the optimal number of application instances and their optimal deployment locations on the edge clouds, even for multiple User Equipment (UE) connectivity scenarios. In addition to that multi-path, also referred to as path-splitting, scenarios with a latency sensitive objective function, which guarantees the optimal network utilization as well as minimum latency in the network slice communication, is included. Resource uncertainty, as well as reuse and overbooking of resources guaranteed by Service Level Agreements (SLAs) are discussed in this work. There is a consensus that over-provisioning of mobile communication bands is economically infeasible and certain risk of network overload is accepted for the majority of the 5G use cases. A probabilistic variant of the NSE problem with an uncertainty-aware objective function and a resource availability confidence analysis are presented. The evaluation shows the advantages and the suitability of the different variants of the NSE formalization, as well as its scalability and computational limits in a practical implementation

Study, evaluation and contributions to new algorithms for the embedding problem in a network virtualization environment

Network virtualization is recognized as an enabling technology for the future Internet. It aims to overcome the resistance of the current Internet to architectural change and to enable a new business model decoupling the network services from the underlying infrastructure. The problem of embedding virtual networks in a substrate network is the main resource allocation challenge in network virtualization and is usually referred to as the Virtual Network Embedding (VNE) problem. VNE deals with the allocation of virtual resources both in nodes and links. Therefore, it can be divided into two sub-problems: Virtual Node Mapping where virtual nodes have to be allocated in physical nodes and Virtual Link Mapping where virtual links connecting these virtual nodes have to be mapped to paths connecting the corresponding nodes in the substrate network. Application of network virtualization relies on algorithms that can instantiate virtualized networks on a substrate infrastructure, optimizing the layout for service-relevant metrics. This class of algorithms is commonly known as VNE algorithms. This thesis proposes a set of contributions to solve the research challenges of the VNE that have not been tackled by the research community. To do that, it performs a deep and comprehensive survey of virtual network embedding. The first research challenge identified is the lack of proposals to solve the virtual link mapping stage of VNE using single path in the physical network. As this problem is NP-hard, existing proposals solve it using well known shortest path algorithms that limit the mapping considering just one constraint. This thesis proposes the use of a mathematical multi-constraint routing framework called paths algebra to solve the virtual link mapping stage. Besides, the thesis introduces a new demand caused by virtual link demands into physical nodes acting as intermediate (hidden) hops in a path of the physical network. Most of the current VNE approaches are centralized. They suffer of scalability issues and provide a single point of failure. In addition, they are not able to embed virtual network requests arriving at the same time in parallel. To solve this challenge, this thesis proposes a distributed, parallel and universal virtual network embedding framework. The proposed framework can be used to run any existing embedding algorithm in a distributed way. Thereby, computational load for embedding multiple virtual networks is spread across the substrate network Energy efficiency is one of the main challenges in future networking environments. Network virtualization can be used to tackle this problem by sharing hardware, instead of requiring dedicated hardware for each instance. Until now, VNE algorithms do not consider energy as a factor for the mapping. This thesis introduces the energy aware VNE where the main objective is to switch off as many network nodes and interfaces as possible by allocating the virtual demands to a consolidated subset of active physical networking equipment. To evaluate and validate the aforementioned VNE proposals, this thesis helped in the development of a software framework called ALgorithms for Embedding VIrtual Networks (ALEVIN). ALEVIN allows to easily implement, evaluate and compare different VNE algorithms according to a set of metrics, which evaluate the algorithms and compute their results on a given scenario for arbitrary parameters

On Sensor Network Localization Using SDP Relaxation

A Semidefinite Programming (SDP) relaxation is an effective computational method to solve a Sensor Network Localization problem, which attempts to determine the locations of a group of sensors given the distances between some of them [11]. In this paper, we analyze and determine new sufficient conditions and formulations that guarantee that the SDP relaxation is exact, i.e., gives the correct solution. These conditions can be useful for designing sensor networks and managing connectivities in practice. Our main contribution is twofold: We present the first non-asymptotic bound on the connectivity or radio range requirement of the sensors in order to ensure the network is uniquely localizable. Determining this range is a key component in the design of sensor networks, and we provide a result that leads to a correct localization of each sensor, for any number of sensors. Second, we introduce a new class of graphs that can always be correctly localized by an SDP relaxation. Specifically, we show that adding a simple objective function to the SDP relaxation model will ensure that the solution is correct when applied to a triangulation graph. Since triangulation graphs are very sparse, this is informationally efficient, requiring an almost minimal amount of distance information. We also analyze a number objective functions for the SDP relaxation to solve the localization problem for a general graph.Comment: 20 pages, 4 figures, submitted to the Fields Institute Communications Series on Discrete Geometry and Optimizatio

The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems

We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low spatial dimension at finite size, a physical scenario where tensor network methods, both Density Matrix Renormalization Group and beyond, have long proven to be winning strategies. Here we explore in detail the numerical frameworks and methods employed to deal with low-dimension physical setups, from a computational physics perspective. We focus on symmetries and closed-system simulations in arbitrary boundary conditions, while discussing the numerical data structures and linear algebra manipulation routines involved, which form the core libraries of any tensor network code. At a higher level, we put the spotlight on loop-free network geometries, discussing their advantages, and presenting in detail algorithms to simulate low-energy equilibrium states. Accompanied by discussions of data structures, numerical techniques and performance, this anthology serves as a programmer's companion, as well as a self-contained introduction and review of the basic and selected advanced concepts in tensor networks, including examples of their applications.Comment: 115 pages, 56 figure

Deliverable DJRA1.2. Solutions and protocols proposal for the network control, management and monitoring in a virtualized network context

This deliverable presents several research proposals for the FEDERICA network, in different subjects, such as monitoring, routing, signalling, resource discovery, and isolation. For each topic one or more possible solutions are elaborated, explaining the background, functioning and the implications of the proposed solutions.This deliverable goes further on the research aspects within FEDERICA. First of all the architecture of the control plane for the FEDERICA infrastructure will be defined. Several possibilities could be implemented, using the basic FEDERICA infrastructure as a starting point. The focus on this document is the intra-domain aspects of the control plane and their properties. Also some inter-domain aspects are addressed. The main objective of this deliverable is to lay great stress on creating and implementing the prototype/tool for the FEDERICA slice-oriented control system using the appropriate framework. This deliverable goes deeply into the definition of the containers between entities and their syntax, preparing this tool for the future implementation of any kind of algorithm related to the control plane, for both to apply UPB policies or to configure it by hand. We opt for an open solution despite the real time limitations that we could have (for instance, opening web services connexions or applying fast recovering mechanisms). The application being developed is the central element in the control plane, and additional features must be added to this application. This control plane, from the functionality point of view, is composed by several procedures that provide a reliable application and that include some mechanisms or algorithms to be able to discover and assign resources to the user. To achieve this, several topics must be researched in order to propose new protocols for the virtual infrastructure. The topics and necessary features covered in this document include resource discovery, resource allocation, signalling, routing, isolation and monitoring. All these topics must be researched in order to find a good solution for the FEDERICA network. Some of these algorithms have started to be analyzed and will be expanded in the next deliverable. Current standardization and existing solutions have been investigated in order to find a good solution for FEDERICA. Resource discovery is an important issue within the FEDERICA network, as manual resource discovery is no option, due to scalability requirement. Furthermore, no standardization exists, so knowledge must be obtained from related work. Ideally, the proposed solutions for these topics should not only be adequate specifically for this infrastructure, but could also be applied to other virtualized networks.Postprint (published version

Enabling Technology in Optical Fiber Communications: From Device, System to Networking

This book explores the enabling technology in optical fiber communications. It focuses on the state-of-the-art advances from fundamental theories, devices, and subsystems to networking applications as well as future perspectives of optical fiber communications. The topics cover include integrated photonics, fiber optics, fiber and free-space optical communications, and optical networking

Multi-provider network service embedding

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