Virtual Network Embedding Approximations: Leveraging Randomized Rounding

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The Virtual Network Embedding Problem (VNEP) captures the essence of many resource allocation problems. In the VNEP, customers request resources in the form of Virtual Networks. An embedding of a virtual network on a shared physical infrastructure is the joint mapping of (virtual) nodes to physical servers together with the mapping of (virtual) edges onto paths in the physical network connecting the respective servers. This work initiates the study of approximation algorithms for the VNEP for general request graphs. Concretely, we study the offline setting with admission control: given multiple requests, the task is to embed the most profitable subset while not exceeding resource capacities. Our approximation is based on the randomized rounding of Linear Programming (LP) solutions. Interestingly, we uncover that the standard LP formulation for the VNEP exhibits an inherent structural deficit when considering general virtual network topologies: its solutions cannot be decomposed into valid embeddings. In turn, focusing on the class of cactus request graphs, we devise a novel LP formulation, whose solutions can be decomposed. Proving performance guarantees of our rounding scheme, we obtain the first approximation algorithm for the VNEP in the resource augmentation model. We propose different types of rounding heuristics and evaluate their performance in an extensive computational study. Our results indicate that good solutions can be achieved even without resource augmentations. Specifically, heuristical rounding achieves 77.2% of the baseline’s profit on average while respecting capacities.BMBF, 01IS12056, Software Campus GrantEC/H2020/679158/EU/Resolving the Tussle in the Internet: Mapping, Architecture, and Policy Making/ResolutioNe

Towards a Virtualized Next Generation Internet

A promising solution to overcome the Internet ossification is network virtualization in which Internet Service Providers (ISPs) are decoupled into two tiers: service providers (SPs), and infrastructure providers (InPs). The former maintain and customize virtual network(s) to meet the service requirement of end-users, which is mapped to the physical network infrastructure that is managed and deployed by the latter via the Virtual Network Embedding (VNE) process. VNE consists of two major components: node assignment, and link mapping, which can be shown to be NP-Complete. In the first part of the dissertation, we present a path-based ILP model for the VNE problem. Our solution employs a branch-and-bound framework to resolve the integrity constraints, while embedding the column generation process to effectively obtain the lower bound for branch pruning. Different from existing approaches, the proposed solution can either obtain an optimal solution or a near-optimal solution with guarantee on the solution quality. A common strategy in VNE algorithm design is to decompose the problem into two sequential sub-problems: node assignment (NA) and link mapping (LM). With this approach, it is inexorable to sacrifice the solution quality since the NA is not holistic and not-reversible. In the second part, we are motivated to answer the question: Is it possible to maintain the simplicity of the Divide-and-Conquer strategy while still achieving optimality? Our answer is based on a decomposition framework supported by the Primal-Dual analysis of the path-based ILP model. This dissertation also attempts to address issues in two frontiers of network virtualization: survivability, and integration of optical substrate. In the third part, we address the survivable network embedding (SNE) problem from a network flow perspective, considering both splittable and non-splittable flows. In addition, the explosive growth of the Internet traffic calls for the support of a bandwidth abundant optical substrate, despite the extra dimensions of complexity caused by the heterogeneities of optical resources, and the physical feature of optical transmission. In this fourth part, we present a holistic view of motivation, architecture, and challenges on the way towards a virtualized optical substrate that supports network virtualization

An Efficient Decomposition Algorithm for Large-Scale Network Slicing

In this paper, we consider the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. We propose an efficient decomposition algorithm for solving this NP-hard problem. The proposed algorithm decomposes the large-scale hard NS problem into two relatively easy function placement (FP) and traffic routing (TR) subproblems and iteratively solves them enabling information feedback between each other, which makes it particularly suitable to solve large-scale problems. Specifically, the FP subproblem is to place service functions into cloud nodes in the network, and solving it can return a function placement strategy based on which the TR subproblem is defined; and the TR subproblem is to find paths connecting two nodes hosting two adjacent functions in the network, and solving it can either verify that the solution of the FP subproblem is an optimal solution of the original problem, or return a valid inequality to the FP subproblem that cuts off the current infeasible solution. The proposed algorithm is guaranteed to find the global solution of the NS problem. We demonstrate the effectiveness and efficiency of the proposed algorithm via numerical experiments.Comment: 5 pages, 4 figures, accepted for publication in IEEE SPAWC 202

A dynamic pricing algorithm for a network of virtual resources

A service chain is a combination of network services (e.g. network address translation (NAT), a firewall, etc.) that are interconnected to support an application (e.g. video-on-demand). Building a service chain requires a set of specialized hardware devices each of which need to be configured with their own command syntax. By moving management functions out of forwarding hardware into controller software, software-defined networking (SDN) simplifies provisioning and reconfiguration of service chains. By moving the network functions out of dedicated hardware devices into software running on standard x86 servers, network function virtualization (NFV) turns the deployment of a service chain into a more (cost)-efficient and flexible process. In an SDN/NFV-based architecture, those service chains are composed of virtual network functions (VNFs) that need to be mapped to physical network components. In literature, several algorithmic approaches exist to do so efficiently and cost-effectively. However, once mapped, a simple revenue model is used for pricing the requested substrate resources. This often leads to a loss of revenue for the infrastructure provider. In this paper, we propose a more advanced, dynamic pricing algorithm for pricing the requested substrate resources. The proposed algorithm increases the infrastructure provider's revenue based on historic data, current infrastructure utilization levels and the pricing of competitors. Our experimental evaluation shows that the proposed algorithm increases the revenue of the infrastructure provider significantly, independent of the average network utilization.Peer Reviewe

Learning Augmented Optimization for Network Softwarization in 5G

The rapid uptake of mobile devices and applications are posing unprecedented traffic burdens on the existing networking infrastructures. In order to maximize both user experience and investment return, the networking and communications systems are evolving to the next gen- eration – 5G, which is expected to support more flexibility, agility, and intelligence towards provisioned services and infrastructure management. Fulfilling these tasks is challenging, as nowadays networks are increasingly heterogeneous, dynamic and expanded with large sizes. Network softwarization is one of the critical enabling technologies to implement these requirements in 5G. In addition to these problems investigated in preliminary researches about this technology, many new emerging application requirements and advanced opti- mization & learning technologies are introducing more challenges & opportunities for its fully application in practical production environment. This motivates this thesis to develop a new learning augmented optimization technology, which merges both the advanced opti- mization and learning techniques to meet the distinct characteristics of the new application environment. To be more specific, the abstracts of the key contents in this thesis are listed as follows: • We first develop a stochastic solution to augment the optimization of the Network Function Virtualization (NFV) services in dynamical networks. In contrast to the dominant NFV solutions applied for the deterministic networking environments, the inherent network dynamics and uncertainties from 5G infrastructure are impeding the rollout of NFV in many emerging networking applications. Therefore, Chapter 3 investigates the issues of network utility degradation when implementing NFV in dynamical networks, and proposes a robust NFV solution with full respect to the underlying stochastic features. 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. • Next, Chapter 4 aims to intertwin the traditional optimization and learning technologies. In order to reap the merits of both optimization and learning technologies but avoid their limitations, promissing integrative approaches are investigated to combine the traditional optimization theories with advanced learning methods. Subsequently, an online optimization process is designed to learn the system dynamics for the network slicing problem, another critical challenge for network softwarization. Specifically, we first present a two-stage slicing optimization model with time-averaged constraints and objective to safeguard the network slicing operations in time-varying networks. Directly solving an off-line solution to this problem is intractable since the future system realizations are unknown before decisions. To address this, we combine the historical learning and Lyapunov stability theories, and develop a learning augmented online optimization approach. This facilitates the system to learn a safe slicing solution from both historical records and real-time observations. We prove that the proposed solution is always feasible and nearly optimal, up to a constant additive factor. Finally, simulation experiments are also provided to demonstrate the considerable improvement of the proposals. • The success of traditional solutions to optimizing the stochastic systems often requires solving a base optimization program repeatedly until convergence. For each iteration, the base program exhibits the same model structure, but only differing in their input data. Such properties of the stochastic optimization systems encourage the work of Chapter 5, in which we apply the latest deep learning technologies to abstract the core structures of an optimization model and then use the learned deep learning model to directly generate the solutions to the equivalent optimization model. In this respect, an encoder-decoder based learning model is developed in Chapter 5 to improve the optimization of network slices. In order to facilitate the solving of the constrained combinatorial optimization program in a deep learning manner, we design a problem-specific decoding process by integrating program constraints and problem context information into the training process. The deep learning model, once trained, can be used to directly generate the solution to any specific problem instance. This avoids the extensive computation in traditional approaches, which re-solve the whole combinatorial optimization problem for every instance from the scratch. With the help of the REINFORCE gradient estimator, the obtained deep learning model in the experiments achieves significantly reduced computation time and optimality loss

GCMD: Genetic Correlation Multi-Domain Virtual Network Embedding algorithm

With the increase of network scale and the complexity of network structure, the problems of traditional Internet have emerged. At the same time, the appearance of network function virtualization (NFV) and network virtualization technologies has largely solved this problem, they can effectively split the network according to the application requirements, and flexibly provide network functions when needed. During the development of virtual network, how to improve network performance, including reducing the cost of embedding process and shortening the embedding time, has been widely concerned by the academia. Combining genetic algorithm with virtual network embedding problem, this paper proposes a genetic correlation multi-domain virtual network embedding algorithm (GCMD-VNE). The algorithm improves the natural selection stage and crossover stage of genetic algorithm, adds more accurate selection formula and crossover conditions, and improves the performance of the algorithm. Simulation results show that, compared with the existing algorithms, the algorithm has better performance in terms of embedding cost and embedding time.Postprint (published version

A efficient mapping algorithm with novel node-ranking approach for embedding virtual networks

Virtual network embedding (VNE) problem has been widely accepted as an important aspect in network virtualization (NV) area: how to efficiently embed virtual networks, with node and link resource demands, onto the shared substrate network that has finite network resources. Previous VNE heuristic algorithms, only considering single network topology attribute and local resources of each node, may lead to inefficient resource utilization of the substrate network in the long term. To address this issue, a topology attribute and global resource-driven VNE algorithm (VNE-TAGRD), adopting a novel node-ranking approach, is proposed in this paper. The novel node-ranking approach, developed from the well-known Google PageRank algorithm, considers three essential topology attributes and global network resources information before conducting the embedding of given virtual network request (VNR). Numerical simulation results reveal that the VNE-TAGRD algorithm outperforms five typical and latest heuristic algorithms that only consider single network topology attribute and local resources of each node, such as long-term average VNR acceptance ratio and average revenue to cost ratio

A Novel Optimal Mapping Algorithm With Less Computational Complexity for Virtual Network Embedding

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Network Virtualization (NV) is widely accepted as one enabling technology for future network, which enables multiple Virtual Networks (VNs) with different paradigms and protocols to coexist on the shared Substrate Network (SN). One key challenge in network virtualization is Virtual Network Embedding (VNE), which maps a virtual network onto the shared SN. Since VNE is NP-hard, existing efforts mainly focus on proposing heuristic algorithms that try to achieve feasible VN embedding in reasonable time, consequently the resulted embedding is not optimal. To tackle this difficulty, we propose a candidate assisted (CAN-A) optimal VNE algorithm with lower computational complexity. The key idea of the CAN-A algorithm lies in constructing the candidate substrate node subset and the candidate substrate path subset before embedding. This reduces the mapping execution time substantially without performance loss. In the following embedding, four types of node and link constraints are considered in the CAN-A algorithm, making it more applicable to realistic networks. Simulation results show that the execution time of CAN-A is hugely cut down compared with pure VNE-MIP algorithm. CAN-A also outperforms the typical heuristic algorithms in terms of other performance indices, such as the average virtual network request (VNR) acceptance ratio and the average virtual link propagation delay