QoS-Aware Virtual Network Embedding 9789811652219, 981165221X

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Chunxiao Jiang Peiying Zhang

QoS-Aware Virtual Network Embedding

QoS-Aware Virtual Network Embedding

Chunxiao Jiang • Peiying Zhang

QoS-Aware Virtual Network Embedding

Chunxiao Jiang School of Information Science and Technology Tsinghua University Beijing, China

Peiying Zhang College of Computer Science and Technology China University of Petroleum (East China) Qingdao, Shandong, China

ISBN 978-981-16-5220-2 ISBN 978-981-16-5221-9 (eBook) https://doi.org/10.1007/978-981-16-5221-9 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Foreword

QoS-aware virtual network embedding provides a wide range of virtual network embedding solutions. As the core problem of network virtualization, virtual network embedding should be paid enough attention. It provides solutions for many real network problems from the perspective of network resource allocation and arrangement. Since virtual network embedding is an NP-hard problem, many heuristic virtual network embedding algorithms are first proposed. This book focuses on the diversity of virtual network embedding algorithms, including heuristic based virtual network embedding algorithm, machine learning based virtual network embedding algorithm, single domain virtual network embedding algorithm, and multi domain virtual network embedding algorithm. Object of This Book Graduate students, professors, researchers, scientists, practitioners, and engineers in the fields of artificial intelligence and networks. Undergraduate students, industry managers, and government research agency in the fields of artificial intelligence and networks. Organization Structure The goal of this book is to give readers a comprehensive understanding of the design and implementation of a variety of virtual network embedded algorithms. Readers can use this book as an entry-level tutorial to enter the field. Through the accumulation of basic virtual network embedded algorithms, readers can innovate on this basis. This book adopts the total-point-total writing format. Part 1: Introduction Introduces the basic concepts of network virtualization technology and virtual network embedding, so that readers have a preliminary understanding of knowledge in this field. Part 2: Security-Aware Virtual Network Embedding Algorithm Includes the introduction of security requirements in VNE, heuristic secure virtual network embedding algorithm, and machine learning secure virtual network embedding algorithm.

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Foreword

Part 3: Service-Aware Virtual Network Embedding Algorithm Includes the description of service-aware requirements in VNE, single domain service-aware VNE algorithm, and multi domain service-aware VNE algorithm. Part 4: Energy-Aware Virtual Network Embedding Algorithm Includes the description of energy consumption requirements in VNE, energy-aware VNE algorithm based on multi objective optimization, and other energy-aware VNE algorithms. Part 5: Load Balance Virtual Network Embedding Algorithm Includes the description of load balance in VNE and the implementation of VNE algorithm based on load balance. Part 6: Conclusion A brief summary of the book.

Preface

The Internet has achieved great success and imposed substantial impact on people’s lives in the last few decades. It stimulates the rapid growth and wide spread of compelling network applications, while it also hinders the creation of innovative network architectures and technologies. Specifically, the rigidity of the traditional network architectures makes it difficult for providing diversiform network services relying on current network architectures and operation mechanisms. Although VPN and overlay networks have been proposed, the scope of their application is still very limited. Network virtualization is an important method to network resource management. It embeds multiple independent and topologically flexible virtual networks into one underlying physical network for the sake of adapting to different applications’ requirement. Virtual network embedding is the core technique of network virtualization, which aims for both efficiently using physical network resources and for meeting user’s diverse quality of service (QoS) and quality of experience (QoE). It provides solutions for many real network problems from the perspective of network resource allocation and arrangement. However, virtual network embedding is an NPhard problem, and hence a range of heuristic virtual network embedding algorithms have been investigated. This book focuses on introducing diversity of virtual network embedding algorithms and their performances in different applications, including heuristic based virtual network embedding algorithms, machine learning based virtual network embedding algorithms, single domain virtual network embedding algorithms, and multi domain virtual network embedding algorithms. Organization Structure The goal of this book is to give readers a comprehensive understanding of the design and implementation of a variety of virtual network embedded algorithms. Readers can use this book as an entry-level tutorial to enter the field. Through the accumulation of basic virtual network embedded algorithms, readers can innovate on this basis. This book adopts the total-point-total writing format.

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Preface

Part 1: Introduction Introduces the basic concepts of network virtualization technology and virtual network embedding, so that readers have a preliminary understanding of knowledge in this field. Part 2: Security-Aware Virtual Network Embedding Algorithm Includes the introduction of security requirements in VNE, heuristic secure virtual network embedding algorithm, and machine learning secure virtual network embedding algorithm. Part 3: Service-Aware Virtual Network Embedding Algorithm Includes the description of service-aware requirements in VNE, single domain service-aware VNE algorithm, and multi domain service-aware VNE algorithm. Part 4: Energy-Aware Virtual Network Embedding Algorithm Includes the description of energy consumption requirements in VNE, energy-aware VNE algorithm based on multi objective optimization, and other energy-aware VNE algorithms. Part 5: Load Balance Virtual Network Embedding Algorithm Includes the description of load balance in VNE and the implementation of VNE algorithm based on load balance. Part 6: Conclusion A brief summary of the book. Beijing, China Qingdao, China July 2021

Chunxiao Jiang Peiying Zhang

Contents

Part I 1

Introduction

Introduction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .

Part II

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Security-Aware Virtual Network Embedding Algorithm

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Introduction of Security Requirements in VNE. . . . .. . . . . . . . . . . . . . . . . . . .

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3

Security Aware Virtual Network Embedding Algorithm Using Information Entropy TOPSIS . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .

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Security Aware Virtual Network Embedding Algorithm Based on Reinforcement Learning.. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .

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VNE Solution for Network Differentiated QoS and Security Requirements from the Perspective of Deep Reinforcement Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .

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Resource Management and Security Scheme of ICPSs and IoT Based on VNE Algorithm . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .

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4 5

6

Part III

Service-Aware Virtual Network Embedding Algorithm

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Description of Service-Aware Requirements in VNE . . . . . . . . . . . . . . . . . . 107

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Virtual Network Embedding Based on Modified Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 109

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VNE-HPSO Virtual Network Embedding Algorithm Based on Hybrid Particle Swarm Optimization . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 129

10 Topology Based Reliable Virtual Network Embedding from a QoE Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 153

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Contents

11 DSCD Delay Sensitive Cross-Domain Virtual Network Embedding Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 173 12 A Multi-Domain Virtual Network Embedding Algorithm with Delay Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 201 Part IV

Energy-Aware Virtual Network Embedding Algorithm

13 Description of Energy Consumption Requirements in VNE. . . . . . . . . . . 227 14 Multi-Objective Enhanced Particle Swarm Optimization in Virtual Network Embedding . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 229 15 Incorporating Energy and Load Balance into Virtual Network Embedding Process .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 245 16 IoV Scenario Implementation of a Bandwidth Aware Algorithm in Wireless Network Communication Mode . . . . . . . . . . . . . . . . 269 Part V

Load Balance Virtual Network Embedding Algorithm

17 Description of Load Balance in VNE . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 297 18 A Multi-Domain VNE Algorithm Based on Load Balancing in the IoT Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 299 19 Virtual Network Embedding Based on Computing, Network, and Storage Resource Constraints .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 327 20 Virtual Network Embedding Using Node Multiple Metrics Based on Simplified ELECTRE Method . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 343 21 VNE Strategy Based on Chaotic Hybrid Flower Pollination Algorithm Considering Multi-Criteria Decision Making . . . . . . . . . . . . . . 373 Part VI

Conclusion

22 Conclusion .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 401

Part I

Introduction

Chapter 1

Introduction

1.1 Virtual Network Embedding Internet technology has become an important foundation to support the comprehensive and rapid development of society. It has profoundly changed people’s way of production and life. Benefiting from the great convenience brought by the development of Internet technology, the end users accessing the Internet show an explosive growth trend every year. Limited by the design mode of infrastructure, traditional Internet only provides users with “best effort” service delivery mode, which leads to severe challenges in flexibility, mobility, security, and service quality. In addition, it is difficult to deploy new network protocols on the existing Internet infrastructure. Therefore, the traditional Internet architecture gradually presents a rigid phenomenon. The emergence of network virtualization (NV) technology provides a new way to solve the rigidity of Internet architecture. NV allows multiple heterogeneous virtual networks to share the underlying physical infrastructure. Virtual network is the resource slice abstracted by the underlying physical network, which consists of virtual nodes and virtual links. The NV architecture is shown in Fig. 1.1. Virtual network embedding (VNE) is one of the core services of NV research. In the NV environment, infrastructure providers manage the underlying network, and service providers rent network resources from infrastructure providers and create virtual networks to provide personalized end-to-end network services. The process of allocating underlying network resources to virtual network requests (VNRs) is VNE, i.e., the essence of VNE is the allocation of physical network resources. Figure 1.2 shows an example of VNE. For the physical network, the circle represents the physical node, and the number next to it represents the node resource capacity. The connection between physical nodes represents the physical link, and the number next to it represents the link resource capacity. For the virtual network, the hexagon represents the virtual node, and the number next to it represents the node resource demand. The connection between virtual nodes represents the virtual © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Jiang, P. Zhang, QoS-Aware Virtual Network Embedding, https://doi.org/10.1007/978-981-16-5221-9_1

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Virtual Network Layer

Virtual Network 1

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Infrastructure Layer Fig. 1.1 Network virtualization architecture

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Fig. 1.2 Virtual network embedding instance

link, and the number next to it represents the link resource demand. Node resources usually include CPU resources, memory resources, storage resources, and so on. Link resources usually include bandwidth resources, delay, and so on. The principle of VNE is to map virtual nodes and links to corresponding physical nodes and links on the basis of resource constraints, location constraints, and access control. The VNE problem is NP-hard. Even after all virtual nodes have been mapped, it is still NP-hard to map virtual links with link resource constraints. VNE is a hot topic in this field, and the research of VNE algorithm has been widely concerned by scholars.

1.3 Organization Structure

5

1.2 Differentiated QoS Requirements Quality of Service (QoS) refers to the ability of a network to use various basic technologies to provide better service capabilities for designated network communications. With the emergence of new Internet applications in an endless stream, the network services that people are pursuing gradually show the characteristics of differentiated QoS. For infrastructure providers, they want to increase the revenue of resource allocation on the basis of accepting as many VNRs as possible, so they pursue the highest revenue service demand. For the majority of Internet users, they want to enjoy efficient Internet services at the lowest possible price, so what they pursue is the lowest cost service demand. For unmanned aerial vehicles (UAVs) or driverless vehicles, they need to receive real-time instructions to judge the surrounding environment, so they pursue the service demand of low delay. For network video users, they need smooth network speed to ensure the image quality, so they pursue the service demand of high bandwidth. For data storage centers, on the one hand, they need to ensure data security; on the other hand, they need to improve data storage efficiency and make effective use of storage space, so what they pursue is the service demand of high security and high storage. The research of VNE algorithm for differentiated QoS requirements has been widely concerned by industry and academia. The satisfaction of users’ differentiated QoS requirements largely depends on the effective allocation of network resources. Therefore, it is of great significance to study VNE algorithms for differentiated QoS requirements.

1.3 Organization Structure The ultimate goal of network technology development is to better serve users and provide users with the best QoS and Quality of Experience (QoE), so service-aware virtual network resource scheduling is a key point of VNE research. In addition, with the continuous expansion of the underlying physical network scale, the number of target users is all over the world, it is necessary to ensure the security of network resource allocation, so the security aware VNE algorithm is also an important work. Efficient scheduling of the underlying network resources is the premise of achieving high-quality services, so it is necessary to design VNE algorithms based on energyaware and load balancing from the bottom of the architecture. The above network resource scheduling scenarios reflect distinct QoS characteristics.

6

1 Introduction

QoS-Aware Virtual Network Embedding

Introduction

Security-Aware Virtual Network Embedding Algorithm

Service-Aware Virtual Network Embedding Algorithm

Energy-Aware Virtual Network Embedding Algorithm

Load Balance Virtual Network Embedding Algorithm

Conclusion Fig. 1.3 Organizational structure of the book

Specifically, we analyze and summarize the VNE algorithms for differentiated QoS requirements from four aspects: security awareness, service awareness, energy consumption awareness, and load balancing. In each chapter, we propose some representative VNE algorithms and introduce the algorithm design and implementation process in detail. The content organization is shown in Fig. 1.3.

Part II

Security-Aware Virtual Network Embedding Algorithm

Chapter 2

Introduction of Security Requirements in VNE

Network virtualization (NV) is an effective manner to address the ossification issue of Internet architecture. Virtual network embedding (VNE) is one of the most critical techniques in NV environments. Because VNE adds a virtual layer to the Internet architecture, it is easy to generate new security problems in the process of resource allocation. Aiming at the security problems in the process of VNE, we introduce four security VNE algorithms in this chapter. Firstly, Security Aware Virtual Network Embedding Algorithm using Information Entropy TOPSIS. We use the information entropy TOPSIS method to rank the importance of substrate nodes with an aim to choose the most appropriate substrate node for accommodating the virtual node. Then, we use the shortest path algorithm to perform the link mapping process. Secondly, Security Aware Virtual Network Embedding Algorithm based on Reinforcement Learning. In the training phase, we use a policy network as a learning agent and take the extracted attributes of the substrate nodes to form a feature matrix as input. The learning agent is trained in this environment to get the mapping probability of each substrate node. In the test phase, we map nodes according to the mapping probability and use the breadth first strategy to map links. For the security problem, we add security requirements level constraint for each virtual node and security level constraint for each substrate node. Virtual nodes can only be embedded on substrate nodes that are not lower than the level of security requirements. Thirdly, VNE Solution for Network Differentiated QoS and Security Requirements: From the Perspective of Deep Reinforcement Learning. Deep reinforcement learning (DRL) agent is trained in the network environment constructed by the above attributes. The purpose is to deduce the mapping probability of each substrate node and map the virtual node according to this probability. Finally, the breadth first strategy is used to map the virtual links. Fourthly, Resource Management and Security Scheme of ICPSs and

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Jiang, P. Zhang, QoS-Aware Virtual Network Embedding, https://doi.org/10.1007/978-981-16-5221-9_2

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2 Introduction of Security Requirements in VNE

IoT Based on VNE Algorithm. We extract the important attribute characteristics of underlying network as the training environment of reinforcement learning (RL) agent. Agent can derive the optimal node embedding strategy through training, so as to meet the requirements of ICPSs for resource management and security. The embedding of virtual links is based on the breadth first search strategy.

Chapter 3

Security Aware Virtual Network Embedding Algorithm Using Information Entropy TOPSIS

Abstract NV is an effective manner to address the ossification issue of Internet architecture. VNE is one of the most critical techniques in network virtualization environments. Several security problems about virtual network embedding are introduced due to the fact that virtual network embedding adds a virtual layer into the Internet architecture. In this section, we propose an approach for security aware VNE called SA-VNE to address the security problems in VNE process. First, we use the information entropy TOPSIS method to rank the importance of substrate nodes with an aim to choose the most appropriate substrate node for accommodating the virtual node. Second, we use the shortest path algorithm to perform the link mapping process. Simulation results demonstrate that our proposed SA-VNE algorithm behaves better that those of state-of-the-art existing security aware VNE algorithms in terms of the long-term average revenue, the long-term average virtual network acceptance ratio, the long-term average revenue to cost ratio, and the running time.

3.1 Introduction The technology of NV gets wide attention from the academics and industry. VNE is one of the key problems to be solved in NV environments. VNE is considered to be a promising technique to address the ossification problem of current Internet architecture, which has become the core technology of the cloud computing paradigm. The majority of the existing algorithms on VNE focus on maximizing the revenue of infrastructure providers (InPs) [1, 2] or minimizing the energy consumption of the substrate network [3–6], using heuristic algorithms [7] or metaheuristic algorithms [8–10] to solve this problem. The literature [11] studies how resource ownership affects the investment motivation of InPs and service provides (SPs), and how to choose the most effective investment in MVN. In this chapter, a general system model is established to exchange multiple physical and virtual

Reprinted from ref. [12], with permission of Springer. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Jiang, P. Zhang, QoS-Aware Virtual Network Embedding, https://doi.org/10.1007/978-981-16-5221-9_3

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3 Security Aware Virtual Network Embedding Algorithm Using Information. . .

resources among multiple InP and SP with complementary relationship in order to obtain the maximum profit. However, NV brings flexibility to network architecture; it also introduces some new security issues due to the injection of the abstraction layer [13]. To address the security problems incurred from NV, the authors of [14] proposed the concept of secure VNE for the first time, and elaborated the necessary constraints for the secure aware VNE. The authors in [15] attempted to address the security problem by provisioning physical isolation during VNE process, which allocated virtual networks onto the substrate nodes and links. The major contribution of their studies is to formulate the security aware VNE problem, which quantifies the security requirements of the nodes and links in virtual network requests (VNRs) and substrate network. A mathematical mixed integer linear program model was formulated in the work [16] with an aim to minimizing the embedding cost. In literature [16], they used the TOPSIS method to rank the local and global importance of the substrate and virtual nodes, which considers node degree centrality, node closeness centrality, and node available resource measurement in the node ranking process. On the foundation of these existing studies, the authors in [17] abstracted the security requirements and the protection mechanisms as numerical concept of security demands and security levels, and incorporated the security constraints into the VNE process. However, the ranking method for the embedding potential of network nodes can be further improved. In this chapter, we improved the node ranking method using information entropy TOPSIS method and used the shortest path algorithm to perform the link mapping process. We highlight the main contributions of this chapter as follows. 1. We deeply investigated the related works about security aware VNE algorithms. On the foundation, we formulated a mixed integer linear programming (MILP) model to address the issue of security aware VNE problem. 2. We proposed a security aware VNE algorithm called SA-VNE. First, the proposed SA-VNE algorithm uses the information entropy TOPSIS method to evaluate the importance of substrate nodes with an aim to choose the most appropriate substrate node for each virtual node. Subsequently, we adopted the shortest path algorithm to perform the link mapping process. 3. We carried out extensive simulation experiments to assess the performance of our proposed SA-VNE algorithms against other security aware VNE algorithms including NSA-VNE, DSA-VNE, and BL-VNE. The remainder of this chapter is organized as follows. Section 3.2 reviews the works about security risk in NV and security aware VNE algorithms. The network model and problem statement are introduced in Sect. 3.3. In Sect. 3.4, we detail the node importance ranking method using information entropy TOPSIS. The proposed security aware VNE algorithm is elaborated in Sect. 3.5. The performance evaluation of our proposed SA-VNE algorithm against other security aware VNE algorithms is conducted in Sect. 3.6. Section 3.7 concludes this chapter and points out the future research work.

3.2 Related Works

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3.2 Related Works 3.2.1 Traditional Virtual Network Embedding Algorithms Recent years, there are a large number of literature on traditional virtual network algorithms [18]. Yu et al. [19] devised an approach of VNE with support for path splitting and migration. Allowing virtual links over multiple substrate paths can bring about the flexibility of link mapping; it also increases the probability of link mapping procedure in the situation that there are a large amount of substrate resource fragments. The authors of [20] devised a novel Linear Programming (LP) formulation to address the problem that the standard LP formulation cannot decompose the VNE solutions into valid embedding. They proposed two rounding heuristics and assessed their performance through extensive simulations. In literature [21], the authors designed a VNE algorithm based on graph theory. Specifically, they used the node similarity between virtual nodes and substrate nodes to accomplish the node mapping process, and utilized the shortest path algorithm to find a link mapping solution. Based on the notion of “storage resource can exchange bandwidth resource to some extent,” the authors of [22] proposed a VNE algorithm based on computing, network, and storage resource constraints. This is the first time to formulate VNE problem using three dimension resource constraints. In their work, they devised two heuristics with an aim to consider it as two baseline algorithms to make progress in VNE algorithms based on 3-D resource constraints.

3.2.2 Security Risk in Network Virtualization NV can address the ossification issue of the Internet architecture. However, the introduction of NV incurs the additional security problems due to the fact that the virtual layer is injected into the Internet architecture. The authors of [14] suggested that both the VNRs and the substrate network should be assigned a security level and a security demand. In their work, they took into consideration three types of additional security constraints: (1) A virtual resource should not be mapped on substrate resources that have a lower security level than the security demand of the virtual resource; (2) A substrate resource should not be used to host virtual resources that have a lower security level than the security demand of the substrate resource; and (3) A virtual resource should not be co-hosted on the same substrate resource together with another virtual resource having a lower security level than the security demand of the first resource. Furthermore, they formulated these three security constraints into formal inequalities. Three types of security issues associated with the VNE process are summarized in literature [23]. These three security issues consist of the node level, the topology level, and the network level. Each category associated with one example is introduced in their work.

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The authors in [24] constructed a VNE model with an aim to satisfy the security requirements. They classified the security requirement of the virtual networks and substrate network into several security levels, and formulated a security VNE model to address this issue. The aim of their study is to solve this problem that none of prior studies has attempted to combine efficient resource allocation with fulfillment of security requirements. Furthermore, they offered three types of confidentiality: endto-end cryptography, point-to-point cryptography, and non-overlapping networks. Two security threats of virtual network are proposed by the authors of [25]. In literature [25], they proposed a novel VNE algorithm with security assurance that considers the trust value and security protection level as the new security constraints during the process of virtual network embedding.

3.2.3 Security Aware Virtual Network Embedding Algorithms The security aware VNE algorithms have been studied in several literature [16, 26– 28]. The authors of [16] quantified the trust degree of the nodes and links for secure aware VNE problems. In their study, they formulated a mathematical model of the secure VNE problem with the aim of minimizing the embedding cost. The classical TOPSIS method is used to measure the embedding potential of substrate nodes in the node mapping procedure, and the shortest path algorithms is employed to perform the link mapping process. In addition, they modified the resource ranking method by choosing the substrate nodes with the lower security level aiming at reducing the embedding cost. Literature [26] proposed a new NV core component solution called online network embedding. Their proposed model took security as a first class citizen, and defined flexible policies in three areas including on the links, on the switches, and across multiple clouds. The security VNE algorithm that guarantees that the virtual networks of the conflicting end users are mapped onto different substrate equipment is proposed by the authors of [27]. Furthermore, their work is the first time attempting to enabling flexibility of choosing a certain bandwidth for each virtual link among a set of discrete bandwidth levels. Recently, the authors of [28] formulated the secure VNE problem as a MILP model with an aim to minimize the embedding cost. In their work, they took into consideration the available resource evaluation, the security attributes, and the neighborhood relationship between the mapping substrate node and the already mapped substrate nodes in order to reduce the embedding cost and try not to change the security levels of substrate nodes. The essential difference between aforementioned algorithms and our proposed algorithm is that we design a framework of VNE algorithm. The framework uses the information entropy TOPSIS method to evaluate the importance of substrate nodes in order to make the evaluation more objectively.

3.3 Network Model and Problem Statement

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3.3 Network Model and Problem Statement 3.3.1 Security Constraint In the environments of NV, some VNRs need higher security such as online payment applications and confidential document transmission; other VNRs do not need higher security such as live streaming and online games. Therefore, we classified the security requirement of each VNR into several security demand grades and security demand levels, rather than set every virtual nodes from each VNR to different security demand grades and security demand levels.

3.3.2 Network Model 3.3.2.1 Substrate Network The underlying substrate network can be modeled as an undirected weighted graph Gs = (Ns , Ls ), where Ns and Ls represent the set of substrate nodes and substrate links, respectively. For a substrate node ns ∈ Ns , its available CPU capacity resource can be denoted by CP U (ns ), and its security demand grade and security level can be denoted by sd(ns ) and sl(ns ), respectively. For a substrate link ls ∈ Ls , its available bandwidth resource can be denoted by BW (ls ).

3.3.2.2 Virtual Network Request The i-th VNR can be defined as V NRi = (Gv , ta , td ), where Gv represents the network topology for the VNR, ta represents the arrival time of the VNR, and td represents the departure time of the VNR. Similar to the substrate network, the virtual network can be modeled as an undirected weighted graph Gv = (Nv , Lv ), where Nv and Lv represent the set of virtual nodes and virtual links, respectively. For a virtual node nv ∈ Nv , CP U (nv ) denotes its required CPU capacity resource, and sd(nv ) and sl(nv ) denote its security demand grade and security level, respectively. Note that the security demand grade and security level of each virtual nodes from VNR are the same as those of the VNR. For a virtual link lv ∈ Lv , BW (lv ) denotes the required bandwidth resource for the virtual link lv .

3.3.3 Security Virtual Network Embedding Problem As illustrated in Fig. 3.1, the left part contains two VNRs, the right part contains a substrate network. For VNR, three numbers in each bracket aside the nodes represent the CPU capacity requirement, the security demand grade, and the security

3 Security Aware Virtual Network Embedding Algorithm Using Information. . .

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level, respectively. The numbers over the links represent the bandwidth resource requirement. For substrate network, three numbers in each bracket aside the nodes represent the available CPU capacity, the security demand grade, and the security level, respectively. The numbers over the links represent the available bandwidth resource. From the Fig. 3.1, it can be seen that the virtual nodes a and b from VNR1 are mapped onto the substrate nodes A and D, respectively. We must note that after the virtual node a is mapped onto the substrate node A, the security demand grade of the substrate node A is changed from 0.3 to 0.5. The main reason is that once the virtual node a is mapped onto the substrate node A, if substrate node A hosts other VNRs with lower security demand grade, it will affect the security levels of the VNRs that have already mapped onto it.

3.3.4 The Formulations The security VNE is a special kind of VNE algorithms, which incorporates the security constraints of nodes and links into the VNE process. In this work, we take the minimum cost of VNE as our optimization objective and formulate the security VNE problem as a MILP model. The formulation is as follows: min

 

  xji 1 + sl(nj ) CP U (ni )

ni ∈Nv nj ∈Ns

 

+

fijuv BW (luv ).

(3.1)

luv ∈Lv lij ∈Ls

Constraints: ∀nj ∈ Nv , ∀nj ∈ Ns , s.t. xji CP U (ni ) ≤ CP U (nj )

(3.2)

xji dis(loc(ni ), loc(nj )) ≤ h(ni ).

(3.3)

3.3 Network Model and Problem Statement

17

Equation (3.2) guarantees that the demanded CPU capacities of virtual nodes are not greater than those of available CPU capacities of substrate nodes. Equation (3.3) guarantees that the maximum Euclidean distance between virtual node ni and substrate node nj does not exceed the maximum threshold h(ni ). ∀lij ∈ Ls , s.t. 

fijuv BW (luv ) ≤ BW (lij )

(3.4)

luv ∈Lv

∀ni ∈ Ns , ∀luv ∈ Lv , 

fijuv −

lij ∈Ls



fjuv i =

lji ∈Ls

⎧ ⎪ ⎪ ⎨BW (luv )

−BW (luv )

⎪ ⎪ ⎩0

xiu = 1 xiv = 1

(3.5)

otherwise.

Equation (3.4) ensures that the required bandwidth resource of virtual link is less than the available bandwidth resource of substrate link. Equation (3.5) ensures that constraints of substrate link connectivity are satisfied. ∀ni ∈ Nv , ∀nj ∈ Ns , ⎧ i ⎪ ⎪ ⎨xj sd(ni ) ≤ sl(nj )

(3.6)

xji sd(nj ) ≤ sl(ni ) ⎪ ⎪ ⎩x i sd(n ) ≤ min j

i

nk ∈Ω(nj ) sl(nj ).

Equation (3.6) represents three security constraints, Ω(nj ) represents the set of virtual nodes which are already mapped onto the substrate node nj . ∀nj ∈ Ns , s.t.



xji ≤ 1.

(3.7)

xji = 1.

(3.8)

nj ∈Nv

∀ni ∈ Nv , s.t.

 nj ∈Ns

Equation (3.7) ensures that the two different virtual nodes from the same VNR are not mapped onto the same substrate node. Equation (3.8) ensures that each virtual node of VNR is only mapped onto one substrate node. ∀ni ∈ Nv , ∀nj ∈ Ns , s.t.xji ∈ {0, 1} ,

(3.9)

∀luv ∈ Lv , ∀lij ∈ Ls , s.t.fijuv ∈ {0, 1} .

(3.10)

Equations (3.9) and (3.10) are two variable constraints.

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3 Security Aware Virtual Network Embedding Algorithm Using Information. . .

3.3.5 Objectives The conventional metrics of evaluating the VNE algorithms are the long-term average revenue, the long-term revenue to cost ratio, and the VNR acceptance ratio. In this section, we introduce the definitions of these three performance metrics for security VNE algorithms. In the section of experimental results and analysis, we use these three redefined metrics to evaluate our proposed methods against other state-of-the-art security VNE algorithms. The obtained revenue of accommodating a VNR at time t can be defined as the sum of node CPU capacity resource and its directly connected link bandwidth resource. In this manner, the revenue of infrastructure provider (InP) can be defined as follows:  R (Gv , t) = (1 + sd(nv )) CP U (nv ) nv ∈Nv

+



BW (lv ),

(3.11)

lv ∈nbr(nv )

where R (Gv , t) denotes the revenue of InP, nbr(nv ) denotes the set of virtual links directly connected to the virtual node nv , and sd(nv ) denotes the security demand grade for virtual node nv . Equation (3.11) indicates that the higher requirements of virtual nodes incur more revenue for the InP. The long-term average revenue of the InP can be defined as follows: R (Gv , t) . T →∞ T

R = lim

(3.12)

The consumed cost of hosting a VNR at time t can be defined as the total substrate resources including node CPU capacity resource and link bandwidth resource. It can be formulated as follows:  C (Gv , t) = (1 + sd(nv )) CP U (nv ) nv ∈Nv

+

 

lv ∈Lv ls ∈Ls

BW (fllsv , lv ),

(3.13)

where fllsv ∈ {0, 1}, when the virtual link lv is allocated onto the substrate link

ls , fllsv = 1; otherwise, fllsv = 0. BW (fllsv , lv ) represents the allocated bandwidth resource of virtual link lv on substrate link ls . The long-term average cost of the InP can be defined as follows: C (Gv , t) . T →∞ T

C = lim

(3.14)

3.4 The Node Ranking Method using Information Entropy TOPSIS

19

The long-term revenue to cost ratio can be defined as the ratio of the long-term average revenue over the long-term average cost. It can be described as follows: R (Gv , t) . T →∞ C (Gv , t)

R/C = lim

(3.15)

The long-term VNR acceptance ratio can be defined as the ratio of the number of already accepted VNRs over the number of arrived VNRs. It can be described as follows: T

AR = lim tT=0 T →∞

V NRaccept ed (t)

t =0 V NRarrived (t)

.

(3.16)

3.4 The Node Ranking Method using Information Entropy TOPSIS 3.4.1 The Metrics of Node Importance In this section, we introduce three attributes that affect the embedding potential of the nodes, including the node CPU capacity resource, the bandwidth resource summation of node adjacent links, and the closeness degree. The CPU Capacity In our work, we use the node CPU capacity resource to evaluate the node available resource. The node CPU capacity resource can be formulated as follows: NR(ni ) = CP U (ni ).

(3.17)

In order to raise the VNR acceptance ratio, we embed the virtual node with the larger CPU capacity demand onto the substrate node with the abundant CPU capacity resource. The Bandwidth Resource Summation The bandwidth resource metric of the nodes can be defined as follows:  DC(ni ) = BW (), (3.18) ∈D(ni )

where D(ni ) represents the set of the links which is directly connected to the node ni .

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3 Security Aware Virtual Network Embedding Algorithm Using Information. . .

The Closeness Degree The node closeness degree can reflect the node importance from the perspective of network topology, which is formulated as follows: CD(ni ) =

1 nj ∈Ψ

dij

,

(3.19)

where CD(ni ) represents the closeness degree of the node ni , it can be calculated using the reciprocal of the sum of distances between the node ni and any other node nj . The notation Ψ denotes the set of substrate nodes, and dij denotes the hop distance between the substrate node ni and substrate node nj . If i = j , then dij = 0. Note that: We extract three main features for each substrate node in order to demonstrate our framework of utilizing the following information entropy TOPSIS method to solve the VNE problem. The readers can use other more features to conduct their experiments such as the degree of the substrate node or the average distance to other host nodes, and so on.

3.4.2 The Information Entropy TOPSIS The information entropy TOPSIS method is the modified version of the conventional TOPSIS method, which uses the information entropy method to compute the weights of various indicators with an aim to eliminate the errors caused by human factors. Therefore, the obtained node importance ranking values are more objective than those of values obtained from the conventional TOPSIS method. The steps of the information entropy TOPSIS method are as follows. Step 1 We suppose that there are N nodes in network, each node has M evaluation indicators. The j -th evaluation indicator for i-th node can be denoted by xij . The importance decision making matrix can be defined as: ⎡

XN×M

x11 ⎢ x21 =⎢ ⎣... xN1

x12 x22 ... xN2

⎤ . . . x1M . . . x2M ⎥ ⎥. ... ... ⎦ . . . aNM

(3.20)

Step 2 Normalizing the decision making matrix, we can obtain the standard  decision making matrix XN×M : ⎡



XN×M



x11 ⎢ x 21 =⎢ ⎣...  xN1



x12  x22 ...  xN2

⎤  . . . x1M  . . . x2M ⎥ ⎥. ... ... ⎦  . . . aNM

(3.21)

3.4 The Node Ranking Method using Information Entropy TOPSIS

21

Step 3 Calculate the information entropy for each evaluation indicator, the computation formula is as follows: ej = −K

n 





(3.22)

xij ln(xij ),

i=1

where K is a constant variable which is associated with the number of evaluation indicators. The information utility value of each indicator can be denoted by hj = 1 − ej ; in this way, the weight of each indicator can be formulated as h Wj = m j h . We can conclude that the smaller the information entropy, the j=1

j

stronger the information order. The stronger information order incurs the larger information utility value. The larger information utility value would cause the larger weight of this indicator. Step 4 Compute the weighted standard decision making matrix using below formula: ⎡



XN×M





x11 ⎢ x  21 =⎢ ⎣...  xN1



x12  x22 ...  xN2

⎤  . . . x1M  . . . x2M ⎥ ⎥, ... ... ⎦  . . . aNM

(3.23)



where xij = xij Wj . Step 5 Compute the positive ideal solution A+ and negative ideal solution A− , respectively. A+ =







1≤i≤N

1≤i≤N



A =



1≤i≤N

 + , = x1+ , x2+ , . . . , xM −



max xi1 , max xi2 , . . . , max xiM



(3.24) 





min xi1 , min xi2 , . . . , min xiM

1≤i≤N

1≤i≤N

 − = x1− , x2− , . . . , xM .

1≤i≤N

(3.25)

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3 Security Aware Virtual Network Embedding Algorithm Using Information. . .

Step 6 Compute the Euclidean distance between the final weighted decision data and these two ideal solutions, respectively.   M   2   + Di =  xij − xj+ ,

(3.26)

j =1

  M   2   − xij − xj− . Di = 

(3.27)

j =1

Step 7 Compute the closeness degree between each solution and the most ideal solution. Ci =

Di−

Di− + Di+

, 0 ≤ Ci ≤ 1.

(3.28)

The node ranking algorithm for substrate nodes is illustrated in Algorithm 1. Algorithm 1 The node ranking algorithm based on information entropy TOPSIS (IETOPSIS) 1: Normalize the decision making matrix with an aim to obtain the standard decision making  matrix XN×M ; 2: Compute the weights for different indicators using information entropy method; 3: Compute the positive ideal solution A+ and negative ideal solution A− ; 4: Compute the Euclidean distance between the final weighted decision data and these two ideal solutions, respectively; 5: Compute the closeness degree between each solution and the most ideal solution; 6: Sort substrate nodes by their closeness degree between each solution and the most ideal solution using non-increasing order; 7: The substrate node with the highest closeness degree is selected as the most appropriate substrate node for mapping the virtual node.

3.4.3 An Example for Information Entropy TOPSIS As illustrated in Fig. 3.2, take the following substrate network into consideration. We suppose that the virtual node b has already mapped onto the substrate node B; the next step is to choose an appropriate substrate node to accommodate the virtual node a. Because the substrate node B has already hosted a virtual node, the

3.4 The Node Ranking Method using Information Entropy TOPSIS

(50,0.3,0.5)

D

a (20,0.7,0.9)

B

50

40

50

20

A

b (30,0.5,0.7)

50

(50,0.3,0.5)

E (30,0.5,0.7)

C 60

Fig. 3.2 An illustration demo for information entropy TOPSIS

23

50

F (20,0.7,0.9)

candidate substrate node set for accommodating the virtual node a only contains the remaining substrate nodes: candi(a) = {A, C, D, E, F }. Each substrate node has three evaluation metrics: the CPU capacity, the bandwidth resource summation, and the closeness degree. Based on these metrics, we compute the importance of every substrate node. Step 1 Compute the importance decision making matrix. Each row denotes a substrate node, from top to bottom, they are substrate nodes A, C, D, E, and F , respectively. Each column denotes a metric, from the left to right, they are the CPU capacity, the bandwidth resource summation, and the closeness degree, respectively. The specific computation details are elaborated in Sect. 3.4.2. ⎤ ⎡ 50 70 19 ⎢20 110 1 ⎥ ⎢ 9⎥ ⎥ ⎢ (3.29) X5×3 = ⎢50 70 19 ⎥ . ⎥ ⎢ ⎣30 140 17 ⎦ 20 110 19 Step 2 We can generate the standard decision making matrix through normalizing the decision making matrix. ⎡



X5×3

⎤ 0.2941 0.14 0.1892 ⎢0.1176 0.22 0.1892⎥ ⎢ ⎥ ⎢ ⎥ = ⎢0.2941 0.14 0.1892⎥ . ⎢ ⎥ ⎣0.1766 0.28 0.2432⎦ 0.1176 0.22 0.1892

(3.30)

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3 Security Aware Virtual Network Embedding Algorithm Using Information. . .

Step 3 Compute the information entropy value for each evaluation indicator. e1 = −

1 ∗ (2 × 0.2941 × ln(0.2941) ln(5)

+ 2 × 0.1176 × ln(0.1176) + 0.1766 × ln(0.1766)) = 0.9503. e2 = −

(3.31)

1 ∗ (2 × 0.14 × ln(0.14) ln(5)

+ 2 × 0.22 × ln(0.22) + 0.28 × ln(0.28)) = 0.9775. e3 = −

(3.32)

1 ∗ (4 × 0.1892 × ln(0.1892) ln(5)

+ 0.2432 × ln(0.2432)) = 0.9966.

(3.33)

Then, we compute the information utility value for each evaluation indicator. h1 = 1 − e1 = 0.0497. h2 = 1 − e2 = 0.0225. h3 = 1 − e3 = 0.0034. Next, we compute the weight coefficient for each evaluation indicator. w1 = h1 +hh12 +h3 = 0.6754. w2 = w3 =

h2 h1 +h2 +h3 h3 h1 +h2 +h3

= 0.2976. = 0.0450.

Step 4 Compute the weighted standard decision making matrix. ⎡ ⎤ 0.2941 ∗ 0.6754 0.14 ∗ 0.2976 0.1892 ∗ 0.0450 ⎢0.1176 ∗ 0.6754 0.22 ∗ 0.2976 0.1892 ∗ 0.0450⎥ ⎢ ⎥  ⎢ ⎥ X5×3 = ⎢0.2941 ∗ 0.6754 0.14 ∗ 0.2976 0.1892 ∗ 0.0450⎥ ⎢ ⎥ ⎣0.1766 ∗ 0.6754 0.28 ∗ 0.2976 0.2432 ∗ 0.0450⎦ 0.1176 ∗ 0.6754 0.22 ∗ 0.2976 0.1892 ∗ 0.0450 ⎡ ⎤ 0.1933 0.0417 0.0085 ⎢0.0773 0.0655 0.0085⎥ ⎢ ⎥ ⎢ ⎥ = ⎢0.1933 0.0417 0.0085⎥ . ⎢ ⎥ ⎣0.1161 0.0833 0.0109⎦ 0.0773 0.0655 0.0085

(3.34)

3.5 Heuristic Algorithm Design

25

Step 5 Compute the positive ideal solution A+ and negative ideal solution A− . A+ = {0.1933, 0.0833, 0.0109}. A− = {0.0773, 0.0417, 0.0085}. Step 6 Compute the Euclidean distance between the final weighted decision data and these two ideal solutions, respectively. D1+ = 0.0417. D2+ = 0.1174. D3+ = 0.0417. D4+ = 0.0772. D5+ = 0.1174. D1− = 0.1160. D2− = 0.0238. D3− = 0.1160. D4− = 0.0569. D5− = 0.0238. Step 7 Compute the closeness degree between each solution and the most ideal solution. C1 = 0.7356, C2 = 0.1686, C3 = 0.7356, C4 = 0.4243, C5 = 0.1686. According to our designed three evaluation metrics, the substrate nodes A and C have the same probability to accommodate the virtual node a. In this situation, we choose one of the most appropriate substrate nodes for the virtual node a. Therefore, we can choose the substrate C to host the virtual node a.

3.5 Heuristic Algorithm Design In this section, we elaborate on our proposed security aware VNE algorithm based on information entropy TOPSIS. The proposed algorithm consists of two stages including node mapping stage and link mapping stage. The detailed algorithm description will be introduced in below sections.

3.5.1 Node Mapping Algorithm The node mapping algorithm is described in Algorithm 2. The lines 1–3 sort the virtual nodes in each VNR by the information entropy TOPSIS value in nonincreasing order. Line 5 constructs the candidate substrate node list candi(nv ) according to the constraints. Lines 6–7, if the candidate substrate node list is null, the node mapping failed. Lines 9–12 sort the candidate substrate nodes by the information entropy TOPSIS value in non-increasing order, and map the virtual node nv onto the substrate node with the highest IETOPSIS values. Line 15 demonstrates that all the virtual nodes are mapped successfully if not return node_embedding_f ailure.

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3 Security Aware Virtual Network Embedding Algorithm Using Information. . .

Algorithm 2 The node mapping algorithm based on information entropy TOPSIS 1: for each nv ∈ Gv do 2: Sort virtual nodes by their IETOPSIS values in non-increasing order, store them in V irtualNodeList. 3: end for 4: for nv ∈ V irtualNodeList do 5: Generate the candidate substrate node list candi(nv ); 6: if candi(nv ) = Φ then 7: return node_embedding_f ailure. 8: else 9: for ns ∈ candi(nv ) do 10: Sort these substrate nodes by their IETOPSIS values in non-increasing order. 11: Embed the virtual node nv onto the substrate node with the highest IETOPSIS value. 12: end for 13: end if 14: end for 15: return node_embedding_success.

3.5.2 Link Mapping Algorithm Here we use the shortest path algorithm to perform the link mapping procedure. The detailed steps of link mapping algorithm are demonstrated in Algorithm 3. Line 1 sorts the virtual links from each VNR by the required bandwidth in nonincreasing order. Lines 2–4 map all the unmapped virtual links in VNR. Line 3 obtains the corresponding two substrate nodes nsst art and nsend for the virtual link lv . Line 4 removes all the substrate links whose bandwidth resource is lesser than the required amount of bandwidth resource for the virtual link lv . Line 5 uses the shortest path algorithm to solve a loop-free substrate path. Line 7 returns link_embedding_success if all the virtual links are mapped successfully. Algorithm 3 The link mapping algorithm based on the shortest path algorithm 1: Sort the virtual links by the required bandwidth in non-increasing order. 2: for all the unmapped virtual links in VNR do 3: fetch two corresponding substrate nodes nsstart and nsend for the virtual link lv ; 4: remove all the substrate links whose bandwidth resource is lesser than the required amount of bandwidth resource; 5: choose a loop-free substrate path between nsstart and nsend using shortest path algorithm. 6: end for 7: return link_embedding_success.

3.6 Experimental Results and Analysis

27

Table 3.1 The compared four methods Notation SA-VNE NSA-VNE DSA-VNE BL-VNE

Description Node mapping process using information entropy TOPSIS algorithm and link mapping process based on shortest path algorithm Node mapping process using TOPSIS algorithm and link mapping process utilizing shortest path algorithm Node mapping process using D-ViNE algorithm and link mapping process utilizing shortest path algorithm Node mapping process using greedy heuristic and link mapping process utilizing shortest path algorithm

3.5.3 Time Complexity Analysis In our simulations, we compared four VNE algorithms which are listed in Table 3.1. In this section, we analyze the time complexities of these four algorithms. The time complexity of the SA-VNE: The time complexities of the proposed SA-VNE algorithm are composed of two parts including node mapping and link mapping. The time complexity of the node mapping algorithm is O(|Ns | + |Nv ||Ns |2 ); the time complexity of the link mapping algorithm is O(k|Ns |(|Ls | + |Ns |lg|Ns |)). Therein, the parameter k denotes that link mapping process adopts the k-shortest path algorithm. Therefore, the time complexity of our proposed SA-VNE is O(k|Ns |(|Ls | + |Ns |lg|Ns |) + k|Ns |(|Ls | + |Ns |lg|Ns |)). The time complexity of the NSA-VNE: Due to the fact that the NSA-VNE algorithm is similar to the SA-VNE, the time complexity of the node mapping algorithm is O(|Ns | + |Nv ||Ns |2 ) and the time complexity of the link mapping algorithm is O(k|Ns |(|Ls | + |Ns |lg|Ns |)). Therefore, the time complexity of the NSA-VNE is O(k|Ns |(|Ls | + |Ns |lg|Ns |) + k|Ns |(|Ls | + |Ns |lg|Ns |)). The time complexity of the DSA-VNE: The time complexity of the node mapping algorithm is O(|Nv ||Ns |) and the time complexity of the link mapping algorithm is O(k|Ns |(|Ls | + |Ns |lg|Ns |)). Therefore, the time complexity of the DSA-VNE is: O(|Nv ||Ns | + k|Ns |(|Ls | + |Ns |lg|Ns |)). The time complexity of the BL-VNE: The time complexity of the node mapping algorithm is O(|Nv ||Ns ||AV G(Ns )| and the time complexity of the link mapping algorithm is O(k|Ns |(|Ls |+|Ns |lg|Ns |)). Therefore, the time complexity of the BLVNE is: O(|Nv ||Ns ||AV G(Ns )| + k|Ns |(|Ls | + |Ns |lg|Ns |)). Therein, |AV G(Ns )| denotes the average degree of substrate nodes in substrate network.

3.6 Experimental Results and Analysis In this section, we first elaborate the settings of our experiments. Then we present the results of our experiments and discuss the results. In this work, we use these aforementioned three metrics including the long-term average revenue, the long-

28

3 Security Aware Virtual Network Embedding Algorithm Using Information. . .

term average R/C ratio, and the long-term VNR acceptance ratio to evaluate our proposed methods. The evaluated four algorithms are listed in Table 3.1.

3.6.1 Experiment Settings In our simulation experiments, the number of substrate network topology is set to value of 100, and the connectivity probability between any two substrate nodes is set to value of 0.5. The initial CPU capacities of substrate nodes are uniformly distributed in U [50, 100], and the initial bandwidth resource values of substrate links are uniformly distributed in U [1000, 3000]. For the VNRs, the average number of each VNR is set to 8, the CPU capacity demand is uniformly distributed in U [1, 10], the bandwidth resource demand of each virtual link is uniformly distributed in U [0, 50], and the connectivity probability between any virtual nodes is set to value of 0.5. The whole of our simulation experiments are conducted on the personal computer, and its configuration is dual-core CPU with Intel 3 GHz, the memory and disk space are 4 GB and 160 GB, respectively. The operation system is Windows 7, and the IDE is Visual Studio 2012.

3.6.2 Results and Discussion VNR Acceptance Ratio The long-term VNR acceptance ratios of these four compared algorithms are illustrated in Fig. 3.3. From Fig. 3.3 we can see that the VNR acceptance ratios of these four algorithms are higher at the beginning stage of the running time; the reason is that the node CPU capacity resource and link bandwidth resource are abundant at the beginning stage. With the progress of VNR embedding, the VNR acceptance ratios of these four algorithms tend to be stable. The VNR acceptance ratio trend of the SA-VNE algorithm is close to that of NSAVNE algorithm. The VNR acceptance ratios of these two algorithms DSA-VNE and BL-VNE are lower than those of two algorithm SA-VNE and NSA-VNE; the reason is that the node ranking methods of these two algorithms DSA-VNE and BL-VNE do not accurately compute the embedding potential of substrate nodes, thereby causing the lower acceptance ratios. Our proposed algorithm SA-VNE takes into consideration of the node CPU capacity, the bandwidth resource summation of node adjacent links and the node closeness degree, and uses the information entropy TOPSIS method to give a comprehensive ranking value of each substrate node. In this manner, the underlying substrate resource utilization is significantly enhanced; the saved substrate resource can accommodate more VNRs, thereby increasing the VNR acceptance ratio.

3.6 Experimental Results and Analysis

29

Fig. 3.3 The long-term average VNR acceptance ratio

The Long-Term Average Revenue The long-term average revenue of these four compared algorithms is depicted in Fig. 3.4. The overall performance of the DSAVNE algorithm is better than that of the BL-VNE algorithm; the reason is that the DSA-VNE algorithm uses the deterministic rounding techniques on the solution of the linear program to approximate the values of the binary variables in the original MIP. The NSA-VNE algorithm is better than those of DSA-VNE and BL-VNE algorithms. Through the deep analysis, we found the reason is that it leverages multiple features of the substrate node to evaluate the embedding potential of the substrate node, which can make the evaluation more reasonable. It can be seen that the performance of our proposed algorithm SA-VNE is slightly over than that of NSA-VNE; the reason is that we adopt the information entropy TOPSIS method to evaluate the importance of substrate nodes with an aim to accurately measure the embedding potential of substrate nodes, which improves the conventional TOPSIS method. The Long-Term R/C Ratio The long-term average R/C ratios of these four algorithms are compared in Fig. 3.5. From Fig. 3.5, we can see that the performance of our proposed algorithm NA-VNE is the best one among the compared four algorithms. The difference between our NA-VNE and NSA-VNE is that these weights of three factors are different. The NA-VNE emphasizes on the nature of information for network topology itself; therefore, it can measure the embedding

30

3 Security Aware Virtual Network Embedding Algorithm Using Information. . .

Fig. 3.4 The long-term average revenue of InP

Fig. 3.5 The long-term average revenue to cost ratio

3.7 Conclusions and Future Work Table 3.2 The running time of these compared four methods

31 Notation SA-VNE NSA-VNE DSA-VNE BL-VNE

Running time/s 13.6 13.3 22.7 12.1

potentials of substrate nodes with the aim of adapting the VNE process. Using our proposed method, the NA-VNE can greatly reduce the consumption of substrate resources, thereby decreasing the cost of accommodating the arrived VNRs. The long-term average revenue to cost ratio of our proposed algorithm NA-VNE is largely more than those of three algorithms; it can validate our proposed NAVNE algorithm. Compared with the long-term average revenue, the overall trend of these four algorithms is smooth and steady. The main reason is that the resource consumption of the substrate network is proportional to the obtained revenue of the SPs. Running Time The running time of these four algorithms is shown in Table 3.2. From the Table 3.2, we can see that the running times of the SA-VNE, NSA-VNE, and BL-VNE are almost 40% lower than that of DSA-VNE, due to the fact that these three algorithms are heuristics. The DSA-VNE is a MILP problem needing relaxation technique to solve it, which incurs a large amount of running time.

3.7 Conclusions and Future Work In our work, we incorporate three factors including the node CPU capacity resource, the bandwidth resource summation of node adjacent links, and the closeness degree into the process of node importance evaluation, and leverage the shortest path to perform the link mapping process. The proposed NA-VNE algorithm takes into consideration of the node resources and the topology of substrate network, thereby significantly increasing the VNR acceptance ratio and the long-term average revenue. Furthermore, it can shorten the running time of VNE process. Simulation results demonstrated that the overall performance of our proposed algorithm SAVNE is better than those of three security aware VNE algorithms. In our future work, we intend to explore the other attributes of substrate network to further improve the performance of security VNE algorithm. In addition, we will investigate more factors of substrate links with an aim to improve the overall performance from the perspective of link mapping process.

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3 Security Aware Virtual Network Embedding Algorithm Using Information. . .

References 1. F. Bianchi, F.L. Presti, A Markov Reward model based greedy heuristic for the virtual network embedding problem, in IEEE International Symposium on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (2016), pp. 373–378 2. J. Wang, C. Jiang, H. Zhang, Y. Ren, K-C. Chen, L. Hanzo, Thirty years of machine learning: the road to Pareto-Optimal Wireless Networks. IEEE Commun. Surv. Tutorials 22(3), 1472– 1514 (2020) 3. N. Raveendran, Y. Gu, C. Jiang, N.H. Tran, M. Pan, L. Song, Z. Han, Cyclic three-sided matching game inspired wireless network virtualization. IEEE Trans. Mob. Comput. 20(2), 416–428 (2021) 4. Z. Zhang, S. Su, J. Zhang, K. Shuang, P. Xu, Energy aware virtual network embedding with dynamic demands: online and offline. IEEE/ACM Trans. Netw. 22(5), 1607–1620 (2014) 5. J.F. Botero, X. Hesselbach, Greener networking in a network virtualization environment. Comput. Netw. 57(9), 2021–2039 (2013) 6. S. Su, Z. Zhang, X. Cheng, Y. Wang, Y. Luo, J. Wang, Energy-aware virtual network embedding through consolidation. Comput. Commun. Workshops 127–132 (2012) 7. L. Purushothaman, T. Truong-Huu, M. Gurusamy, Time and bandwidth-aware virtual network embedding and migration in hybrid optical-electrical data centers, in IEEE International Conference on Advanced Information NETWORKING and Applications (2017), pp. 947–954 8. P. Zhang, Y. Hong, X. Pang, C. Jiang, VNE-HPSO: virtual network embedding algorithm based on hybrid particle swarm optimization. IEEE Access 8, 213389–213400 (2020) 9. P. Zhang, H. Yao, C. Fang, Y. Liu, Multi-objective enhanced particle swarm optimization in virtual network embedding. EURASIP J. Wirel. Commun. Netw. 2016(1), 167 (2016) 10. J. Inführ, G. Raidl, A memetic algorithm for the virtual network mapping problem. J. Heuristics 22(4), 475–505 (2016) 11. Y. Zhang, C. Jiang, L. Song, W. Saad, Z. Dawy, Z. Han, Complementary investment of infrastructure and service providers in wireless network virtualization. GLOBECOM 1–6 (2016) 12. P. Zhang, H. Li, Y. Ni, F. Gong, M. Wang, F. Wang, Security aware virtual network embedding algorithm using information entropy TOPSIS. J. Netw. Syst. Manag. 28(1), 35–57 (2020) 13. C. Jiang, S. Fan, C. Chen, J. Ma, Y. Ren, Effective management of secondary user’s density in cognitive radio networks. IEICE Trans. Commun. E93-B(9), 2443–2447 (2010) 14. A. Fischer, H.D. Meer, Position paper: secure virtual network embedding. PIK - Praxis der Informationsverarbeitung und Kommunikation 34(4), 190–193 (2011) 15. S. Liu, Z. Cai, H. Xu, M. Xu, Towards security-aware virtual network embedding. Comput. Netw. 91(C), 151–163 (2015) 16. S. Gong, J. Chen, C. Huang, Q. Zhu, Trust-aware secure virtual network embedding algorithm. J. Commun. 36(11), 1–10 (2015) 17. S. Gong, J. Chen, C. Huang, Q. Zhu, S. Zhao, Virtual network embedding through security risk awareness and optimization. KSII Trans. Internet Inf. Syst. 10(7), 2892–2913 (2016) 18. H. Cao, H. Hu, Z. Qu, L. Yang, Heuristic solutions of virtual network embedding: a survey. China Commun. 15(3), 186–219 (2018) 19. M. Yu, Y. Yi, J. Rexford, M. Chiang, Rethinking virtual network embedding: substrate support for path splitting and migration. ACM Sigcomm. Comput. Commun. 38(2), 17–29 (2008) 20. M. Rost, S. Schmid, Virtual network embedding approximations: leveraging randomized rounding. IEEE/ACM Trans. Netw. 27(5), 2071–2084 (2019) 21. Z. Sun, Y. Bai, S. Wang, Y. Cao, S. Xu, A virtual network embedding algorithm based on graph theory. IFIP Int. Conf. Netw. Parallel Comput. 1–12 (2013) 22. P. Zhang, H. Yao, Y. Liu, Virtual network embedding based on computing, network, and storage resource constraints. IEEE Int. Things J. 5(5), 3298–3304 (2018) 23. Y. Wang, P. Chau, F. Chen, A framework for security-aware virtual network embedding. Int. Conf. Comput. Commun. Netw. 1–7 (2015)

References

33

24. L.R. Bays, R.R. Oliveira, L.S. Buriol, M.P. Barcellos, L.P. Gaspary, Security-aware optimal resource allocation for virtual network embedding. Netw. Serv. Manag. 378–384 (2012) 25. C. Xing, J. Lan, Y. Hu, Virtual network with security guarantee embedding algorithms. J. Comput. 8(11) (2013) 26. M. Alaluna, L. Ferrolho, J.R. Figueiraand, N. Neves, F.M.V. Ramo, Secure virtual network embedding in a multi-cloud environment. 1–10 (2017). https://arxiv.org/pdf/1703.01313 27. C. Be¸sikta¸s, D. Gözüpek. A. Ula¸s, E. Lokman, Secure virtual network embedding with flexible bandwidth-based revenue maximization. Comput. Netw. 121, 89–99 (2017) 28. X. Liu, B. Wang, S. Liu, Z. Yang, Z. Zhao, Heuristic algorithm for secure virtual network embedding. Syst. Eng. Elect. 40(3), 676–681 (2018)

Chapter 4

Security Aware Virtual Network Embedding Algorithm Based on Reinforcement Learning

Abstract VNE algorithm is always the key problem in NV technology. At present, the research in this field still has the following problems. The traditional way to solve VNE problem is to use heuristic algorithm. However, this method relies on manual embedding rules, which does not accord with the actual situation of VNE. In addition, as the use of intelligent learning algorithm to solve the problem of VNE has become a trend, this method is gradually outdated. At the same time, there are some security problems in VNE. However, there is no intelligent algorithm to solve the security problem of VNE. For this reason, this chapter proposes a security aware VNE algorithm based on RL. In the training phase, we use a policy network as a learning agent and take the extracted attributes of the substrate nodes to form a feature matrix as input. The learning agent is trained in this environment to get the mapping probability of each substrate node. In the test phase, we map nodes according to the mapping probability and use the breadth-first strategy (BFS) to map links. For the security problem, we add security requirements level constraint for each virtual node and security level constraint for each substrate node. Virtual nodes can only be embedded on substrate nodes that are not lower than the level of security requirements. Experimental results show that the proposed algorithm is superior to other typical algorithms in terms of long-term average return, long-term revenue consumption ratio, and VNR acceptance rate.

4.1 Introduction With the rapid development of social economy, the number of network end users shows a blowout growth trend, which is expected to reach 40 billion in the near future [1, 2]. A large number of terminal resource requests bring great pressure to the underlying network. Because the Internet only provides “best effort” resource delivery, it cannot allocate the underlying resources reasonably and efficiently, so it gradually becomes rigid [3]. In recent years, NV has gradually come into people’s

© [2020] IEEE. Reprinted, with permission, from ref. [4]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Jiang, P. Zhang, QoS-Aware Virtual Network Embedding, https://doi.org/10.1007/978-981-16-5221-9_4

35

36

4 Security Aware Virtual Network Embedding Algorithm Based. . .

vision. It is considered to be an efficient and dynamic network framework for managing network resources. The virtual network consists of several virtual nodes (such as virtual router and virtual server), which are connected by several virtual links. The problem of VNE is to map virtual network to shared substrate network and provide sufficient computing and bandwidth resources for requests [5–7]. It cannot be ignored that NV brings flexibility to network architecture, but also brings some new security problems. In the NV environment, some VNRs require high security. For example, in recent years, online payment and online shopping, which are closely related to money, have become more and more popular. Some VNRs have relatively low security requirements, such as online chat and online video [8]. Because a large number of terminal devices need to request network resources, when the network is in a “busy” state, it is easy to ignore the security issues. At this time, the network may be attacked by some malicious software or cause the leakage of important information. Therefore, it is necessary to consider the security problem in virtual network mapping [8–11]. The problem of VNE has been proven to be NP-hard. Most of the traditional solutions are heuristic algorithms. By making a series of rules and constraints, they embed every VNR manually. In addition, most heuristic algorithms divide the VNE process into two stages: node mapping and link mapping [12]. However, the relationship between these two stages is not fully considered. In this way, the mapping results may fall into the local optimal solution. Due to the rich network features, resource constraints and location constraints are usually used to represent nodes, and bandwidth constraints and delay constraints are used to represent links, which is not perfect. In recent years, with the rise of cloud computing, artificial intelligence (AI), machine learning (ML), and other emerging fields, using intelligent learning algorithm to solve the problem of VNE has become a trend [13, 14]. ML algorithms process a large amount of data collected over a period of time, automatically learn the required information from the data, and then classify or predict [15–17]. As an excellent representative of ML, RL can be used to solve the problem of VNE. We incorporate the RL algorithm with the VNE algorithm with security awareness. The RL agent is trained and tested by reasonably extracting the attributes of the substrate nodes. Considering the security requirements of VNRs, we set the security level attribute for substrate nodes and the security requirement level attribute for virtual nodes. Finally, the experimental results show that our algorithm has achieved good results. As far as we know, there is no research on the combination of security of VNE and intelligent learning algorithm to address the VNE problem. The main contributions of this chapter are as follows. 1. This chapter proposes a security aware VNE algorithm based on RL. Under the condition that the basic virtual network is embedded (the computational resource constraint and link bandwidth constraint of the node), the security requirement level constraint is bounded to each virtual node. Security level constraint is bounded to each substrate node. Virtual nodes can only be embedded in substrate

4.2 Related Work

37

nodes no lower than the security requirement level. This can ensure the security of VNE algorithm. 2. We mainly apply RL algorithm to node embedding stage. Specifically, the whole algorithm is divided into training stage and testing stage. In the training phase, we use the policy network to train the learning agent. We take the five features of the substrate nodes as the input of the policy network. The result is to deduce the probability of each substrate node and map the virtual nodes according to the probability. The shortest path algorithm based on BFS is used for link mapping. In the test phase, the training results are directly utilized to complete the embedding of VNR. 3. We compare our algorithm with other representative algorithms in terms of long-term average revenue, long-term revenue consumption ratio, and VNR acceptance rate. The experimental results show that the algorithm based on RL is better than other algorithms. The security level constraint can also be applied to the VNE problem; therefore, it has some practical significance. The rest of this chapter is organized as follows. Section 4.2 describes the related work of the VNE algorithms. Section 4.3 models security aware VNE process and proposes evaluation metrics. Section 4.4 introduces the RL algorithm based on policy network in detail. Section 4.5 introduces and analyzes the simulation experiments and experimental results. Finally, the whole chapter is summarized and prospected.

4.2 Related Work 4.2.1 Virtual Network Embedding Related Algorithms The traditional heuristic algorithm can be divided into single-stage mapping algorithm and two-stage mapping algorithm according to the application of the model in the mapping stage. The difference is whether the node map and the link map are mapped simultaneously. In reference [18], a mixed integer regularization algorithm is proposed. In this algorithm, node mapping process and link mapping process are considered to be a whole. Two mapping algorithms of certainty and randomness are obtained by relaxing integer constraints. After the virtual node mapping process, the multi-commodity flow algorithm is used to complete the link mapping process. Vhub linear programming method is adopted in reference [19]. The VNE problem is treated as mixed integer programming problem using the p-hub median method. The best location of VNE can be determined after the location problem of hub is solved. Reference [20] proposes a two-stage VNE algorithm for path separation and migration. The algorithm fully measures the capability of the underlying network and fully considers the embeddability of the virtual network. Then the strategy of path segmentation and path migration is proposed. It effectively utilizes the substrate bandwidth and improves the robustness of the mapping strategy.

38

4 Security Aware Virtual Network Embedding Algorithm Based. . .

The security aware VNE algorithm based on RL also divides the VNE problem into two stages: node mapping and link mapping. Therefore, it belongs to two-stage VNE algorithm. Different from the above algorithm, the algorithm proposed in this chapter does not use heuristic method to solve the problem of VNE. With the rapid development of intelligent learning algorithm in recent years, RL algorithm has been proven to be an efficient way to solve practical problems. Therefore, this chapter uses RL to solve the problem of VNE.

4.2.2 Security Aware Virtual Network Embedding Algorithms At present, some researches have discussed the security problems of VNE. Liu et al. [21] proposed a security VNE algorithm based on multi-attribute evaluation and path optimization. He modeled the mapping process of security virtual network as a multi-objective MILP model and completed the embedding of virtual network by establishing node mapping function and link mapping function. However, his algorithm does not fully consider the security performance of each virtual node and physical node, but gives the security level to the entire VNR, which is not rigorous. Zhang et al. [22] proposed a security enhancement strategy for edge computing. Firstly, edge nodes are divided into different types of virtual networks, which are deployed between edge nodes and cloud servers. Secondly, according to the different security requirements of different information transmission methods, a security policy based on security level measurement is proposed. This strategy can be used for reference to enhance the security of virtual network mapping. Gong et al. [23] proposed a trust aware security VNE algorithm. He introduced trust relationship and trust degree into virtual network resource allocation, and quantitatively analyzed the security problems in NV environment. The method of approaching ideal ordering is used to rank the importance of multi-attribute nodes. However, the algorithm makes the rules of VNE manually, which is not in line with the reality. The security aware VNE algorithm based on RL and the above two algorithms also pay attention to the security of VNE. The main solution is to add security attributes to the virtual network and the substrate network. Different from the above algorithm, we set the security requirement level for each virtual node and set the security level for each substrate node, rather than setting the security attributes for the entire VNR. In addition, the above algorithm uses heuristic method to solve the problem of VNE. We adopt RL strategy to solve this practical problem. Practice shows that RL algorithm is a more efficient method.

4.2.3 Machine Learning-Based Virtual Network Embedding Algorithms The above heuristic methods to solve the VNE problem cannot fully reflect the real situation of the network in reality. Most of them are based on artificial rules

4.3 Network Models and Evaluation Indicators

39

and cannot automatically optimize network parameters, which may lead to local optimization of embedding results. At present, a large number of scholars have used ML algorithms to solve the problem of VNE. Reference [24] proposed Monte Carlo search tree algorithm. The algorithm considers the node mapping process as a Markov decision process (MDP). When the VNR arrives, the Monte Carlo search tree is used to embed the node. Then the shortest path algorithm or multi-commodity flow algorithm is used for link mapping. Reference [25] introduced the neural network algorithm into the VNE problem. This algorithm proposes an autonomous system based on artificial neural network to improve the mapping efficiency of virtual network. In reference [26], Q-learning algorithm in RL is used to solve the VNE problem by using the optimal mapping mechanism of reward mechanism learning. Reference [27] proposes to use the Policy Gradient algorithm in the RL algorithm and gradually learn the optimal mapping mechanism by using the RL agent. The algorithm applies the Policy Gradient method to the VNE domain and mainly to the node embedding stage. This model explores how to strike a balance between exploring better solutions and developing existing models. Our algorithm also uses a policy network as a learning agent to derive the probability of each substrate node. It should be noted that our work is different from the above research. It is the first time to combine the security attribute with the intelligent learning algorithm to study the problem of VNE. Secondly, we extract five important node attributes to train learning agents, including the key security attributes. More importantly, the overall performance of the algorithm is kept at a good level when the node attributes are extracted reasonably. More feature extraction allows the agent to learn more about the substrate network, making the VNE algorithm more practical. In addition, the above algorithms do not pay attention to the impact of security factors on the VNE algorithm. Our algorithm adds security attributes to nodes, which can well meet the security requirements of VNE.

4.3 Network Models and Evaluation Indicators 4.3.1 Network Models The substrate network can be modeled as an undirected weighted graph GS = {N S , LS }. Where N S represents the set of all substrate nodes and LS represents the set of all substrate links. Substrate node ns ∈ N S , whose attributes are represented by computing power CP U (ns ) and security level sl(ns ). The security level of substrate node is an important embodiment of substrate network security. The higher the level, the more secure the proof maps to the substrate node, and the less vulnerable it is to security issues. Substrate link l s ∈ LS , whose attributes are expressed as bandwidth capability BW (l s ). (c) in Fig. 4.1 represents a substrate network.

40

4 Security Aware Virtual Network Embedding Algorithm Based. . . (20,0) (5,1)

a

8

(15,2)

c

b

6

(10,3)

10

e

(a)

d

3

f

14

(5,2)

(16,2)

(b) (54,2)

a

(60,0)

A

20

c

B

(80,1)

C

25

(66,3) 30

d

D

34

24

28

26

32

30

b

E (55,2)

25

F

G

30

e

(67,2)

(92,3)

27

H (70,2)

f

(c)

Fig. 4.1 Schematic diagram of virtual network embedding substrate network. (a) virtual network 1, (b) virtual network 2, (c) substrate network

The same undirected weighted graph GV = {N V , LV } is used to model the virtual network. Where N V represents the set of all virtual nodes and LV represents the set of all virtual links. Virtual node nv ∈ N V , whose attributes are represented by calculated resource requirement CP U (nv ) and security requirement level sr(nv ). The security requirement level of virtual node represents the security requirement of VNR. In order to ensure the security of VNRs, virtual nodes can only be mapped to substrate nodes no less than their security requirements. Virtual link l v ∈ LV , whose attributes are represented by bandwidth resource requirement BW (l v ). The (a) and (b) in Fig. 4.1 represent two virtual networks. We summarize all the symbols in Table 4.1. The VNE problem can be expressed as GV (N V , LV ) → GS (N Si , LSi ), where S N i ∈ N S , LSi ∈ LS . The above process needs to meet the following constraints: V |N |

(nv , nvi ) = 0.

(4.1)

(ns , nsj ) = 0.

(4.2)

i=1 S |N |

j =1

4.3 Network Models and Evaluation Indicators

41

Table 4.1 Symbol summary Symbol GS GV NS LS CP U (ns ) BW (l s ) sl(ns ) NV LV CP U (nv ) BW (l v ) sr(nv )

Description Substrate network Virtual network Set of all substrate nodes Set of all substrate links The computational power of a substrate node The amount of bandwidth resources of a substrate link Substrate node security level Set of all virtual nodes Set of all virtual links Compute resource requirements for a virtual node Bandwidth resource requirements for a virtual link Security level requirements for a virtual node

Formulas (4.1) and (4.2) indicate that neither a virtual node nv nor a substrate node ns exists independently. There must be other nodes connected to it. S |N |

(nvi → nsj ) = 1.

(4.3)

j =1

Formula (4.3) indicates that a virtual node nvi can only be embedded into a physical node nsj , where nvi ∈ N V , nsj ∈ N S . |N |  s

∀nvi

∈ V NRk ,

nvs ij ≤ 1.

(4.4)

nsj ∈N S

Formula (4.4) indicates that the virtual node nvi in the same VNR cannot be mapped to the same substrate node nsj . |L |  (liv → ljs ) ≥ 1. S

(4.5)

j =1

Formula (4.5) indicates that a virtual link liv can be embedded into one or more substrate links ljs , where liv ∈ LV , ljs ∈ LS . v vs s nvs ij CP U (ni ) ≤ nij CP U (nj ),

(4.6)

42

4 Security Aware Virtual Network Embedding Algorithm Based. . .

where CP U (nvi ) represents the computing resource demand of the virtual node nvi . CP U (nsj ) represents the computing resource available from the substrate node nsj . lijvs BW (liv ) ≤ lijvs BW (ljs ),

(4.7)

where BW (liv ) represents the bandwidth demand of virtual link liv . BW (ljs ) represents the bandwidth resources available for the substrate link ljs . sl(ns ) ≥ sr(nv ),

(4.8)

where sl(ns ) represents the security level of the substrate node. sr(nv ) represents the level of security requirements for the virtual node. Figure 4.1 shows two virtual networks embedded in a substrate network. For two virtual networks, the first number in parentheses next to the node represents the calculated resource requirements of the node. The second number represents the level of security requirements for the node. The number on a virtual link represents the bandwidth requirements for that link. For the substrate network, the first number in parentheses next to the node represents the computing resources that the node can provide. The second number represents the security level of the node. The number on a substrate link represents the amount of bandwidth resources that the link can provide. Figure 4.1 shows the successful embedding of two VNRs into the base network. The corresponding relation of specific nodes is: a → A, b → E, c → C, d → D, e → G, f → H .

4.3.2 Evaluation Indicators We evaluate the security aware VNE algorithm based on RL from three aspects: long-term average revenue, long-term revenue consumption ratio, and VNR acceptance rate. The VNE revenue is represented by Re(GV , t, tp ), where tp represents the duration of the VNR to arrive. Specifically, it is calculated based on node computing resource consumption CP U (nv ) and link bandwidth resource consumption BW (l v ). The expression method is shown in formula (4.9): ⎡ ⎤     Re GV , t, tp = tp · ⎣ CP U (nv ) + BW (l v )⎦ . nv ∈N V

(4.9)

l v ∈LV

The VNE consumption is expressed as Co(GV , t, tp ). Specifically, it is calculated according to the calculated resource consumption CP U (nv ) of the node

4.4 Introduction of Reinforcement Learning Algorithm Based on Policy Network

43

and the total bandwidth resource consumption BW (lvs ) of the embedded multiple substrate links. As shown in formula (4.10): ⎡ ⎤      Co GV , t, tp = tp · ⎣ CP U (nv ) + BW (lvs )⎦ . nv ∈N V

(4.10)

l v ∈LV l s ∈LS

The long-term average revenue is shown in formula (4.11): T ime Avg_Re =

t =0

lim

T ime→∞

R(GV , t, tp ) , T ime

(4.11)

where T ime is the elapsed time. Long-term revenue consumption is shown in formula (4.12): T ime RC =

lim

T ime→∞

t =0

Re(GV , t, tp )

t =0

Co(GV , t, tp )

T ime

(4.12)

.

The VNR acceptance rate can be expressed as follows: T ime Acp =

lim

T ime→∞

t =0

Accept (GV , t, tp )

t =0

Arrive(GV , t, tp )

T ime

,

(4.13)

where Accept (GV , t, tp ) represents the number of successful VNRs mapped in the time range tp . Arrive(GV , t, tp ) represents the total number of VNRs that arrive within the time range tp .

4.4 Introduction of Reinforcement Learning Algorithm Based on Policy Network 4.4.1 Extraction of Substrate Node Attributes We need to train RL agents in a substrate network as close to reality as possible, so we need to create a more “real” environment for agents. Because there are many properties of the substrate nodes, it will increase the computational complexity to represent them. We extract the following five attributes to represent the substrate nodes as input to the policy network. 1. Computing capacity (CPU): Computing capacity is one of the most important attributes to represent a node. The stronger the computing power of the node, the

44

4 Security Aware Virtual Network Embedding Algorithm Based. . .

greater the probability that the substrate node receives the virtual node. The CPU can be represented as follows: CP U (ns )r = CP U (ns ) −



CP U (ns ),

nv →ns

(4.14)

where CP U (ns )r represents the remaining computing power of the substrate node. CP U (ns ) represents the initial computing power of the substrate node. s nv →ns CP U (n ) represents the sum of computational resources consumed by all VNRs for virtual nodes embedded in ns . 2. Degree (DEG): The number of substrate links connected to the substrate node is called degree. The greater the degree of a node, the more nodes it is connected to. DEG can be expressed as: DEG(ns ) =



Link(ns , nsi ),

(4.15)

nsi ∈N S

if ns is connected to nsi , Link(ns , nsi ) = 1; if not, it is 0. 3. Sum of bandwidth (SUM_BW): The sum of the bandwidth of all the links connected to a substrate node. The larger the node bandwidth, the larger the virtual node that is mapped to the substrate node will have more link options, resulting in a better mapping effect. SUM_BW can be expressed as: SU M_BW =



BW (l s ),

(4.16)

l s ∈LSn

where LSn represents the substrate link connected to node ns . l s is one of LSn . 4. Average distance from mapped node to this node (AVG_DIS): This property is considered for the link mapping phase. The above attributes take into account the local importance of the node, which takes into account the global importance of the node. This property depicts the average distance to the mapped node, so the smaller the attribute, the greater the probability of the node being mapped. Finally, the shortest path algorithm based on BFS is used to map the link. AVG_DIS can be expressed as: AV G_DI S =

Nvs ∈N S

DI S(ns , nsv )

count + 1

,

(4.17)

where DI S(ns , nsv ) represents the distance from ns to the mapped node. count is the number of nodes that have been mapped, plus 1 is to prevent the denominator from being 0. 5. Security level (SL): The higher the security level of the substrate node, the safer the mapping to the node. Virtual nodes can only be mapped to substrate nodes with a higher level of security requirements.

4.4 Introduction of Reinforcement Learning Algorithm Based on Policy Network

45

We characterize the above properties of the i-th substrate node as a 5dimensional vector, as follows: vi = (CP U (nsi ), DEG(nsi ), SU M_BW (nsi ),

(4.18)

AV G_DST (nsi ), SL(nsi )).

The attribute vectors of all the substrate nodes are put into a feature matrix F M, which is taken as the input of the policy network. F M = (v1 , v2 . . . vn )T .

(4.19)

The feature matrix is expressed as follows:  CP U (ns ) DEG(ns ) SU M_BW (ns ) AV G_DI S(ns ) SL(ns ) 1

1

1

1

1

CP U (ns2 ) DEG(ns2 ) SU M_BW (ns2 ) AV G_DI S(ns2 ) SL(ns2 ) ... ... ... ... ... CP U (nsk ) DEG(nsk ) SU M_BW (nsk ) AV G_DI S(nsk ) SL(nsk )

.

(4.20)

4.4.2 Policy Network We use a policy network as a learning agent, which is essentially a convolutional neural network commonly used in ML [28, 29]. Taking the policy matrix as input, the mapping probability of each substrate node is output by training the learning agent. The greater the probability, the more likely the substrate node is to be mapped. The policy network consists of an input layer, a convolution layer, a softmax layer, and a node selector, as shown in Fig. 4.2. As the input of the policy network, the feature matrix is transferred from the input layer to the convolution layer. The main function of convolution layer is to convolute the feature matrix. Convolution operation originally refers to the operation of generating the third function from two functions. Here, the feature vector of each node can be obtained after convolution of the feature matrix. We call it the available resource vector, which is specifically expressed as: arvi = ω · vi + d,

(4.21)

where arvi is the i-th output of the convolution layer, ω is the weight vector of the convolution kernel, and d is the deviation. The vector is then transferred to the softmax layer, and the softmax function of logistic regression is used to generate a probability for each node [27]. The higher the probability, the more likely the virtual node is to map to that node. Some substrate nodes may not be able to map part of the virtual nodes due to insufficient computing power or security level, so the probability of this part of substrate nodes being mapped cannot be deduced. We add a node selector to select a group of candidate nodes with enough computing power and security level.

46

4 Security Aware Virtual Network Embedding Algorithm Based. . .

ConvoluƟon Layer

Input Layer

FM

available resource vector

vn

CPU DEG

SUM_ AVG_ BW DST

SL

v2

CPU DEG

SUM_ AVG_ BW DST

SL

available resource vector

v1

CPU DEG

SUM_ AVG_ BW DST

SL

available resource vector

c1

c2 …

selector

…

cn

Fig. 4.2 Policy network

4.4.3 Training and Testing We use the policy network as a learning agent. First, the policy network is initialized to the unlearned state. After the feature matrix is input, we take the feature matrix as the learning environment of the agent. By fully learning each node attribute in the feature matrix, the agent selects those substrate nodes that satisfy both the computational resource requirements of the virtual node and the security performance requirements. The final policy network outputs a set of available substrate nodes and the probabilities that the virtual nodes map to them. After obtaining the probability of each substrate node, we use the probability distribution model to generate a sample from the substrate network set, from which a substrate node is selected as the node to be mapped. Because the initialization of the policy network is random, the node with the highest probability does not mean that it can be mapped to the optimal result. This process is repeated until all virtual nodes are allocated or VNE is terminated due to insufficient resources of the substrate node. If all virtual node mappings are successful, the link mapping continues. The training process can be represented as Fig. 4.3.

4.4 Introduction of Reinforcement Learning Algorithm Based on Policy Network

Itera on ...

policy network randomly ini alized parameters

47

policy network policy network input

output

policy network

available nodes and their probabili es

FM

extract FM

choose

substrate network

reward

train reinforcement learning agent

Fig. 4.3 Training process diagram

In RL, learning effect is determined by the action taken by learning agent, so we need to set a reward standard for learning agent. If the agent’s current behavior can make the algorithm achieve greater benefits or better results, then the agent should be encouraged to continue to take the current action to obtain the cumulative reward. If the result of the agent’s current action is small or harmful, the reward signal will become small or even disappear. The agent will stop the current action and take a new action instead. So an appropriate reward signal is very important. In the problem of VNE, we use the long-term revenue consumption ratio as a reward signal. This index reflects the utilization of the substrate resources, especially the link bandwidth resources. If the agent’s current action can produce a higher revenue consumption ratio, then the agent will receive a larger reward signal, and continue to explore the action that produces a greater revenue consumption ratio. On the contrary, the agent stops its action and then takes a new action. In the training process, we set a target symbol for each virtual node in the VNRs. This symbol represents the substrate node to which the virtual node is embedded. Assuming that the target symbol of virtual node nvi is j , it means that the j -th dimension of the feature vector corresponding to substrate node nsj is 1, and other dimensions are 0. It is expressed as follows: nsj = (01 , 02 , . . . 1j . . . , 0k )T .

(4.22)

The next step is to output the error between the target vector vjs and nsj , that is, the cross entropy loss: Loss(nsj , vjs ) = −

 j

nsj log(vjs ).

(4.23)

48

4 Security Aware Virtual Network Embedding Algorithm Based. . .

Then we use gradient descent algorithm to calculate the loss of gradient gf : gl = gf · α · reward.

(4.24)

Where reward is the reward signal and α is the learning rate. The learning rate α control calculates the size of the gradient. If the gradient is too large, the learning agent’s action adjustment direction will be too large, may miss some of the more expensive action. Therefore, no amount of training can achieve better results. If the gradient is too small, the training of the agent will be extremely slow and waste a lot of time. Therefore, the learning rate should be carefully adjusted. We adopt batch gradient descent algorithm to update the strategy network, which not only improves the convergence speed of the agent training, but also guarantees the stability of the network [30]. The training process is shown in algorithm 4. Algorithm 4 Training phase algorithm Require: number of epoches, epoch; learning rate, α; trainingset; Ensure: parameters of the policy network; 1: while iteration < epoch do 2: for request ∈ trainingset do 3: counter = 0; 4: for v_node ∈ request do 5: F M = getF eatureMatrix(); 6: dis = getOutP ut (F M); 7: if sn.cpu ≥ vn.cpu and sl ≥ sr then 8: c = sample(dis); 9: getGradient (c); 10: end if 11: end for 12: if isMapped(∀ v_node ∈ request) then 13: BF SLinkMap(request); 14: end if 15: if isMapped(∀ v_node ∈ request) then 16: if (∀ v_link ∈ request) then 17: reward = revenue(request); 18: else 19: stacking gradient = 0; 20: end if 21: end if 22: counter + +; 23: if counter == batch_size then 24: counter = 0; 25: end if 26: end for 27: iteration + +; 28: end while 29: return parameters;

4.4 Introduction of Reinforcement Learning Algorithm Based on Policy Network

49

The input parameter epoch indicates that all training data will be sent to the policy network to complete a forward calculation and back propagation process. In each epoch, we input all VNRs for training. Line 5 of the algorithm indicates that the feature matrix is obtained. Line 6 is the probability distribution of the substrate nodes. Lines 7–10 represent the node mapping. Line 13 shows the link mapping. Lines 15–21 compute the rewards obtained after the nodes and links are successfully embedded. In the test phase, we select the node with the highest probability as the mapping node directly. The test process is shown in Algorithm 5. Where line 5 represents the node map and line 8 represents the link map using BFS. Ends if all virtual nodes and virtual links are mapped successfully. Algorithm 5 Test phase algorithm Require: test_set; Ensure: long term average revenue, acceptance rate, long term revenue consumption ratio; 1: I nitialize the policy network; 2: for request ∈ test_set do 3: for v_node ∈ request do 4: F M = getF eatureMatrix(); 5: candi_node = getP robability(c); 6: end for 7: if isMapped(∀ v_node ∈ request) then 8: BF SLinkMap(request); 9: end if 10: if isMapped(∀ v_node ∈ request, ∀ v_link ∈ request) then 11: return (success); 12: end if 13: end for

4.4.4 Algorithm Complexity Analysis The algorithm complexity of our proposed security aware VNE algorithm based on RL is O(CV NR (Cns · d + Cnv + Cl v )). Where CV NR represents the number of incoming VNRs. Cns represents the number of substrate nodes. d is the dimension of the feature matrix. Cnv and Cl v represent the number of successfully embedded virtual nodes and the number of virtual links, respectively. The specific derivation of algorithm complexity is shown in Table 4.2.

50

4 Security Aware Virtual Network Embedding Algorithm Based. . .

Table 4.2 Algorithm complexity analysis Algorithm steps Complexity of computing feature matrix for every VNR The embedded complexity of every VNR computing node The embedded complexity of every VNR computing link Complexity of successful embedding of every VNR Complexity of successful embedding of all VNRs

Algorithm complexity O(Cns · d) Cnv Cl v O(Cns · d + Cnv + Cl v ) O(CV NR (Cns · d + Cnv + Cl v ))

4.5 Experimental Setup and Result Analysis 4.5.1 Experimental Setup The substrate topology is generated by GT-ITM tool, which is commonly adopted in virtual network mapping algorithm [31, 32], to form a substrate network with 100 nodes and 570 links. We set the computing resource and security level for each substrate node. The computing resource of each substrate node is evenly distributed between 50 and 100 units. The security level of each substrate node is evenly distributed between 0 and 3. In addition, we set the bandwidth resource of each substrate link to a range from 20 to 50. Similarly, we generate 2000 VNRs, 1000 of which are used as training set and another 1000 as test set. Each of these requests has between 2 and 10 virtual nodes at random. The computing resource requirements of virtual nodes are uniformly distributed between 0 and 50 units. The security requirements of virtual nodes are evenly distributed between 0 and 3. The bandwidth resource requirements of the virtual link are evenly distributed between 0 and 50. Virtual nodes are connected with each other with a probability of 50%. The arrival of VNR simulates the Poisson process. The summary of parameters is shown in Table 4.3.

Table 4.3 Parameter setting Parameter names Number of substrate nodes Number of substrate links Substrate node resource Substrate link resource Security level Number of nodes per VNR Virtual node computing resource requirements Virtual link bandwidth resource requirements Virtual node connection probability Safety requirements level

Parameter values 100 570 U[50, 100] U[20, 50] U[0, 3] U[2, 10] U[0, 50] U[0, 50] 50% U[0, 3]

4.5 Experimental Setup and Result Analysis

51

The experimental platform uses PyCharm and Python language to write experimental code. The training results and test results are shown in the diagram by Origin 8.5. We used TensorFlow to build the policy network. TensorFlow is an open source software library for high-performance numerical calculations. With its flexible architecture, computing can be easily deployed to a variety of platforms [33–35]. Firstly, the four-tier structure of the policy network is constructed according to the description in Sect. 4.2. The flexibility and ease of use of TensorFlow makes it easier to construct the four-tier structure. We initialize the policy network with parameters that conform to normal distribution. Set the learning rate of the learning agent to 0.005. We trained 100 epoch agents by gradient descent method.

4.5.2 Training Results and Analysis Figures 4.4, 4.5, and 4.6 show the changes in long-term average revenue, long-term revenue consumption ratio, and VNR acceptance rate over 100 epochs, respectively. As can be seen from the figures, the training process of RL is difficult to converge. Because RL agents need to constantly be aware of the state of the environment as they interact with it. We extract five attributes of the substrate node to form the feature matrix, which is used as the learning environment of the agent. The agent should fully learn how each feature might affect the final result. The agent is 1120

long-term average revenue

1100

1080

1060

1040

1020

1000

980 0

20

40

60

epoch Fig. 4.4 Long-term average revenue on training

80

100

4 Security Aware Virtual Network Embedding Algorithm Based. . .

long-term revenue consumption ratio(%)

52

0.40

0.38

0.36

0.34

0.32

0.30 0

20

40

60

80

100

80

100

epoch Fig. 4.5 Long-term revenue consumption ratio on training

VNR acceptance rate(%)

0.675 0.670 0.665 0.660 0.655 0.650 0.645 0

20

40

60

epoch Fig. 4.6 VNR acceptance rate on training

4.5 Experimental Setup and Result Analysis

53

rewarded for making the decision. The training difficulty of RL agents, especially in NP-hard problems such as VNE, takes longer to converge. In the early stage of training (0 F (xi )af t er , F (xi )bef ore = F (xi )af t er , F (xi )bef ore < F (xi )af t er ,

(18.25)

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18 A Multi-Domain VNE Algorithm Based on Load Balancing in the IoT Networks

where ns ∈ goal node set, the goal node set is defined as a set of goal nodes selected by mutant gene set, and it can also be called post-mutation nodes. The Δ(2)τns of the mutation stage is different from the Δ(1)τns of the crossover stage, and it can be formulated as i = Δ(2)τns

|F (xi )af t er − F (xi )bef ore | , num(mutant gene set)

(18.26)

i represents the pheromones released by x on the substrate node n , where Δ(2)τns i s and num(mutant gene set) represents the number of genes in mutant gene set. According to the proportion of pheromones amount of each node in the mutation stage to the total pheromones amount of all substrate nodes in the individual, a certain number of different mutation genes were obtained by roulette algorithm, and these genes were used to form mutant gene set for mutation. The proportion of pheromone can be formulated as follows:

pheromone proportion =

τns (t) . ns ∈Xi τns (t)

(18.27)

In addition, since all physical nodes must release pheromones in the crossover phase, τns (t) must be greater than 0.

18.5 Heuristic Algorithm Design Based on the dynamic crossover probability, the load balancing and the resource constraints strategy, and the gene selection strategy, a hybrid genetic algorithm for VNE problem solving strategy LB-HGA is proposed.

18.5.1 Node Mapping Algorithm We use the optimized genetic algorithm to complete the mapping of nodes. In this model, we take the real number encoding method and define the individuals as j Xi = {Xi1 , Xi2 , . . . Xi . . . Xin }, where Xi represents the individual numbered i in the population. In addition, n is the number of virtual nodes in the virtual network, j xi represents the substrate node corresponding to the virtual node numbered j , and the gene belongs to the individual Xi . And we use formula (18.1) as the fitness function F (xi ). We modified the iterative steps based on the framework of the traditional genetic algorithm. Therein, the elite selection strategy was adopted to retain half of the individuals with lower fitness. For cross process, select a pair of individuals at random and decide whether to generate offspring through the dynamically calcu-

18.5 Heuristic Algorithm Design

315

lated crossover probability. If crossover is determined, several pairs of alleles are randomly selected and exchanged. In addition, for each newly generated offspring, mutation is determined according to a certain probability. Moreover, a strategy named cataclysm is used to jump out of the local optimal solution. It occurs when the maximum number of iterations × 0.6 consecutive iterations does not update the optimal solution. Only the first third of the individuals with the lowest fitness were retained, and then the initialized individuals were generated to complete the population, so that the number of individuals in the population was maintained at X. The detailed steps of node mapping algorithm are illustrated in Algorithm 34. Algorithm 34 The node mapping algorithm based on optimized genetic algorithm Require: Substrate network Gs = {N s , Ls }, and VNR Gv = {N v , Lv }. Ensure: Virtual network node mapping scheme. 1: Pm ← mutation probability; 2: X ← maximum population capacity; 3: k ← 0; 4: Pc ← 0; 5: Randomly generate X individuals; 6: Initialize the pheromones in the substrate network; 7: for not reached max iterations do 8: Use elite choice strategy to select X2 individuals; 9: while the number of individuals is less than X do 10: Select a pair of individual at random and calculate the cor11: responding crossover probability Pc ; 12: if random decimal < Pc then 13: Crossing this two individuals; 14: end if 15: Feasibility judgment; 16: end while 17: Update the pheromones based on pheromone update strategy; 18: for each individual in the new offspring do 19: Calculate fitness; 20: if random decimal < Pm then 21: Mutation; 22: end if 23: end for 24: Update the pheromones of genes in the mutant gene 25: set and goal node set; 26: if the optimal solution has been updated then 27: k = 0; 28: else 29: k++; 30: if k == max iterations × 0.6 then 31: Cataclysm; 32: k = 0; 33: end if 34: end if 35: end for 36: return The individual with the lowest fitness;

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18 A Multi-Domain VNE Algorithm Based on Load Balancing in the IoT Networks

Algorithm 35 The link mapping algorithm based on shortest path algorithm Require: Virtual network node mapping scheme. Ensure: Virtual network link mapping scheme. 1: Sort the virtual links by the required bandwidth in nonincreasing order; 2: for all the unmapped virtual links in VNR do 3: Gets the corresponding two substrate endpoints; 4: Update the weight of each substrate link; 5: Obtain the shortest path between the two endpoints; 6: end for 7: return Link mapping scheme;

18.5.2 Link Mapping Algorithm The detailed steps of link mapping algorithm are illustrated in Algorithm 35.

18.6 Performance Evaluation In this section, we describe the setup of the simulation environment, including the parameters of the substrate network and algorithm, and give the experimental results. We used the five evaluation criteria defined earlier to measure the performance of our method against the others. In addition, we also describe the mapping process and parameter setting of other algorithms.

18.6.1 Environment Settings The experiment was run on a PC with Intel Core i5 2.90 GHz CPU and 8 GB memory. The substrate network topology and VNR topology are generated by the GT-ITM [46–49] tool. The substrate network includes a total of 4 domains, and each domain includes 30 substrate nodes. Therein, the CPU capacity of the substrate nodes ranges from [100,300], the bandwidth of the links within the domain ranges from [1000,3000], and the bandwidth of the inter-domain links ranges from [3000,6000]. The unit price of the bandwidth and the unit price of the CPU are both in the range of [1,10]. In addition, the value range of the number of virtual nodes in a virtual network is [5,10], and the value range of the CPU capacity required by the virtual node and the bandwidth resource required by the virtual link are both [1,10]. The above variables all obey uniform distribution. In addition, the number of VNRs follows a Poisson distribution with an average of 10 within 100 time units. The simulation time is 2200 time units, and the life of the virtual network is 1000 time units.

18.6 Performance Evaluation

317

Table 18.1 Introduction of three algorithms compared with LB-HGA Notation T-GA MDPSO

IVERM

Description Traditional genetic algorithm and SP algorithms are used. For each virtual node in virtual network, obtain a group of candidate nodes and then use PSO algorithm to obtain the mapping scheme of virtual nodes. The mapping of virtual links is based on the traditional SP algorithm. The single-domain mapping is carried out when there are enough resources in alternative domain, and the cross-domain mapping based on genetic algorithm is used when resources are insufficient. The mapping of virtual links is based on the shortest path algorithm.

Table 18.2 Parameter setting of four algorithms MDPSO IVERM

T-GA LB-HGA

The number of particles and iterations are 10 and 50, and the ω, ρ1, and ρ2 in the velocity update formula are 0.1, 0.2, and 0.7. The number of particles and iterations are 20 and 50, the probability of crossover and mutation are 0.85 and 0.15, the probability of gene exchange in crossover is 0.7, and the number of candidate fields is 3. The number of individuals and iterations are 50 and 50, and the probability of crossover and mutation are 0.7 and 0.03. The number of individuals and iterations are 40 and 50, the λ1 , λ2 , and λ are 1.2, 0.8, and 1, and the probability of mutation is 0.2.

18.6.2 Algorithm Parameters We compared the designed algorithm with the other three existing heuristic VNE problem solving methods. Table 18.1 shows the comparison and introduction of the mapping process of the other three algorithms, and Table 18.2 shows the parameter settings of the all four algorithms.

18.6.3 Evaluation Results In this section, we analyze the performance of the four algorithms according to five evaluation indexes and give the experimental results and the causes of the results. Figure 18.8 uses the standard deviation of resource allocation of the substrate network link as the measurement method of link load balancing. As can be seen from the figure, LB-HGA algorithm performs best. This is because although the four algorithms all use the shortest path algorithm to map the virtual link, the LBHGA algorithm considers the link load balancing. Figure 18.9 uses revenue–cost ratio to compare the resource allocation efficiency of the algorithm. As can be seen from the figure, LB-HGA algorithm performs best. This is because LB-HGA algorithm will obtain the best solution based on fitness,

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18 A Multi-Domain VNE Algorithm Based on Load Balancing in the IoT Networks

Fig. 18.8 The diagram of load balancing of the substrate link

Fig. 18.9 The diagram of revenue–cost ratio

18.6 Performance Evaluation

319

which takes into account price and resource consumption, so the benefit–cost ratio performs well. As can be seen from Fig. 18.10, LB-HGA algorithm performs best in the acceptance rate of VNRs. This is because LB-HGA has added the preliminary evaluation of the substrate link resources into the shortest path algorithm, so that the algorithm can bypass the substrate link with insufficient resources, which can avoid most mapping failures. However, the other three algorithms did not clearly consider resource constraints in the link mapping stage, nor did they have a good re-mapping method, so the acceptance rate was poor. As can be seen from Fig. 18.11, in the early stage when resources are relatively sufficient, the mapping revenue of LB-HGA algorithm is stable, and in the later stage, the revenue will slight decline due to insufficient resources. However, even at an early stage with sufficient resources, the revenue of the other three algorithms is reduced by mapping failures. This can reflect the good performance of LB-HGA algorithm from the side. Figure 18.12 uses the product of the resource unit price and the required resource as a measure of the mapping scheme quotation. As can be seen in the figure, the performance of LB-HGA algorithm is second only to IVERM algorithm. This is because LB-HGA algorithm increased the consideration of load balancing, so the quotation was slightly higher than the IVERM algorithm that gave priority to

Fig. 18.10 The diagram of the VNR acceptance ratio

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18 A Multi-Domain VNE Algorithm Based on Load Balancing in the IoT Networks

Fig. 18.11 The diagram of mapping average earnings

Fig. 18.12 The diagram of mapping average quotation

18.6 Performance Evaluation

321

Fig. 18.13 The diagram of the total running time

single-domain mapping. However, our algorithm is more stable, which means that our algorithm can get better results with less leeway within the same number of iterations. As can be seen from Fig. 18.13, the total running time of IVERM, T-GA, and LBHGA algorithms are all low and not significantly different. This shows that even if LB-HGA algorithm adds a variety of strategies to ensure the performance of the algorithm, the running time does not increase significantly. Figure 18.14 shows the average running time of the four algorithms mapping a virtual network. It can be seen that the running time of LB-HGA algorithm is slightly higher than that of IVERM and T-GA algorithm. This is because the LB-HGA algorithm will re-map when the link map fails to improve the VNR acceptance ratio, but this also leads to an increase in the running time. But we use inexact resource constraints to replace precise resource constraints in algorithm iteration, which has reduced the running time as much as possible, making it not much different from other algorithms.

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18 A Multi-Domain VNE Algorithm Based on Load Balancing in the IoT Networks

Fig. 18.14 The diagram of the average total running time

18.7 Conclusion Heuristic algorithms are suitable for solving NP-hard problems, so they are widely used to solve VNE problems. However, in solving the VNE problem, there are some unresolved problems in the existing work. For example, VNE method based on genetic algorithms usually uses the traditional design method with large randomness, which usually leads to the instability of the quality of the algorithms’ results. It is a problem worthy of attention in the IoT environment that requires high network stability and algorithm reliability. In addition, the traditional algorithm’s dependence on experience reduces its usefulness, and its low flexibility makes it unable to adapt to increasingly complex network environments. In this chapter, the operational optimization of the genetic algorithm is discussed. As a result, the calculation method of crossover probability in three cases is given, as well as the gene scoring strategy for selecting mutated genes. The purpose is to accelerate the convergence speed and make the algorithm more flexible to adapt to different simulation environments. In addition, taking into account different link mapping methods, we analyze the resource constraints and the use of the shortest path algorithm, and we design a link mapping strategy enforcing load balancing. In addition, this strategy improves the accuracy of fitness estimation while improving the acceptance rate by avoiding links with insufficient resources. Simulation results show that our algorithm performs best in link load balance, mapping revenue–cost

References

323

ratio, and VNR acceptance rate and performs well in mapping average quotation and algorithm running time. In addition, compared with other algorithms, LB-HGA algorithm is significantly more stable and can perform well even in the later stage of the experiment. In the future work, we will consider better neural network design approaches and hybrid strategies for multiple intelligent algorithms, and we will consider information security in our algorithm. In addition, we intend to study machine learning (ML)-based algorithms [50, 51] to address the issues of computer networks.

References 1. P. Zhang, F. Liu, C. Jiang, A. Benslimane, J.-L. Gorricho, J. Serrat-Fernandez, A multi-domain VNE algorithm based on load balancing in the IoT networks. Mobile Netw. Appl. (2021) 2. H. Guo, J. Liu, UAV-enhanced intelligent offloading for Internet of Things at the edge. IEEE Trans. Ind. Inform. 16(4), 2737–2746 (2020) 3. P. Zhang, X. Huang, Y. Wang, Chunxiao Jiang, S. He, H. Wang, Semantic similarity computing model based on multi model fine-grained nonlinear fusion. IEEE Access 9, 8433–8443 (2021) 4. J. Zhao, Q. Li, Y. Gong, K. Zhang, Computation offloading and resource allocation for cloud assisted mobile edge computing in vehicular networks. IEEE Trans. Veh. Technol. 68(8), 7944– 7956 (2019) 5. H. Guo, J. Liu, J. Lv, Toward intelligent task offloading at the edge. IEEE Netw. 1–7 (2019) 6. H. Guo, J. Zhang, J. Liu, FiWi-enhanced vehicular edge computing networks: collaborative task offloading. IEEE Veh. Technol. Mag. 14(1), 45–53 (2019) 7. J. Du, C. Jiang, Z. Han, H. Zhang, S. Mumtaz, Y. Ren, Contract mechanism and performance analysis for data transaction in mobile social networks. IEEE Trans. Netw. Sci. Eng. 6(2), 103– 115 (2019) 8. J. Du, C. Jiang, H. Zhang, Y. Ren, M. Guizani, Auction design and analysis for SDN-based traffic offloading in hybrid satellite-terrestrial networks. IEEE J. Sel. Areas Commun. 36(10), 2202–2217 (2018) 9. J. Du, E. Gelenbe, C. Jiang, H. Zhang, Y. Ren, Contract design for traffic offloading and resource allocation in software defined ultra-dense networks. IEEE J. Sel. Areas Commun. 35(11), 2457–2467 (2017) 10. C. Jiang, Y. Chen, K.J.R. Liu, Distributed adaptive networks: a graphical evolutionary gametheoretic view. IEEE Trans. Signal Process. 61(22), 5675–5688 (2013) 11. T. Anderson, L. Peterson, S. Shenker, J. Turner, Overcoming the Internet impasse through virtualization. Computer 38(4), 34–41 (2005) 12. K. Tutschku, T. Zinner, A. Nakao, T.G. Phuoc, Network virtualization: implementation steps towards the future internet. J. Hum. Behav. Soc. Environ. 22(4), 463–478 (2009) 13. E. Amaldi, S. Coniglio, A.M.C.A. Koster, M. Tieves, On the computational complexity of the virtual network embedding problem. Electron. Notes Discrete Math. 52(1), 213–220 (2016) 14. C. Jiang, S. Fan, C. Chen, J. Ma, Y. Ren, Effective management of secondary user’s density in cognitive radio networks. IEICE Trans. Commun. E93-B(9), 2443–2447 (2010) 15. C. Ouyang, S. Wu, Chunxiao Jiang, J. Cheng, H. Yang, Physical layer security over mixture gamma distributed fading channels with discrete inputs: a unified and general analytical framework. IEEE Commun. Lett. 25(2), 412–416 (2021) 16. X. Lin, L. Kuang, Z. Ni, C. Jiang, S. Wu, Approximate message passing-based interference cancellation technique for asynchronous NOMA. IEEE Commun. Lett. 24(3), 534–538 (2020)

324

18 A Multi-Domain VNE Algorithm Based on Load Balancing in the IoT Networks

17. Z. Yong, M.H. Ammar, Algorithms for assigning substrate network resources to virtual network components, in Infocom IEEE International Conference on Computer Communications (2006) 18. M. Diallo, A. Quintero, S. Pierre, An efficient approach based on ant colony optimization and Tabu search for a resource embedding across multiple cloud providers. IEEE Trans. Cloud Comput. (2019) 19. Q. Yang, T. Jiang, N. Beaulieu, J. Wang, C. Jiang, S. Mumtaz, Z. Zhou, Heterogeneous semiblind interference alignment in finite-SNR networks with fairness consideration. IEEE Trans. Wirel. Commun. 19(4), 2472–2488 (2020) 20. F. Li, H. Yao, J. Du, C. Jiang, Y. Qian, Stackelberg game-based computation offloading in social and cognitive industrial Internet of Things. IEEE Trans. Ind. Inform. 16(8), 5444–5455 (2020) 21. H. Cao, H. Han, Z. Qu, L. Yang, Heuristic solutions of virtual network embedding: a survey. China Commun. 15(3), 186–214 (2018) 22. H. Yao, S. Ma, J. Wang, P. Zhang, C. Jiang, S. Guo, A continuous-decision virtual network embedding scheme relying on reinforcement learning. IEEE Trans. Netw. Serv. Manag 17(2), 864–875 (2020) 23. J. Lischka, H. Karl, A virtual network mapping algorithm based on subgraph isomorphism detection, in Proceedings of the 1st ACM Workshop on Virtualized Infrastructure Systems and Architectures (2009), pp. 81–88 24. N.M.M.K. Chowdhury, M.R. Rahman, R. Boutaba, Virtual network embedding with coordinated node and link mapping, in Infocom (2009) 25. X. Gao, H. Yu, V. Anand, S. Gang, D. Hao, A new algorithm with coordinated node and link mapping for virtual network embedding based on LP relaxation, in Asia Communications & Photonics Conference & Exhibition (2010), pp. 152–153 26. H. Cao, S. Wu, G. Aujla, Q. Wang, L. Yang, H. Zhu, Dynamic embedding and quality of service driven adjustment for cloud networks. IEEE Trans. Ind. Inform. 16(2), 1406–1416 (2019) 27. H. Cao, S. Wu, Y. Hu, R. Mann, Y. Liu, L. Yang, H. Zhu, An efficient energy cost and mapping revenue strategy for inter-domain NFV-enabled networks. IEEE Internet Things J. 7(7), 5723– 5736 (2019) 28. H. Cao, Y. Zhu, G. Zheng, L. Yang, A novel optimal mapping algorithm with less computational complexity for virtual network embedding. IEEE Trans. Netw. Serv. Manag. 15(1), 356–371 (2018) 29. H. Cao, L. Yang, H. Zhu, Novel node-ranking approach and multiple topology attributes-based embedding algorithm for single-domain virtual network embedding. IEEE Internet Things J. 5(1), 108–120 (2018) 30. Z. Zhang, C. Xiang, S. Su, Y. Wang, L. Yan, A unified enhanced particle swarm optimizationbased virtual network embedding algorithm. Int. J. Commun. Syst. 26(8), 1054–1073 (2013) 31. W. Li, Q. Hua, J. Zhao, Y. Guo, Virtual network embedding with discrete particle swarm optimisation. Electron. Lett. 50(4), 285–286 (2014) 32. X. Mi, X. Chang, J. Liu, L. Sun, B. Xing, Embedding virtual infrastructure based on genetic algorithm, in International Conference on Parallel and Distributed Computing, Applications and Technologies (2012) 33. L. Yang, H. Yao, J. Wang, C. Jiang, A. Benslimane, Y. Liu, Multi-UAV-enabled load-balance mobile-edge computing for IoT networks. IEEE Internet Things J. 7(8), 6898–6908 (2020) 34. H. Yao, X. Yuan, P. Zhang, J. Wang, C. Jiang, M. Guizani, A machine learning approach of load balance routing to support next-generation wireless networks, in 2019 15th International Wireless Communications & Mobile Computing Conference (IWCMC) (2019), pp. 1317–1322 35. H. Zhang, C. Jiang, Z. Feng, Z. Zhang, V.C. Leung, 5g technologies for future wireless networks. Mobile Netw. Appl. 23(6), 1459–1461 (2018) 36. I. Pathak, D.P. Vidyarthi, A model for virtual network embedding across multiple infrastructure providers using genetic algorithm. Sci. China Inform. Sci. 60(4), 040308 (2017) 37. L. Zhuang, G. Wang, M. Wang, K. Zhang, A virtual network embedding algorithm based on cellular automata genetic mechanism. MATEC Web Conf. 232(4), 01019 (2018)

References

325

38. C. Jiang, Y. Chen, K.J. Liu, Ray, Y. Ren, Renewal-theoretical dynamic spectrum access in cognitive radio network with unknown primary behavior. IEEE J. Sel. Areas Commun. 31(3), 406–416 (2013) 39. J. Cai, X. Nian, H. Gu, L. Zhang, A user priority-based virtual network embedding model and its implementation, in IEEE International Conference on Electronics Information & Emergency Communication (2013) 40. B. Zhou, G. Wen, S. Zhao, X. Lu, D. Zhong, C. Wu, Y. Qiang, Virtual network mapping for multi-domain data plane in Software-Defined Networks, in International Conference on Wireless Communications (2014) 41. C. Jiang, Y. Chen, Y. Gao, K.J.R. Liu, Joint spectrum sensing and access evolutionary game in cognitive radio networks. IEEE Trans. Wirel. Commun. 12(5), 2470–2483 (2013) 42. M. Dorigo, C. Blum, Ant colony optimization theory: a survey. Theor. Comput. Sci. 344(2–3), 243–278 (2005) 43. G. Shang, X. Jiang, K. Tang, Hybrid algorithm combining ant colony optimization algorithm with genetic algorithm, in 2007 Chinese Control Conference (2007), pp. 701–704 44. M.G. Lee, K.M. Yu, Dynamic path planning based on an improved ant colony optimization with genetic algorithm, in 2018 IEEE Asia-Pacific Conference on Antennas and Propagation (APCAP) (2018), pp. 1–2 45. Y.I. Wei, J.W. Wang, H.B. Pan, L.I. Li, Ant colony chaos genetic algorithm for mapping task graphs to a network on chip. Acta Electron. Sin. 39(8), 1832–1836 (2011) 46. E.W. Zegura, K.L. Calvert, S. Bhattacharjee, How to model an Internet work. IEEE Infocom 2, 594–602 (1996) 47. C. Jiang, H. Zhang, Y. Ren, H.-H. Chen, Energy-efficient non-cooperative cognitive radio networks: micro, meso, and macro views. IEEE Commun. Mag. 52(7), 14–20 (2014) 48. C. Jiang, Y. Chen, K.R. Liu, Y. Ren, Network economics in cognitive networks. IEEE Commun. Mag. 53(5), 75–81 (2015) 49. N. Raveendran, Y. Gu, C. Jiang, N. Tran, M. Pan, L. Song, Z. Han, Cyclic three-sided matching game inspired wireless network virtualization. IEEE Trans. Mobile Comput. 20(2), 416–428 (2021) 50. C. Jiang, H. Zhang, Y. Ren, Z. Han, K. Chen, L. Hanzo, Machine learning paradigms for nextgeneration wireless networks. IEEE Wirel. Commun. 24(2), 98–105 (2017) 51. H. Yao, X. Chen, M. Li, P. Zhang, L. Wang, A novel reinforcement learning algorithm for virtual network embedding. Neurocomputing 284, 1–9 (2018)

Chapter 19

Virtual Network Embedding Based on Computing, Network, and Storage Resource Constraints

Abstract NV can offer more flexibility and better maintainability for the current Internet through allowing multiple heterogeneous virtual networks to share the network resource of a common infrastructure provider (InP). The main challenge in this respect is the efficient embedding of the virtual nodes and virtual links from the VNRs onto the limited substrate network resources. The notion that storage resource can exchange bandwidth resource to some extent gives us a hint that the efficient utilization of storage resource can relieve the bandwidth resource consumption. The existing VNE model does not consider the storage resource constraints on substrate nodes and virtual nodes and does not keep up with the need of actual situation. In this chapter, we propose a novel VNE model based on three-dimensional resource constraints including computing, network, and storage and devise two heuristic algorithms as the baseline algorithms to deal with the VNE problem. To our best of our knowledge, this is the first time to propose VNE problem based on threedimensional resources including computing, network, and storage.

19.1 Introduction With the development of NV, VNE technique is considered to be one of the most promising techniques to overcome the ossification of the current Internet architecture. Over the past decades, there are several of VNE algorithms to be proposed. These VNE algorithms can roughly be divided into three categories according to their optimization strategies, including heuristic algorithms, metaheuristic algorithms, and accurate algorithms. The most representatives of the heuristic algorithms are node importance ranking based algorithm [2], multiple priority classes based algorithm [3], path splitting and migration based algorithm [4], learning and inference for VNE [5], energy-aware VNE [6], topology-aware VNE [7–11], and multiple attribute node ranking based algorithm [12]. These algorithms mainly employ the node importance ranking methods to evaluate the

© [2018] IEEE. Reprinted, with permission, from Ref. [1] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Jiang, P. Zhang, QoS-Aware Virtual Network Embedding, https://doi.org/10.1007/978-981-16-5221-9_19

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importance of the substrate nodes and virtual nodes to finish the node mapping stage and use the K-shortest path algorithm to perform the link mapping stage. The meta-heuristic algorithms include ant colony optimization algorithms [13], PSO algorithms [14–17], and memetic algorithms [18, 19]. The accurate algorithms mainly utilize extra optimization tools such as GLPK [20] and CPLEX [21] to solve the integer linear programming (ILP) problems, and the most representatives of these algorithms are coordinated node and link mapping algorithm [22], virtual network assignment with reconfiguration and without reconfiguration [23], optimal VNE [24, 25], and optimal VNE based dynamic threshold [26]. However, the existing VNE model cannot adapt to the actual situation where the storage resource of substrate nodes and virtual nodes must be taken into account, due to the fact that storage resource can exchange bandwidth resource to some extent. In this chapter, we introduce the storage resource constraint on the substrate nodes and virtual nodes by modifying the existing VNE model. The modified VNE model takes into consideration the three-dimensional resources including computing, network, and storage. Specifically, we consider the CPU capacity and storage capacity constraints on substrate nodes and virtual nodes and consider the bandwidth resource constraints on substrate links and virtual links. This work for the first time tries to formulate the VNE problem based on these three-dimensional resources that can meet the actual needs of VNRs. We summarize the major contributions of this chapter as follows. • We formulate a three-dimensional resource based VNE model that considers the CPU and storage capacity constraints on nodes and bandwidth resource constraints on links. To the best of our knowledge, this work for the first time strives to model the VNE problem in this manner based on computing, network, and storage resources. • We devise two VNE algorithms based on the greedy node mapping strategy. These two algorithms NRM-VNE and RCR-VNE can be considered to be two baseline heuristic algorithms with regard to the three-dimensional resource based VNE problem. • We conduct a thorough comparison between two proposed algorithms in terms of the long-term average revenue, VNR acceptance ratio, and revenue to cost ratio and discuss the simulation results from different perspectives. The remainder of this chapter is organized as follows. In Sect. 19.2, we describe the network model and problem statement. Section 19.3 presents the Mixed Integer Programming formulation based on computing, network, and storage. We introduce the heuristic algorithm design in Sect. 19.4. We give the experimental results and analysis in Sect. 19.5 and conclude this chapter in Sect. 19.6.

19.2 Network Model and Problem Statement

329

19.2 Network Model and Problem Statement 19.2.1 Substrate Network We model the substrate network as a weighted undirected graph and denote it E by Gs = {Ns , Es , AN s , As }, where Ns represents the set of substrate nodes in substrate network, Es represents the set of substrate links in substrate network, AN s denotes the attribute set of the substrate nodes ns ∈ Ns including the CPU capacity CP U (ns ) and storage capacity ST (ns ), and AE s denotes the attribute set of the substrate links es ∈ Es referring to the bandwidth capacity BW (es ). As depicted in Fig. 19.1, the right side of Fig. 19.1 is a substrate network. The numbers in the left part of the box denote the total CPU capacity and the remaining CPU capacity, respectively. The numbers in the right part of the box denote the total storage capacity and the remaining storage capacity, respectively. The numbers aside the links denote the total bandwidth resource and the remaining bandwidth resource, respectively. We denote the set of all the substrate paths by Ps and the set of the substrate paths from s ∈ Ns to t ∈ Ns by Ps (s, t).

19.2.2 Virtual Network We model each VNR as a weighted undirected graph and denote it by Gv = E {Nv , Ev , AN v , Av }, where Nv represents the set of virtual nodes in VNRs, Ev represents the set of virtual links in VNRs, AN v denotes the attribute set of the virtual nodes nv ∈ Nv including the required CPU capacity CP U (nv ) and required storage capacity ST (nv ), and AE v denotes the attribute set of the virtual links ev ∈ Ev mainly referring to the required bandwidth capacity BW (ev ).

Fig. 19.1 An example of a virtual network and a substrate network

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The left side of Fig. 19.1 shows a VNR. In Fig. 19.1, the numbers in the boxes aside the virtual nodes denote the required CPU and storage resources, respectively. The numbers across the links denote the required bandwidth resources for the virtual links.

19.2.3 The Metric of Substrate Network Resource The residual or the available CPU capacity and storage capacity of a substrate node ns can be defined as the available CPU capacity and storage capacity of the substrate node ns ∈ Ns , respectively. N RCP U (ns ) = CP U (ns ) −



CP U (nv ),

(19.1)

∀nv ↑ns N RST (ns ) = ST (ns ) −



ST (nv ),

(19.2)

∀nv ↑ns

where CP U (ns ) denotes the total amount of CPU capacity of substrate node ns , ST (ns ) denotes the total amount of storage capacity of substrate node ns , CP U (nv ) denotes the required amount of CPU capacity of virtual node nv , ST (nv ) denotes N N the required amount of storage capacity of virtual node nv , RCP U (ns ), and RST (ns ) denotes the residual amount of CPU and storage capacity of substrate node ns , respectively. The notation nv ↑ ns means that the virtual node nv is mapped onto the substrate node ns . Likewise, the residual bandwidth capacity of a substrate link es can be defined as the total amount of the available bandwidth capacity on the substrate link es ∈ Es . E (es ) = BW (es ) − RBW



BW (ev ),

(19.3)

∀ev ↑es

where BW (es ) denotes the total amount of bandwidth capacity of substrate link es , BW (ev ) denotes the required amount of bandwidth capacity of virtual link ev , and E (e ) denotes the residual amount of bandwidth capacity of substrate link e . RBW s s

19.2.4 Virtual Network Embedding Problem Upon the arrival of a VNR, the substrate network has to decide whether to accept the VNR or not. If the VNR is accepted, the substrate network must allocate the demanded network resource to the VNR including CPU and storage capacity on

19.2 Network Model and Problem Statement

331

substrate nodes and bandwidth capacity on substrate links. The allocated network resources are released upon the termination of the VNR. The VNE process can be partitioned into two major stages: Node Mapping For the same VNR, each virtual node can only be mapped onto a different substrate node, and the mapping function can be denoted by MN : NV → NS from the virtual nodes to the substrate nodes and subject to: N CP U (nv ) ≤ RCP U (MN (nv )).

(19.4)

N (MN (nv )). ST (nv ) ≤ RST

(19.5)

The two constraints Eqs. (19.4) and (19.5) ensure that the mapped substrate node MN (nv ) has the abundant substrate resources including CPU computing resource and storage resource so as to satisfy the resource requirements of virtual node nv . Link Mapping Each virtual link can be mapped onto a loop-free substrate path (unsplittable flow) or a set of substrate paths (splittable flow), and the two end substrate nodes of the substrate path correspond to the two end virtual nodes of the virtual link. We denote the mapping by ME : EV → ES from the virtual links to the substrate links and subject to: E (ME (ev )). BW (ev ) ≤ RBW

(19.6)

Equation (19.6) ensures that the mapped substrate link ME (ev ) has the abundant substrate resource mainly referring to bandwidth capacity in order to satisfy the required bandwidth of virtual link ev .

19.2.5 Objectives Our main goal in this chapter is to propose online VNE algorithms with the constraints of CPU and storage capacity on nodes and bandwidth capacity on links to maximize the revenue of InPs and minimize the embedding cost in the long run. Similar to the work [4, 23], we define the revenue of a VNR as follows: R(Gv ) =



{CP U (nv ) + ST (nv )} +

nv ∈Nv



BW (ev ).

(19.7)

ev ∈Ev

Accordingly, the cost of InPs accommodating a VNR can be defined as the total amount of substrate resources allocated to that virtual network. C(Gv ) =

 nv ∈Nv

{CP U (nv ) + ST (nv )} +

 ev ∈Ev

BW (ev ) × hops(ev ).

(19.8)

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19 Virtual Network Embedding Based on Computing, Network, and Storage. . .

From the InP’s perspective, the main goal of online VNE algorithm is to maximize the revenue of InPs and increase the resource utilization of substrate network by accommodating as more VNRs as possible or improving the revenue to cost ratio in the long run. We define three performance metrics to evaluate our proposed algorithms, including the long-term average revenue, revenue to cost ratio, and the VNR acceptance ratio. The long-term average revenue can be formulated as follows: T R = lim

t =0 R(Gv , t)

t →∞

T

.

(19.9)

The revenue to cost ratio can be expressed by T R(Gv , t) R/C = lim tT=0 . t →∞ t =0 C(Gv , t)

(19.10)

The VNR acceptance ratio can be defined by T V NRacc acceptance = lim tT=0 , t →∞ t =0 V NRarr

(19.11)

where V NRacc denotes the number of already accepted VNRs, and V NRarr denotes the number of arrived VNRs.

19.3 Mixed Integer Programming Formulation for VNE In this chapter, we formulate the MILP model with the aim of minimizing the embedding cost of InPs for accommodating these VNRs. Variables: fijuv : A binary variable, which has the value of 1 if the substrate path (i, j ) accommodates the virtual link (u, v); otherwise, it has the value of 0. xiu : A binary variable, which has the value of 1 if the virtual node u is mapped onto the substrate node i; otherwise, it has the value of 0. luv : A variable to represent the bandwidth of virtual link (u, v). Objective: minimize





(u,v)∈Ev (i,j )∈Es

fijuv × BW (luv ).

(19.12)

19.3 Mixed Integer Programming Formulation for VNE

333

Constraints: – Capacity Constraints: N ∀u ∈ Nv , ∀i ∈ Ns , xiu × CP U (u) ≤ RCP U (i).

(19.13)

N (i). ∀u ∈ Nv , ∀i ∈ Ns , xiu × ST (u) ≤ RST

(19.14)

E (eij ). ∀(i, j ) ∈ Es , ∀(u, v) ∈ Ev , fijuv × BW (euv ) ≤ RBW

(19.15)

– Flow Associated Constraints: ∀i ∈ Ns , ∀(u, v) ∈ Ev , 

fijuv −

(i,j )∈Es



fjuv i =

(j,i)∈Es

⎧ ⎪ ⎪ ⎨BW (euv )

−BW (euv ) ⎪ ⎪ ⎩0

xiu = 1, xiv = 1,

(19.16)

otherwise.

– Variable Constraints: 

∀i ∈ Ns ,

xiu = 1,

(19.17)

xiu = 1,

(19.18)

u∈Nv

∀u ∈ Nv ,

 i∈Ns

∀i ∈ Ns , ∀u ∈ Nv , xiu ∈ {0, 1},

(19.19)

∀(i, j ) ∈ Es , ∀(u, v) ∈ Ev , fijuv ∈ {0, 1}.

(19.20)

Remarks The objective function (19.12) of the MIP strives to minimize the embedding cost of InPs for accommodating the VNR. Since for a VNR, the required CPU and storage capacity are constant, the differences among different embedding solutions are their consumed bandwidth resource due to the fact that the number of hops for their link embedding solutions is different. Hence, in this chapter, we take into consideration the embedding cost of bandwidth resource. Equation (19.13) guarantees that the CPU capacity of substrate node i ∈ Ns can satisfy the required CPU capacity of virtual node u ∈ Nv ; Eq. (19.14) guarantees that the storage capacity of substrate node i ∈ Ns can satisfy the required storage capacity of virtual node u ∈ Nv ; Eq. (19.15) guarantees that the bandwidth resource of substrate node i ∈ Ns can satisfy the required bandwidth resource of virtual node u ∈ Nv . Equation (19.16) is the connectivity constraint. In the node mapping stage, virtual nodes u ∈ Nv and v ∈ Nv are mapped onto the substrate nodes i ∈ Ns and j ∈ Ns

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19 Virtual Network Embedding Based on Computing, Network, and Storage. . .

respectively, and then in subsequent link mapping stage, the virtual link (u, v) ∈ Ev is mapped onto the substrate link P (i, j ). In the source substrate node i ∈ Ns , the outflow amount has the value of 1, the inflow amount has the value of 0, and then (i,j )∈Es fijuv − (j,i)∈Es fjuv i = 1; in the destination substrate node j ∈ Ns , the outflow amount has the value of 0, the inflow amount has the value of 1, and then (i,j )∈Es fijuv − (j,i)∈Es fjuv nodes, both the i = −1; in the other substrate outflow amount and inflow amount have the value of 1, and then (i,j )∈Es fijuv − uv (j,i)∈Es fj i = 0. Equations (19.17) and (19.18) guarantee that a substrate node can only host a virtual node from the same VNR, and a virtual node can only be mapped onto a substrate node. Equations (19.19) and (19.20) ensure that fijuv and xiu are two binary variables.

19.4 Heuristic Algorithm Design Due to the fact that MILP problem is NP-hard, obtaining the optimal solution of VNE problem is NP-hard. The solutions to this problem can be divided into two categories: accurate algorithms and heuristic algorithms. The main drawback of the accurate algorithms is that the computation time cannot satisfy the actual need when the problem size is large. Therefore, we devise two heuristic approaches called NRM-VNE and RCR-VNE to deal with the VNE problem. In this subsection, we describe the details of our proposed algorithms.

19.4.1 Two Node Ranking Measurements Our proposed two algorithms are two-stage VNE algorithms, consist of node mapping phase and link mapping phase. Node mapping process can be achieved by choosing substrate nodes with sufficient CPU and storage capacity resources, and link mapping process can be performed by choosing substrate paths with sufficient bandwidth resources. We define the node ranking metric by multiplying the CPU and storage capacity of the node and bandwidth capacity of its adjacent links, which is similar to the literature [4]. The node ranking metric can be formulated as follows: NRM(n) = {CP U (n) + ST (n)} ×



BW (e),

(19.21)

e∈nbr(n)

where NRM(n) represents the node ranking metric for the node n. Our proposed NRM-VNE method adopts this measurement to choose the substrate node with the most sufficient substrate resources to perform the node mapping and uses shortest path algorithm [27] to perform the link mapping.

19.4 Heuristic Algorithm Design

335

In order to avoid the unbalanced consumption of CPU and storage resources, we define the resource consumption ratio between the CPU capacity and the storage capacity as follows: CP U RST (n) =

N RCP U (n) N (n) RST

.

(19.22)

CP U The resource consumption ratio of the node denoted by RST (n) can reflect the resource consumption of CPU and storage capacity, in order to balance the CPU load and the storage load of substrate nodes in substrate network to accept more VNRs; we choose the substrate node of which resource consumption ratio is closest to that of virtual node to contain the virtual node avoid of causing unbalanced resource consumption. Our proposed RCR-VNE method adopts this algorithm to perform the node mapping and uses the shortest path algorithm to perform the link mapping.

19.4.2 NRM-VNE Method NRM-VNE is a two-stage VNE algorithm. In the first node mapping phase, we first compute the node ranking metric for each substrate node and virtual node and then sort the substrate nodes and virtual nodes in non-increasing order according to their node ranking metric values. The detailed steps of the node mapping algorithm are shown in Algorithm 36. Algorithm 36 NRM-VNE node mapping algorithm Require: 1: The set of VNRs, V NR; 2: Ensure: 3: The node mapping results for each of VNRs; 4: Sort the virtual nodes by the node ranking metric defined in Eq. (19.21) in non-increasing order. 5: for all the unmapped virtual nodes in V NR do 6: choose the virtual node nv with the highest NRM(nv ); 7: Sort the substrate nodes by its node ranking metric NRM(ns ) and denote is by Ω; 8: for each ns in Ω do 9: if ns is not mapped and CP U (ns ) ≥ CP U (nv ) and ST (ns ) ≥ ST (nv ) then 10: MN (nv ) = ns ; 11: break; 12: end if 13: end for 14: end for

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19 Virtual Network Embedding Based on Computing, Network, and Storage. . .

In the second link mapping phase, NRM-VNE performs the link mapping using the shortest path algorithm to map the virtual links to the substrate paths. The link mapping stage is similar to the previous work [4]. The link mapping algorithm is detailed in Algorithm 37. Algorithm 37 NRM-VNE link mapping algorithm Require: 1: The set of virtual network requests, V NR; 2: The node mapping results for each of VNRs; 3: Ensure: 4: The link mapping results for each of VNRs; 5: Sort the virtual links by the required bandwidth in non-increasing order. 6: for all the unmapped virtual links in V NR do 7: choose the virtual link ev with the highest BW (ev ); 8: fetch two corresponding substrate nodes nsstart and nsend for the virtual link lv ; 9: remove all the substrate links whose bandwidth resource is lesser than the required amount of bandwidth resource; 10: choose a loop-free substrate path between nsstart and nsend using shortest path algorithm. 11: end for

19.4.3 RCR-VNE Method To address the issue of unbalanced CPU and storage resource allocation, we design another two-stage VNE algorithm called RCR-VNE. Distinguished from the first algorithm NRM-VNE, RCR-VNE adopts the closest resource consumption ratio strategy to choose the substrate node for virtual node aiming to reduce the unbalanced CPU and storage resource consumption. The node mapping process is shown in Algorithm 38. The link mapping process is illustrated in Algorithm 39.

19.5 Performance Evaluation In this section, we first describe the simulation environment setting parameters and then present our main performance evaluation results. Comparing our algorithms with prior research work is difficult because previous work does not consider the storage resource on the nodes; therefore, there is no compared algorithms since they do not start with the same problem. In this section, we give the simulation results of our proposed algorithms in order to consider them as two baseline algorithms aim at promoting the advancement in terms of VNE problem based on three-dimensional resource constraints.

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337

Algorithm 38 RCR-VNE node mapping algorithm Require: 1: The set of VNRs, V NR; 2: Ensure: 3: The node mapping results for each of VNRs; 4: Sort the virtual nodes by the node ranking metric defined in Eq. (19.21) in non-increasing order. 5: for all the unmapped virtual nodes in V NR do 6: choose the virtual node nv with the highest NRM(nv ); CP U (nv ) of the mapping virtual node 7: Sort the substrate nodes by the distance between RST nv and that of substrate nodes in decreasing order, and denote is by Ω; 8: for each ns in Ω do 9: if ns is not mapped and CP U (ns ) ≥ CP U (nv ) and ST (ns ) ≥ ST (nv ) then 10: MN (nv ) = ns ; 11: break; 12: end if 13: end for 14: end for

Algorithm 39 RCR-VNE link mapping algorithm Require: 1: The set of VNRs, V NR; 2: The node mapping results for each of VNRs; 3: Ensure: 4: The link mapping results for each of VNRs; 5: Sort the virtual links by the required bandwidth in non-increasing order. 6: for all the unmapped virtual links in V NR do 7: choose the virtual link ev with the highest BW (ev ); 8: fetch two corresponding substrate nodes nsstart and nsend for the virtual link lv ; 9: remove all the substrate links whose bandwidth resource is lesser than the required amount of bandwidth resource; 10: choose a loop-free substrate path between nsstart and nsend using shortest path algorithm. 11: end for

19.5.1 Simulation Environment Settings We have implemented a discrete event simulator based on the ViNE-Yard [28]. The topology of substrate network in our experiments is randomly generated with 50 nodes using the GT-ITM [29]; each pair of substrate nodes is connected with the probability of 0.5. The CPU, storage, and bandwidth resources of the substrate nodes and links are real numbers that are uniformly distributed between 50 and 100. We assume that the arrival of VNRs follows the Poisson distribution with an average rate of 4 virtual networks per 100-time units, and each VNR has a duration with an average of μ = 1000 time units, which follows exponential distribution.

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19 Virtual Network Embedding Based on Computing, Network, and Storage. . .

Fig. 19.2 The VNR acceptance ratio of our proposed two algorithms

19.5.2 Performance Evaluation Results VNR Acceptance Ratio Comparison The VNR acceptance ratio of our proposed two algorithms is illustrated in Fig. 19.2. From Fig. 19.2, we can observe that the overall VNR acceptance ratio of these two algorithms is comparable. The NRMVNE algorithm measures the node importance from the point of view of resource capacity including CPU, storage, and total adjacent bandwidth resources, while the RCR-VNE algorithm measures the node importance from the point of view of load balancing between CPU capacity and storage capacity. From the experimental results, we can see that the two algorithms almost have the same VNR acceptance ratio. The overall trend of these two algorithms is decreased with the running time goes by, due to the fact that the available substrate resources including CPU, storage, and bandwidth are diminishing with the running time goes by; thus the available substrate resources aiming to accept future VNRs are decreased; the VNR acceptance ratio is decreased. The Long-term Revenue to Cost Ratio Comparison The long-term revenue to cost ratio of our proposed two algorithms is illustrated in Fig. 19.3. We can observe that the overall performance of NRM-VNE algorithm is slightly better than that of RCR-VNE algorithm. Figure 19.3 demonstrates that the resource capacity measurement is slightly better than the load balancing measurement; the conclusion agrees with the people intuition. The Long-term Average Revenue Comparison Figure 19.4 represents the longterm average revenue of our proposed two algorithms. From Fig. 19.4, we can see that the overall trend of these two algorithms is decreased with the running time, due

19.5 Performance Evaluation

339

Fig. 19.3 The long-term revenue to cost ratio of our proposed two algorithms

Fig. 19.4 The long-term average revenue of our proposed two algorithms

to the substrate resources for accommodating incoming VNRs are reduced with the running time goes by. From the overall trend aspect, these two compared algorithms are almost comparable. The NRM-VNE algorithm is slightly better than the RCRVNE algorithm; the experimental results indicate the fact that the resource capacity measurement is slightly better than the load balancing measurement, which is in accord with the people intuition.

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19.6 Conclusions To make the VNE model satisfy the actual needs, we formulate a Mixed Integer Programming model for the VNE problem with three-dimensional resource constraints including computing, network, and storage resources. In this chapter, we proposed two heuristic algorithms NRM-VNE and RCR-VNE for VNE as two baseline algorithms and presented our simulation results in terms of the long-term average revenue, revenue to cost ratio, and VNR acceptance ratio. With the advancement of NV especially in cloud-based data center environments, the storage resource constraint on nodes is necessary to store or cache some information resources, e.g., deploying the stream media program close to users that needs the storage resource on substrate nodes. This chapter proposed two baseline VNE algorithms based on three-dimensional resource constraints including computing, network, and storage resources. The main goal of this chapter is to consider it as two baseline algorithms to make progress in VNE algorithms based on three-dimensional resource constraints. In our future work, we intend to devise some improved algorithms to deal with the VNE algorithms to further improve the resource utilization of substrate network. In addition, the unit price of computing resources is different from the unit price of storage resources, and then we will take the unit price of substrate resources into consideration when evaluating their node ranking values. Due to the fact that the separation of node mapping and link mapping would decrease the resource utilization of substrate network, we will devise a more coordinated one-stage VNE algorithm to address this issue and consider some factors in the node mapping stage with the purpose of facilitating the subsequent link mapping stage.

References 1. P. Zhang, H. Yao, Y. Liu, Virtual network embedding based on computing, network, and storage resource constraints. IEEE Internet Things J. 5(5), 3298–3304 (2018) 2. P. Zhang, H. Yao, Y. Liu, Virtual network embedding based on the degree and clustering coefficient information. IEEE Access 4, 8572–8580 (2016) 3. N. Ogino, T. Kitahara, S.I. Arakawa, M. Murata, Virtual network embedding with multiple priority classes sharing substrate resources. Comput. Netw. 112, 52–66 (2017) 4. M. Yu, Y. Yi, J. Rexford, M. Chiang, Rethinking virtual network embedding: substrate support for path splitting and migration. ACM SIGCOMM Comput. Commun. Rev. 38(2), 17–29 (2008) 5. J. Liao, M. Feng, S. Qing, T. Li, J. Wang, LIVE: learning and inference for virtual network embedding. J. Netw. Syst. Manag. 24(2), 227–256 (2016) 6. A. Beloglazov, J. Abawajy, R. Buyya, Energy-aware resource allocation heuristics for efficient management of data centers for cloud computing. Future Gener. Comput. Syst. 28(5), 755–768 (2012) 7. X. Cheng, S. Su, Z. Zhang, H. Wang, F. Yang, Y. Luo, J. Wang, Virtual network embedding through topology-aware node ranking. ACM SIGCOMM Comput. Commun. Rev. 41(2), 38– 47 (2011)

References

341

8. H. Zhang, C. Jiang, R.Q. Hu, Y. Qian, Self-organization in disaster-resilient heterogeneous small cell networks. IEEE Netw. 30(2), 116–121 (2016) 9. J. Wang, C. Jiang, K. Zhang, X. Hou, Y. Ren, Y. Qian, Distributed q-learning aided heterogeneous network association for energy-efficient IIoT. IEEE Trans. Ind. Inform. 16(4), 2756–2764 (2019) 10. H. Zhang, B. Wang, C. Jiang, K. Long, A. Nallanathan, V.C. Leung, H.V. Poor, Energy efficient dynamic resource optimization in NOMA system. IEEE Trans. Wirel. Commun. 17(9), 5671– 5683 (2018) 11. R. Zhang, X. Jing, S. Wu, C. Jiang, J. Mu, F.R. Yu, Device-free wireless sensing for human detection: the deep learning perspective. IEEE Internet Things J. 8(4), 2517–2539 (2021) 12. S. Gong, J. Chen, S. Zhao, Q. Zhu, Virtual network embedding with multi-attribute node ranking based on TOPSIS, in KSII Transactions on Internet & Information Systems (2016), p. 10 13. F. Zhu, H. Wang, A modified ACO algorithm for virtual network embedding based on graph decomposition,. Comput. Commun. 80, 1–15 (2015) 14. Z. Zhang, C. Xiang, S. Su, Y. Wang, L. Yan, A unified enhanced particle swarm optimizationbased virtual network embedding algorithm. Int. J. Commun. Syst. 26(8), 1054–1073 (2013) 15. H.U. Ying, L. Zhuang, J. Lan, M.A. Ding, Energy aware virtual network embedding using particle swarm optimization algorithm based on adaptive cooperative coevolution. J. Electron. Inform. Technol. 38(10), 2667–2673 (2016) 16. C. Wang, Y. Su, L. Zhou, S. Peng, Y. Yuan, H. Huang, A virtual network embedding algorithm based on hybrid particle swarm optimization (2016) 17. P. Zhang, H. Yao, C. Fang, Y. Liu, Multi-objective enhanced particle swarm optimization in virtual network embedding. EURASIP J. Wirel. Commun. Netw. 2016(1), 167 (2016) 18. A.A. Shahin, Memetic multi-objective particle swarm optimization-based energy-aware virtual network embedding. Int. J. Adv. Comput. Sci. Appl. 6(4) (2015) 19. J. Infhr, G. Raidl, A memetic algorithm for the virtual network mapping problem. J. Heuristics 22(4), 475–505 (2016) 20. GLPK, GNU linear programming kit (2008). http://www.org/software/glpk 21. Inc. ILOG, ILOG CPLEX: high-performance software for mathematical programming and optimization (2012). http://www.ilog.com/products/cplex/ 22. N.M.M.K. Chowdhury, M.R. Rahman, R. Boutaba, Virtual network embedding with coordinated node and link mapping, in Infocom (2009) 23. Z. Yong, M.H. Ammar, Algorithms for assigning substrate network resources to virtual network components, in Infocom IEEE International Conference on Computer Communications (2006) 24. M. Melo, S. Sargento, U. Killat, A. Timm-Giel, J. Carapinha, Optimal virtual network embedding: node-link formulation. IEEE Trans. Netw. Serv. Manag. 10(4), 1–13 (2013) 25. M. Melo, Rcio, S. Sargento, U. Killat, A. Timm-Giel, J. Carapinha, Optimal virtual network embedding. Comput. Netw. Int. J. Comput. Telecommun. Netw. 91(C), 184–195 (2015) 26. I. Pathak, D.P. Vidyarthi, An optimal virtual network mapping model based on dynamic threshold. Wirel. Pers. Commun. 3, 1–21 (2015) 27. D. Eppstein, Finding the k shortest paths, in Symposium on Foundations of Computer Science (1994), pp. 154–165 28. N.M. Mosharaf Kabir Chowdhury, ViNE-Yard. http://www.mosharaf.com/ViNE-Yard.tar.gz 29. E.W. Zegura, K.L. Calvert, S. Bhattacharjee, How to model an Internet work. IEEE Infocom 2, 594–602 (1996)

Chapter 20

Virtual Network Embedding Using Node Multiple Metrics Based on Simplified ELECTRE Method

Abstract The concept of NV has attracted significant attention from academia to industry. One of the key challenges in NV is resource allocation problem that is also termed as VNE problem. It involved mapping virtual networks onto a substrate network by adhering to some constraints such as CPU capacity on the nodes and bandwidth resource on the links. However, prior heuristic VNE algorithms mostly concentrate on measuring the embedding potential of substrate nodes using the multiplication of different nodes’ resource metrics. Due to the fact that different resource metrics have different impacts on the node ranking, these traditional methods have some limitations that would cause unbalanced embedding problems. Furthermore, the number of hops for the substrate paths that virtual links are mapped onto will have a large impact on the resource utilization of substrate links in substrate network. In this chapter, based on the topology analysis of six situations, we first propose a novel five-node ranking metric to quantify the importance of substrate nodes. Then we give a comprehensive measurement method for substrate nodes using the simplified ELECTRE method to avoid an unbalanced embedding solution. We present a novel two-stage VNE algorithm that chooses the substrate nodes with the maximum embedding potential to perform the node mapping procedure and uses the shortest path algorithm to accomplish the link mapping procedure. Extensive simulation results demonstrated that our proposed method behaves better than the other state-of-the-art algorithms in terms of the longterm average revenue, the revenue to cost ratio, and the VNR acceptance ratio.

20.1 Introduction Over the past decades, the current Internet has achieved great success. However, due to the coexistence of multiple Internet service providers (ISPs) with the contradictory purposes and strategies, the deployment and installation of new Internet services and protocols on the current Internet architecture are increasingly more

© [2018] IEEE. Reprinted, with permission, from ref. [1]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Jiang, P. Zhang, QoS-Aware Virtual Network Embedding, https://doi.org/10.1007/978-981-16-5221-9_20

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and more difficult, which is called as Internet ossification. To fend off the Internet ossification and satisfy the demands of the increasing number of diverse applications with various QoS requirements, VNE has been propounded as a building block for the future Internet architecture, which has exerted a tremendous fascination on many researchers. In the NV environments, traditional ISPs are separated into infrastructure providers (InPs) and service providers (SPs). InPs are in charge of maintaining substrate network infrastructures, while SPs perform the role of providing the customized end-to-end network services. Specifically, SPs create heterogeneous virtual networks through aggregating distributed or centralized resources from multiple InPs with an aim to provide diverse services. VNE is a process that maps the VNRs onto the substrate network infrastructures with the constraints of CPU capacity on nodes and bandwidth resource on links. Due to the constraints of nodes and links, the VNE problem is proved to be an NP-hard problem. Due to its considerable runtime when in medium-size or large-size substrate network, a variety of heuristic algorithms have been proposed to address this issue, with the aim of finding the practical embedding solutions [2–4]. The VNE problem typically consists of two stages: (1) node mapping stage where virtual nodes from VNRs are mapped onto substrate nodes meanwhile satisfying the constraints such as CPU capacity on nodes; (2) link mapping stage where virtual links connecting to these virtual nodes are mapped onto the substrate paths meanwhile satisfying the constraints such as bandwidth demand on links. Prior works mainly concentrate on the greedy node mapping algorithms with the aim of giving priority to these substrate nodes with more embedding potential. However, these traditional VNE algorithms measure the node importance simply by the product of their CPU capacity and the total amount of bandwidth resources for their directly connected links [5]. Some heuristic methods incorporate the topological attributes of the substrate network into the node importance ranking process. The aim of these methods is to give embedding priority to the substrate node with the biggest embedding potential [6–9]. This would lead to the imbalance problem of these metrics and decrease the resource utilization of substrate network. ELECTRE is a family of multi-criteria decision analysis methods originated in Europe in the mid-1960s. The simplified ELECTRE method can increase the computation efficiency and reduce the order complexity, without compromising the algorithm performance. Therefore, we adopt the simplified ELECTRE method to choose the most appropriate substrate node for virtual node in our node mapping process. The main contributions and our main ideas are summarized as follows: 1. We define five metrics of node ranking using multiple attributes of substrate nodes in the substrate network. These five metrics can reflect the different aspects of substrate nodes in the substrate network and facilitate the node mapping procedure from different perspectives. 2. Based on the simplified ELECTRE method, we devise a two-stage VNE algorithm, which is called ELECTRE-VNE, with multiple metrics of node ranking.

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In the stage of node mapping, based on simplified ELECTRE method, we use multiple node importance ranking metrics to address the issue of the imbalance problem on different evaluation metrics. In the stage of link mapping, we employ the shortest path algorithm to perform the link mapping procedure. 3. Extensive simulations demonstrated that our method is better than the other traditional methods in terms of the long-term average revenue, the revenue to cost ratio, and the VNR acceptance ratio. The remainder of this chapter is organized as follows. Section 20.2 reviews the existing methods for VNE. Section 20.3 introduces the network model and problem statement. In Sect. 20.4, based on the multiple attributes of substrate nodes in the substrate network, we present the multiple metrics of node ranking. In Sect. 20.5, we describe our proposed method ELECTRE-VNE in detail. The performance of our method and other methods is evaluated in Sect. 20.6. Section 20.7 concludes this chapter.

20.2 Related Works Due to the constraints of nodes and links, the VNE problem is an NP-hard problem even when the topologies of VNRs are known in advance. In the literature [10], the authors presented a survey of current studies in the VNE area and introduced a VNE taxonomy. Based on whether the topologies of VNRs are known or not in advance, the VNE algorithms can be classified into two categories. One is the online VNE algorithms, and the other is the offline VNE algorithms. Due to the fact that knowing all the VNRs in advance is not practical in the real situation, most of researchers advocate the online VNE algorithms. Given that the VNE problem is NP-hard [11], existing approaches can be roughly divided into three categories: (i) the optimal algorithms based on solving the integer linear programming (ILP) formulation; (ii) the heuristic algorithms based on various node resource estimation methods; and (iii) the meta-heuristic algorithms based on PSO or memetic algorithms. In this section, we will review some prior studies in terms of these three aspects.

20.2.1 Optimal Algorithms The most typical optimal algorithm is a VNE algorithm based on subgraph isomorphism detection [12]. The authors embedded nodes and links during the same stage. In the same year, the authors of [13] addressed the VN embedding problem with the aim of coordinating two mapping stages including node mapping and link mapping. They constructed an augmented substrate graph based on the node location constraints and formulated the VN embedding problem as a MILP problem. The authors designed two VN embedding algorithms D-ViNE and R-

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ViNE using deterministic and randomized techniques, respectively. The authors in [14] presented a compact path-based integer linear programming model to tackle with the VNE problem. Additionally, they proposed a branch-and-price framework that embeds a column generation process to address the formulated model. The simulation results demonstrated that the proposed framework can lead to the optimal or near optimal solution. However, this type of algorithms can only deal with the small size of topology for the substrate network and virtual networks due to its exponentially increasing computation time. The studies in [15] formulated an integer linear programming model to address the online VNE issue with the purpose of minimizing the resource consumption and balancing the network load. The authors in [15] presented three cost functions striving for the minimization of resource consumption and load balancing. Experimental results indicated that the Weighted Shortest Distance Path (WSDP) was the one considered to be the optimal cost function. The work in [16] formulated an integer programming model to deal with the energy-aware VNE for the purpose of coordinating node mapping and link mapping. The authors proposed two different objective functions to address the resource consumption and energy consumption, respectively. The classical and exact VNE algorithm was proposed by the work in [17], where the authors utilized the max-flow/min-cut approach to address the two InPs cases and then extended them to multiple InPs cases. In their work, the authors employed the branch and bound algorithm, so as to solve the MIP program to provide the exact VNE solution with simultaneous mappings of nodes and links. Due to its considerable runtime when in medium-size or large-size substrate networks, our work mainly concentrates on the uncoordinated VNE heuristic algorithm to address the VNE problem. Therefore, we do not make a comparison with these exact or optimal algorithms [13, 17, 18]. Instead, we will address these issues in our future work.

20.2.2 Heuristic Algorithms Due to the fact that the optimal VNE algorithms would consume a large amount of computation time, some works on VNE mainly focus on the heuristic algorithms that consider the local resources of the nodes or the topological information of the substrate network more or less. The most classical heuristic VNE algorithm is Greedy-VNE proposed in [19]. The authors used the local resources of nodes to measure the node importance and employed the shortest path algorithm to perform the link mapping. Subsequently, inspired by the PageRank theory, Cheng et al. [20] presented a novel node ranking method using Markov random walk (RW) to improve the node ranking method. The authors devised two VN embedding algorithms, which were called RW-MaxMatch and RW-BFS. Extensive experimental results demonstrated that the topology-aware node ranking method was better than the classical resource evaluation method. The work in [7] exploited the topological information of substrate network and virtual networks and introduced the network

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centrality analysis and the closeness analysis into the VNE process, by proposing two embedding algorithms to deal with the node ranking problem of substrate nodes. The improved closeness algorithm can dynamically measure the importance of substrate nodes in the substrate network and can increase the revenue of InPs in the long run. The authors of [21] modified and improved the exact existing energyaware VNE algorithms where the objective is to power off as many network nodes and interfaces as possible by consolidating the virtual networks into a subset of active physical networking equipment. The authors of [22] presented an efficient online VNE algorithm, formulated a new multiple objective linear programming optimization problem, and divided it into two stages including node mapping and link mapping. The authors of [22] used Blocking Island (BI) to address the efficient resource allocation problem. The main aim of the proposed method Presto was to maximize the revenue of InPs and minimize the embedding cost of the VNRs. The authors of [23] defined an optimization strategy using path algebra method to address the linear or nonlinear parameters of substrate nodes and links in substrate network and proposed two novel algorithms called NPA and I-NPA to deal with the VNE problem in a coordinated node and link mapping manner. Our work is similar to one in [24], the major difference is that our method presents five metrics of node importance estimation based on the topology analyses of the substrate network, and these metrics are different from those in the work [24]. In addition, we use the simplified ELECTRE method to calculate the node ranking values of substrate nodes in the substrate network, whose computation complexity is lower than the TOPSIS based on the computation time complexity analysis. Different from [25], where the authors mainly used the product of multiple metrics of substrate nodes in the substrate network to estimate the node importance, thereby determining the embedding sequences of substrate nodes, our work takes use of multiple metrics of node importance estimation to give each substrate node a comprehensive estimation value using simplified ELECTRE method; hence, they are essentially different.

20.2.3 Meta-Heuristic Algorithms As the optimal solution for large instances is difficult to find [26], meta-heuristics such as simulated annealing [27], genetic algorithm [28], ant colony optimization [29], or PSO [3] can be used to find near optimal solutions by iteratively improving a candidate solution. The authors of [30] employed ant colony optimization metaheuristic algorithm to deal with the VNE problem with the aim of minimizing the rejection rate of requests and maximizing returns for the substrate network provider. Zhang et al. [3] presented a unified enhanced PSO method to address the VNE issue aiming to increase the acceptance ratio of VNs and the revenue of InPs by optimizing VNE costs. The authors of [31] utilized multi-objective enhanced PSO method to minimize the energy consumption of the substrate network by

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consolidating the major load into the small number of active substrate nodes and links. The authors of [32] introduced the memetic algorithm into the VNE problem and studied the influence of diverse kinds of hybrid techniques on the VNE problem. The advantage of these meta-heuristic algorithms is that it leverages the PSO algorithm to improve a candidate solution. However, the weakness of these algorithms is that it would consume a large amount of running times. This type of algorithm is a tradeoff between exact VNE algorithms and heuristic VNE algorithms. Our work only focuses on the heuristic VNE algorithm; therefore, the comparison with these algorithms is beyond our research work. We intend to do this work in our future work.

20.3 Network Model and Problem Statement 20.3.1 Substrate Network Model We model the substrate network as a weighted undirected graph and denote it by Gs = {N s , Ls }, therein, N s and Ls represent the set of substrate nodes and the set of substrate links, respectively. Each substrate node ns ∈ N s is characterized by its functional or non-functional attributes such as CPU capacity, storage capacity, and geographic location. Each substrate link ls ∈ Ls is characterized by its communication capacity such as bandwidth capacity. For each substrate link ls (i, j ) ∈ Ls , therein, i and j represent the two ends of the substrate link ls (i, j ), and we use BW (ls ) to denote the total amount of the available bandwidth resources. We denote the set of all the substrate paths by Ps and denote the set of substrate paths from the source node s to destination node t by Ps (s, t). The left part of Fig. 20.1 illustrates a substrate network. The numbers over the links represent the total bandwidth resources and the residual bandwidth resources separating by a vertical line. The numbers aside the nodes represent the total

Fig. 20.1 The diagram of substrate network and a virtual network request

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CPU capacity in the first rectangular box and residual CPU capacity in the second rectangular box.

20.3.2 Virtual Network Model Similarly, a virtual network can also be modeled as a weighted undirected graph and denoted by Gv = {N v , Lv }, therein, N v and Lv represent the set of virtual nodes and the set of virtual links in each VNR, respectively. For a virtual node nv ∈ N v , its computing demand can be expressed by CP U (nv ). For a virtual link lv ∈ Lv , its required bandwidth resource can be expressed by BW (lv ). A VNR that consists of three virtual nodes and three virtual links is illustrated in the right part of Fig. 20.1. The number in the rectangular box aside the node represents the demanded CPU capacity of the node, and the number over the link represents the required bandwidth resource of the link.

20.3.3 Virtual Network Embedding Problem Description 

The VNE problem can be modeled as a mapping M : Gv {N v , Lv } → Gs {N s , Ps }  from Gv to a subset of Gs , therein, N s ⊂ N s . The mapping process is typically decomposed of two mapping steps: (i) node mapping stage that assigns the virtual nodes to the heterogeneous substrate nodes meanwhile satisfying the resource constraints on the nodes and (ii) link mapping stage that assigns the virtual links to a loop-free substrate paths on the substrate links meanwhile satisfying the resource constraints on the links. The left part of Fig. 20.1 indicates a VNE solution for a VNR that is depicted in the right part of Fig. 20.1. The mapping solution can be represented by node mapping solution {a → E, b → D, c → C} and link mapping solution {Pv (a, b) → Ps (E, D), Pv (b, c) → Ps (D, C), Pv (a, c) → Ps (E − B − C)}.

20.3.4 Objectives The main goal of VNE is how to make efficient use of the limited substrate network resources to accommodate as many VNRs as possible so as to obtain more revenue from the InPs’ point of view. Generally, there are three main objectives to measure the performance of VNE algorithms, i.e., the long-term average revenue, the longterm revenue to cost ratio, and the VN request acceptance ratio. Similar to the previous studies [18, 19], for the InPs, the obtained revenue of accepting a VNR

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at time t can be defined as the total amount of network resources that VN request required, which can be formulated as follows: R(Gv , t) =





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(20.1)

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(20.5)

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(20.6)

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the resource utilization of substrate network in the long run. If the long-term average revenue of the VNE algorithms is almost the same, we make use of the long-term revenue to cost ratio to quantify the efficiency of resource utilization of substrate network. In addition to these above two metrics of the algorithms, we can also use the VNR acceptance ratio to distinguish the compared methods.

20.4 The Evaluation Metrics of Node Ranking Based on Multiple Attributes 20.4.1 Motivations In the node mapping stage, most of the heuristic algorithms are based on the resource evaluation metric of node ranking to give mapping priority to the substrate nodes with the larger metric values. Several greedy node mapping methods measure the embedding potential for each substrate node aiming to determine the mapping sequence of the substrate nodes. Therefore, the evaluation metric of node ranking has a significant influence on the performance of VNE algorithms. The authors of [19] proposed a classical evaluation metric of node ranking that measures the node resource availability by the product of the node CPU capacity and the total amount of the available bandwidth resources of its outgoing links. The evaluation metric of node ranking can be formulated as Eq. (20.7), and most of the VNE methods utilize the same node ranking method to perform the node mapping procedure. H (n) = CP U (n) ×



BW (l),

(20.7)

l∈neighbor(n)

where H (n) represents the resource evaluation metric of node ranking for the node n, CP U (n) represents the CPU capacity of the node n, BW (l) represents the available bandwidth resource of the link l, and neighbor(n) represents the set of links that directly connect to the node n. However, this evaluation metric of node ranking has the following drawbacks. First, it only takes the local resource metrics of the nodes into consideration while ignoring the resource metrics of their neighborhood nodes, which may lead to the mapping failure during the subsequent link mapping process. For example, as illustrated in Fig. 20.2, where the numbers in the rectangular boxes next to the nodes represent the CPU capacity of the nodes and the numbers over the lines represent the available bandwidth resources of the links. As demonstrated in Fig. 20.2, the evaluation metric of node B is calculated as H (B) = 30 ∗ (40 + 40 + 40) = 3600, and the evaluation metric of node F is calculated as H (F ) = 30 ∗ (40 + 40 + 40) = 3600; hence, the node B and node F have the same resource evaluation metric of node ranking measured by Eq. (20.7). Nevertheless, the selection of substrate node F could have more opportunity to obtain the success of subsequent link mapping

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procedure, due to the fact that the CPU capacity of its neighborhood nodes for node F is more than the corresponding CPU capacity of its neighborhood nodes for node B. Therefore, we assume that the embedding potential of node F is more than that of node B. Second, as illustrated in Fig. 20.3, we suppose that the CPU capacity of neighborhood nodes for node B is the same as node F , but the node D has less bandwidth resources than the node H . Apparently, mapping a virtual node onto the node F is better than mapping it onto the node B since the node H has more local resources than the node D in terms of its bandwidth resources. Third, the aforementioned evaluation metric of node ranking ignores the bandwidth resource constraints on the links and will be prone to cause the failure of the subsequent link mapping procedure. As demonstrated in Fig. 20.4, a VNR is shown in the left side of Fig. 20.4, provided that the virtual node a is already mapped onto the substrate node A, the substrate nodes B and E are two nodes with the second largest evaluation metric of node ranking, both of their evaluation metric values are 1800, i.e., H (B) = 30∗(20+20+20) = 1800, H (E) = 60∗(10+10+10) = 1800, and if we map the virtual node b onto the substrate E, the subsequent link mapping

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will fail due to the fact that the available bandwidth resources of substrate path denoted by Ps (A, E) are lesser than the required bandwidth resources of the virtual link denoted by lv (a, b). Hence, not only the CPU capacity of the node and the amount of available bandwidth resources of its outgoing links should be taken into consideration, but also the minimum bandwidth requirement of virtual link that connects the already mapped virtual node and the mapping virtual node should be emphasized. Fourth, the classical evaluation metric of node ranking only considers the local resources of the nodes while regardless of the topological attribute influence of the substrate network, which cannot give each node a comprehensive metric value. As illustrated in Fig. 20.5, in addition to the resource evaluation metrics of its neighborhood nodes and its required bandwidth resources, the node degree should also be taken into consideration. For instance, the substrate nodes B and F have the same evaluation metric values based on the above two metrics, but the degree of substrate node B is degree(B) = 3, the degree of substrate node F is degree(F ) = 4, and it means that mapping the virtual node onto the substrate node F has more opportunity to obtain the success during the subsequent node mapping and link mapping process. Therefore, with the purpose of improving the performance of VNE algorithm, the degree of substrate nodes should also be incorporated into the evaluation metric computation process.

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Fifth, for each solution of VNR, the allocated CPU capacity over the substrate nodes for virtual nodes is constant, and the difference between two mapping solutions is the allocated bandwidth resource over the substrate paths for virtual links from each VNR. To achieve a higher resource utilization of the substrate network aiming at accommodating more VNRs, and thereby improving the profitability of the InPs, we should map the two adjacent virtual nodes onto the two substrate nodes that are not far away from each other so as to reduce the unnecessary bandwidth consumption of substrate links and decrease the resource fragmentation of the substrate network. As illustrated in Fig. 20.6, the node mapping sequences of virtual nodes and substrate nodes computed by Eq. (20.7) in the virtual network and substrate network are nva > nvb and nsC > nsA > nsG > nsF > nsE > nsD > nsB , respectively. Based on the greedy node mapping strategy, the node mapping result is MN (nva ) = nsC , MN (nvb ) = nsA , therein, MN () represents the node mapping function. When the virtual node nva has been mapped onto the substrate node nsC , the next virtual node nvb will be mapped onto the substrate node nsA because the substrate node nsA is the unmapped substrate node with the largest node ranking value measured by Eq. (20.7). However, the substrate node nsG is the most appropriate candidate substrate node although it has a lower node ranking value than the substrate node nsA . Mapping the virtual node nvb onto the substrate node nsG will consume less bandwidth resource for virtual link lv (a, b) during the subsequent link mapping process. The prerequisite is that the substrate node nsG has enough CPU capacity resources to satisfy the computing demand of virtual node nvb . Therefore, the number of hops between the mapping substrate node and the set of already mapped substrate nodes has a significant effect on the resource utilization of substrate network and should be incorporated into the calculating resource evaluation metric of node ranking. Sixth, apart from these above-mentioned aspects that need to be considered in the node mapping stage, the CPU utilization ratio of the substrate node is crucial to the performance of VNE algorithm, as depicted in Fig. 20.7. Provided that we are mapping the virtual node nva , the substrate nodes nsB and nsE are two candidate substrate nodes that can be mapped onto, the CPU demand of the virtual node nva is CP U (nva ) = 10, and mapping the virtual node nva onto the substrate node nsB will

20.4 The Evaluation Metrics of Node Ranking Based on Multiple Attributes Fig. 20.7 A motivational example 6 to illustrate the drawback of the metric H (n)

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consume all of its CPU capacity resources and almost cut off the connection between substrate nodes nsA and nsC , and will generate network resource fragmentation. This situation may lead to the failure of subsequent link mapping. Therefore, the CPU utilization ratio of the substrate node has a significant effect on the greedy node mapping algorithm and must be taken into consideration to avoid this situation.

20.4.2 The Evaluation Metric of Node Ranking Analysis Since different evaluation metrics of node ranking will lead to different node mapping sequences, single evaluation metric of node ranking or the multiplication by several evaluation metrics will cause imbalanced evaluation of embedding potential for the substrate nodes and result in the lower resource utilization of the substrate network. In this section, we introduce some definitions to measure substrate node importance aiming to facilitate the node mapping process. Definition 1 Resource capacity can be defined as the sum of node resource evaluation metric and the resource evaluation metric values obtained from its neighborhood nodes. The resource capacity value of substrate node ni can be formulated as follows: RC(ni ) = H (ni ) +

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BW (lij )

,

(20.8)

nk ∈nbr(nj )BW (ljk )

where RC(ni ) represents the resource capacity of the node ni , nbr(ni ) represents the set of its neighborhood nodes that are directly connected to the node ni . If ni ∈ N v , H (ni ) represents the resource evaluation metric value for the virtual node ni , BW (lij ) represents the required bandwidth resource of the virtual link lij . If ni ∈ N s , H (ni ) represents the available resource evaluation metric value for the substrate node ni , and BW (lij ) represents the available bandwidth resources of the substrate

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20 Virtual Network Embedding Using Node Multiple Metrics Based on Simplified. . .

link lij . Note that we take the bandwidth resource account for the proportion of total bandwidth resource as the probability and incorporate the probability information into Eq. (20.8). The definition 1 can deal with the first and second situations. Definition 2 Modified resource evaluation value can be defined as the multiplication of the node CPU capacity and the total amount of bandwidth resource of its adjacent links whose available bandwidth resources are more than the minimum demand of the virtual links. The modified resource evaluation value of the node can be formulated as follows:  BW (l), (20.9) MREV (ni ) = CP U (ni ) × l∈nbr(ni )∧BW (l)≥δ

where MREV (ni ) denotes the modified resource evaluation value of the node ni , CP U (ni ) denotes the available CPU capacity of the node ni , nbr(ni ) represents the set of adjacent links for the node ni , BW (l) represents the available bandwidth resources of the link l, and δ represents a threshold that is set in advance or the minimum bandwidth resource requirement. The definition 2 can deal with the third situation. Definition 3 Node degree can be defined as the number of its outgoing links. The node degree for the node ni can be formulated as follows: ND(ni ) = degree(ni ),

(20.10)

where ND(ni ) represents the degree of the node ni , and degree(ni ) refers to the number of the outgoing links of the node ni . There are some studies [25, 33] that resort to the other centrality metrics such as closeness centrality, betweenness centrality, eigenvector centrality, Katz centrality, and so on. The definition 3 can deal with the fourth situation. Definition 4 The HOPS between the mapping substrate node and the set of already mapped substrate nodes can be defined as the minimum number of hops between the mapping substrate node and any mapped node from the set of already mapped substrate nodes. The HOPS between the mapping substrate node and the set of already mapped substrate nodes can be expressed as follows: H OP S(ni , Ω) = minn∈Ω H OP S(ni , n),

(20.11)

where ni represents the mapping substrate node, Ω represents the set of already mapped substrate nodes, and H OP S(ni , Ω) represents the hops between the mapping substrate node ni and the set of already mapped substrate nodes Ω. The definition 4 can deal with the fifth situation.

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Definition 5 The CPU utilization ratio of the substrate node can be defined as the ratio between the demanded CPU capacity of each virtual node and the available CPU capacity of the substrate node nsi . U R(nsi ) =

CP U (nvi )required , CP U (nsi )available

(20.12)

where U R(nsi ) represents the CPU utilization ratio of the substrate node nsi , and the subscript required and available represent the required CPU capacity for the virtual node nvi and the available CPU capacity for the substrate node nsi , respectively. The definition 5 can deal with the sixth situation.

20.4.3 Simplified ELECTRE Algorithm The ELECTRE is a notable classical method of multiple attribute decision making, which was first proposed in [34], and the authors of [35] reported on the works of the European consultancy company SEMA with respect to a specific real-world problem. There are many multiple attribute decision making methods such as TOPSIS [36], ELECTRE, and so on. The reason we choose simplified ELECTRE is that its time complexity can satisfy our needs. In this section, the substrate node is regarded as a solution, the multiple evaluation metric values of substrate nodes are regarded as solution attributes, and then the comprehensive metric of substrate node importance can be transformed into a multiple attribute decision making problem. The steps of the simplified ELECTRE algorithm are as follows: Step 1 Evaluate each solution denoted by a1 , a2 , . . . , an , where each solution has m evaluation criteria. We calculate the metric values of evaluation criteria for each solution aij , and we can obtain a decision making matrix and formulate it as follows: ⎡

An×m

a11 ⎢a21 =⎢ ⎣. . . an1

a12 a22 ... an2

⎤ . . . a1m . . . a2m ⎥ ⎥, ... ...⎦ . . . anm

(20.13)

where each element aij represents the metric value of j-th evaluation criterion of i-th solution. Step 2 Normalize the decision making matrix. The normalized matrix denoted by R can be obtained through the normalization of column vectors, aiming to eliminate the impacts of different metric values in different dimensionalities. ⎡

Rn×m

r11 ⎢r21 =⎢ ⎣. . . rn1

r12 r22 ... rn2

⎤ . . . r1m . . . r2m ⎥ ⎥ , therein, rij = * aij n 2 . ... ...⎦ i=1 aij . . . rnm

(20.14)

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20 Virtual Network Embedding Using Node Multiple Metrics Based on Simplified. . .

Step 3 Calculate the weighted normalized decision making matrix. The weight of each criterion can be formulated as a weighted vector denoted by W(j = 1, 2, . . . , m), where wj represents the weight coefficient of j-th evaluation criterion to measure the importance of each metric, and must satisfy the constraint equation m j =1 wj = 1. The weighted normalized decision making matrix V can be defined as follows: Vij = rij · wj .

(20.15)

Step 4 Calculate the consistent matrix and non-consistent matrix: (i) To compare the two element values in any two different rows in the weighted normalized matrix V , if the i-th row value is larger than the j-th row value in k-th column, the k can be grouped into a consistent set Cij ; otherwise, the k can be grouped into a non-consistent set Dij , where k = 1, 2, . . . , m. The consistent set and non-consistent set can be formulated as follows: Cij = {k|vik ≥ vj k }&Dij = {k|vik ≤ vj k }.

(20.16)

(ii) To calculate the consistent matrix. The consistent matrix C can be obtained by adding the weighted value of each element in each consistent set. The formulation of the consistent matrix C can be defined as follows: k∈Cij wk C = [cij ]n×n , cij = m , (20.17) k=1 wk where cij represents the relative dominating index of the solution ai compared to the solution aj . (iii) To calculate the non-consistent matrix. We first compute the maximum value of the differences between any pair of the weighted values for each element corresponding to two solutions. Then we divided it by the maximum value of the differences between any pair of the weighted values for each element corresponding to all of the solutions. Finally, we can obtain the relative inferior value of the two solutions. The non-consistent matrix can be expressed as follows: max |wk (aik − aj k )|

D = [dij ]n×n , dij =

k∈Dij

max |wk (aik − aj k )|

,

(20.18)

k∈S

where dij represents the relative inferior index of the solution ai compared to the solution aj . We take the weight information of the index into consideration when calculating the relative inferior index. Relative to cij that only contains the weight information of the index, dij increases the differences between two index values, thus, not only contains the weight information, but also has the

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359

index information. Furthermore, the relative dominating index and the relative inferior index are not complementary. dij can reflect the relative inferiority of the solution ai compared to the solution aj . The smaller value means the lower inferiority degree of the solution ai compared to the solution aj . (iv) To calculate the modified non-consistent matrix. The authors of [37–39] redefined the non-consistent matrix; the formulation can be defined as follows: D  = [dij ]n×n , dij = 1 − dij .

(20.19)

Step 5 Calculate the modified weighted summation matrix. The non-consistent matrix in the traditional ELECTRE method can be modified in order to make the element value in the modified non-consistent matrix and the element value in the modified consistent matrix have the same value. The greater the value, the higher the preference degree is. Therefore, we use the product of these two element values between the element value in consistent matrix and the corresponding element value in non-consistent matrix to obtain the modified weighted summation matrix, and formulate it as follows: E = [eij ]n×n , eij = cij · dij .

(20.20)

Step 6 Calculate the net dominating value. The concept of net dominating value is put forward by Van Delft and Nijkamp in 1976. The net dominating value can be defined as follows: Ck =

n  i=1∧i =k

eki −

n 

ej k ,

(20.21)

j =1∧j =k

where Ck represents the weighted sum of the solution ak to the other solutions minus the weighted sum of the solution ai , and it can reflect the weighted sum of the net dominating value for the solution Ck . The bigger the value of Ck is, the better the solution ak is. Step 7 Sort the solutions by their weighted sum of the net dominating values. We sort the solutions by their weighted sum of the net dominating values and can obtain the sequences of the solutions from the best to the worst. In this chapter, we take the resource capacity (RC), modified resource evaluation value (MREV), node degree (ND), hops (HOPS), and CPU utilization ratio (UR) as the evaluation criteria of substrate node importance. We take the reciprocals of HOPS and UR in order to make all of these evaluation criterions the larger the better. Then, we can obtain the ranking orders for substrate nodes through the simplified ELECTRE method.

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20 Virtual Network Embedding Using Node Multiple Metrics Based on Simplified. . .

a 100 60 20

a

10 15

b

A

10

B

40

100 40

100 40

40

C

40

D

100 30

Fig. 20.8 A illustration demo for simplified ELECTRE

20.4.4 An Example for Simplified ELECTRE Considering the following topologies of the virtual network and the substrate network as illustrated in Fig. 20.8. We assume that the virtual node a has already mapped onto the substrate node A, and the subsequent step is to choose another substrate node for virtual node b. For the sake of simplification, here we only annotate the available bandwidth resource for substrate links. The Computation of Resource Evaluation Metrics for Substrate Nodes H (A) = 3000, H (B) = 2000, H (C) = 3200, H (D) = 2400. The Computation of Resource Capacity for Substrate Nodes RC(A) = 5960, RC(B) = 4520, RC(C) = 5900, RC(D) = 5000. The Computation of Modified Resource Evaluation Value for Substrate Nodes MREV (A) = 2400, MREV (B) = 1600, MREV (C) = 3200, MREV (D) = 2400. Note that when mapping the virtual node b, the minimum required bandwidth resource value is 15. Therefore, when we compute the modified resource evaluation value for substrate nodes A and B, the virtual link ls (A, B) should be removed. The Computation of Node Degree for Substrate Nodes ND(A) = 2, ND(B) = 2, ND(C) = 2, ND(D) = 2. The Computation of HOPS for Substrate Nodes H OP S(A) = 0, H OP S(B) = 3, H OP S(C) = 1, H OP S(D) = 2. Note that the number of HOPS between substrate node B and the set of already mapped substrate nodes Ω = {A} is 3, due to the fact that the bandwidth resource of virtual link ls (A, B) cannot satisfy the minimum requirement. The Computation of CPU Utilization Ratio for Substrate Nodes U R(A) = 1 1 1 1 6 , U R(B) = 4 , U R(C) = 4 , U R(D) = 3 . The Construction of Decision Making Matrix Since the substrate node A is allocated to virtual node a, the candidate substrate nodes do not contain the substrate node A. Note that each row represents five metrics of substrate nodes B, C, and D.

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Each column represents RC, MREV, ND, reciprocal of HOPS, and reciprocal of UR, respectively.

A3×5

⎡ ⎤ 4520 1600 2 0.33 4 = ⎣5900 3200 2 1 4⎦ . 5000 2400 2 0.5 3

(20.22)

The normalized decision making matrix:

R3×5

⎡ ⎤ 0.50 0.37 0.58 0.28 0.62 = ⎣0.66 0.74 0.58 0.86 0.62⎦ . 0.56 0.56 0.58 0.43 0.47

(20.23)

The computation of weighted normalized decision making matrix: We set every weight coefficient to 0.2. ⎡

V3×5

⎤ 0.100 0.074 0.116 0.056 0.124 = ⎣0.132 0.148 0.116 0.172 0.124⎦ . 0.112 0.112 0.116 0.086 0.094

(20.24)

The consistent matrix and non-consistent matrix are formulated as follows: ⎡

C3×5

⎤ − 0.4 0.4 = ⎣0.6 − 0.8⎦ . 0.6 0.2 −

(20.25)

⎡

D3×5

⎤ − 1 1 = ⎣ 0 − 0⎦. 1 800 1 −

(20.26)

The modified non-consistent matrix can be formulated as follows: ⎤ − 0 0 =⎣ 1 − 1⎦. 0.99875 0 − ⎡

 D3×5

(20.27)

The modified weighted summation matrix can be formulated as follows: ⎡

E3×5

⎤ − 0 0 = ⎣ 0.6 − 0.8⎦ . 0.5993 0 −

(20.28)

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20 Virtual Network Embedding Using Node Multiple Metrics Based on Simplified. . .

The computation of the net dominating value for substrate nodes B, C, and D. CB = −0.11993, CC = 1.4, CD = −0.2007. We sort the solutions by their weighted sum of the net dominating values and can obtain the sequences of the solutions from the best to the worst is: CC > CD > CB . Therefore, we should map the virtual node b onto the substrate node C.

20.5 Heuristic Algorithm Design Based on the multiple attribute decision making method and five resource evaluation metrics, we propose a novel heuristic algorithm called as ELECTRE-VNE to deal with the VNE problem that consists of node mapping process based on simplified ELECTRE method and link mapping process based on the shortest path algorithm.

20.5.1 Node Mapping Algorithm The detailed steps of node mapping algorithm are illustrated in Algorithm 40. The proposed method is similar to the greedy node mapping approach, and the only difference between them is the node ranking method for substrate nodes in the substrate network. Note that we rank the virtual nodes according to H not ELECRRE, the reason is that through conducting experiments we found that when the number of virtual nodes is less, using ELECTRE method would not improve the performance of node ranking than using the H method but increasing the computation time. Therefore, we consist on ranking the virtual nodes according to H.

20.5.2 Link Mapping Algorithm Here we use the shortest path algorithm to perform the link mapping procedure. The larger number of hops will consume a large amount of bandwidth resources but increase the VNR acceptance ratio. The less number of hops will cause the virtual network mapping failure due to the bandwidth resource bottleneck of substrate links but decrease the ratio of VNR acceptance. The detailed steps of link mapping algorithm are demonstrated in Algorithm 41.

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363

Algorithm 40 The node mapping algorithm based on simplified ELECTRE method 1: Sort the virtual nodes by H in non-increasing order. 2: for all the unmapped virtual nodes in VNR do 3: choose a virtual node nv with the highest H ; 4: for each substrate node ns in substrate network do 5: Calculate RC(ns ), MREV (ns ), ND(ns ), H OP S(ns ), and U R(ns ); 6: Calculate the node ranking values for substrate nodes using simplified ELECTRE method; 7: Sort the substrate nodes by their node ranking values in descending order and denote it by Ω; 8: for each ns in Ω do 9: if ns is not mapped and CP U (ns ) ≥ CP U (nv ) then 10: MN (nv ) = ns ; 11: break; 12: end if 13: end for 14: end for 15: end for 16: return true.

Algorithm 41 The link mapping algorithm based on the shortest path algorithm 1: Sort the virtual links by the required bandwidth in non-increasing order. 2: for all the unmapped virtual links in VNR do 3: fetch two corresponding substrate nodes nsstart and nsend for the virtual link lv ; 4: remove all the substrate links whose bandwidth resource is lesser than the required amount of bandwidth resource; 5: choose a loop-free substrate path between nsstart and nsend using shortest path algorithm. 6: end for 7: return true.

20.5.3 Time Complexity Analysis We denote the number of virtual nodes and virtual links in each VN request by |N v |, |Lv |, respectively. We denote the number of substrate nodes and substrate links in the substrate network by |N s |, |Ls |, respectively. The average time of iteration in RW-VNE is denoted by |itertimes|. The Time Complexity of Greedy-VNE The time complexity of node mapping process is O(|N s |2 ), and the time complexity of link mapping process is O(|Lv ||N s |2 ). The Time Complexity of RW-VNE The time complexity of node mapping process is O(|itertimes|×|N s |2 ), and the time complexity of link mapping process is O(|Lv ||N s |2 ). The Time Complexity of IC-VNE The time complexity of node mapping process is O(|N s |3 ), and the time complexity of link mapping process is O(|Lv ||N s |2 ).

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20 Virtual Network Embedding Using Node Multiple Metrics Based on Simplified. . .

The Time Complexity of ELECTRE-VNE The time complexity of node ranking computation for each VNR is O(|N v |2 ). The time complexities of computing RC(ns ), MERV (ns ), ND(ns ), H OP S(ns ), and U R(ns ) are O(|N s |2 ), O(|N s |2 ), O(|N s ||Ls |), O(|N s |3 ), and O(|N s |2 ), respectively. Therefore, the time complexity of Algorithm 40 is O(|N s |3 ). The time complexity of Algorithm 41 is O(|Lv ||N s |2 ).

20.6 Performance Evaluation In this section, we describe the settings of our simulation environment in detail and then present our experimental results. We use the aforementioned three evaluation criteria including the long-term average revenue, the long-term R/C ratio, and the VNR acceptance ratio to measure the performance of our method compared with the other methods.

20.6.1 Environment Settings Similar to the prior works [8, 18, 19], we use the GT-ITM [40] to generate the topologies of the substrate network and virtual networks. The number of substrate nodes in substrate network is set to 100, and the connectivity probability between any two substrate nodes is set to 0.5. The CPU capacities of substrate nodes in substrate network are real numbers that follow the uniform distribution between 50 and 100, and the bandwidth resources of substrate links in substrate network are real numbers that follow the uniform distribution between 50 and 100. We assume that the arrival of VNR is a Poisson process, and the mean arrival rate is 5 VNRs/100 time units. The duration of each VNR follows negative exponential distribution with an average of 1000 time units. The demanded CPU capacities of virtual nodes in each VNR are real numbers uniformly distributed between 0 and 50, and the required bandwidth resources of virtual links in each VNR are real numbers uniformly distributed between 0 and 50. The number of nodes in each VNR is uniformly distributed between 2 and 20, and the connectivity probability between any two virtual nodes is assigned to 0.5. Our simulation experiments evaluate four methods that are listed in Table 20.1. The Greedy-VNE algorithm [19] is the classical VNE algorithm, the RW-VNE algorithm [20] is a topology-aware node ranking VN embedding algorithm, the ICVNE algorithm [7] is an approach of VN embedding based on network centrality analysis and closeness centrality, and the ELECTRE-VNE algorithm is our proposed method. In our work, we do not take into consideration the situation where link mapping solution supports the path splitting.

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Table 20.1 The compared four methods Notation Greedy-VNE RW-VNE IC-VNE ELECTRE-VNE

Description Node mapping process based on classical node resource evaluation metric and link mapping process based on shortest path algorithm Node mapping process based on the random walk (RW) algorithm and link mapping process utilizing shortest path algorithm Node mapping process based on the node closeness and link mapping process utilizing shortest path algorithm Node mapping process using node multiple metrics based on the simplified ELECTRE method and link mapping process utilizing shortest path algorithm

20.6.2 Evaluation Results The existing work generally set the maximum number of hops range from 3 to 7. In our work, we want to maximize the ratio of VNR acceptance and avoid unnecessary consumption of bandwidth resource in substrate network. Therefore, we set the maximum number of hops to 5 according to our experiences. In order to fully evaluate our method compared with the other three methods from different perspectives, we carried out two experiments aiming to validate the effectiveness and feasibility of our method. Simulation Experiment 1 The first experiment aims to evaluate the performance of our method compared with the other methods. We use the long-term average revenue, the long-term R/C ratio, and the VN request acceptance ratio to measure the performances of these compared methods. Figure 20.9 shows the long-term average revenue of the compared four methods. From Fig. 20.9, we can observe that our method ELECTRE-VNE is the highest one among these compared methods. According to quantitative analysis from the specific data, the long-term average revenue of our method ELECTRE-VNE is 22.01% higher than GREEDY-VNE, 14.66% higher than RW-VNE, and 6.83% higher than IC-VNE. The main reason is that ELECTRE-VNE incorporates the hops between the mapping substrate node and the set of already mapped substrate nodes into substrate node ranking computation process. Then we can avoid unnecessary bandwidth resource consumption so as to save more bandwidth resource to accommodate more VNRs, which leads to the largest long-term average revenue. Figure 20.10 presents the R/C ratio of the compared four methods. From Fig. 20.10, we can observe that our method ELECTRE-VNE is the optimal one among these four methods. According to the quantitative analysis from the obtained data, the R/C ratio of our method ELECTRE-VNE is almost 13.67% higher than GREEDY-VNE, 9.14% higher than RW-VNE, and 5.15% higher than IC-VNE. The main reason is that our method takes into consideration the number of the hops between the mapping substrate node and the set of already mapped substrate nodes and embeds the adjacent virtual nodes onto the two substrate nodes that are not far

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20 Virtual Network Embedding Using Node Multiple Metrics Based on Simplified. . .

Fig. 20.9 The long-term average revenue of substrate network

Fig. 20.10 The long-term revenue to cost ratio of substrate network

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367

Fig. 20.11 The VNR acceptance ratio

away from each other with the aim of reducing unnecessary bandwidth resource consumption. Therefore, it can make the R/C ratio higher than the other three methods. Figure 20.11 illustrates the VN request acceptance ratio of the compared four methods. From Fig. 20.11, we can observe that the VNR acceptance ratio of our method ELECTRE-VNE is the highest one among these compared four algorithms. Based on the quantitative analysis from the concrete data, the VNR acceptance ratio of our method ELECTRE-VNE is 27.67% higher than GREEDY-VNE, 14.93% than RW-VNE, and 9.24% than IC-VNE. Due to the fact that our method ELECTREVNE incorporates the multiple metrics of node ranking into the node importance computation process, which would increase the VNR acceptance ratio from the long run. The main reason is that node degree, modified resource evaluation value, and CPU utilization ratio can give a comprehensive node ranking value, and the number of hops between the mapping substrate node and the set of already mapped substrate nodes can save bandwidth resources to accommodate more VNRs. Both of them can increase the acceptance ratio of VNRs. Simulation Experiment 2 The second experiment aims to measure the performance of our method on the VN requests with different CPU capacity requirements. We carried out the second experiment and let the required CPU capacity of virtual nodes uniformly distribute between 0 and Cn , therein Cn increases from 10 to 100 step 10. We evaluate our method compared with the other three methods in terms

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20 Virtual Network Embedding Using Node Multiple Metrics Based on Simplified. . .

Fig. 20.12 The long-term average revenue with increasing CPU capacity

of the long-term average revenue, the long-term R/C ratio, and the VNR acceptance ratio. Figure 20.12 shows the long-term average revenue of the compared four methods with increasing demand of CPU capacity on nodes. We can observe that our method ELECTRE-VNE is the best one among these compared four methods. According to the quantitative analysis from the concrete data, the long-term average revenue of our method ELECTRE-VNE is almost 50% higher than GREEDY-VNE, 31.07% higher than RW-VNE, and 16.98% higher than IC-VNE. From the overall trend, the long-term average revenue is decreasing with the increasing demanded CPU capacity on nodes due to the fact that substrate resources are diminishing with the increasing requirements of CPU capacity on nodes. From the overall trend of four lines, it can be seen that our proposed five definitions do contribute to the performance of our method. There is no obvious fluctuation with the increasing demanded CPU capacities on nodes that can justify our proposed method. Figure 20.13 presents the R/C ratio of the compared four methods with increasing demand of CPU capacity on nodes. We can observe that our method ELECTREVNE outperforms the other three methods; the main reason is that our method ELECTRE-VNE takes into consideration the hops between the mapping substrate node and the set of already mapped substrate nodes with an aim to reduce the unnecessary bandwidth resource consumption of substrate links. Through incorporating the multiple metrics of node ranking into the node importance computation process, we can choose the substrate node with the most embedding potential to

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Fig. 20.13 The long-term revenue to cost ratio with increasing CPU capacity

perform the node mapping process and thereby increase the R/C ratio of VNE algorithm. According to the quantitative analysis from the obtained data, our method ELECTRE-VNE is 17.93% higher than GREEDY-VNE, 13.97% higher than RWVNE, and 11.56% higher than IC-VNE. Figure 20.14 illustrates the VN request acceptance ratio of the compared four methods with increasing demand of CPU capacity on nodes. We can observe that our method ELECTRE-VNE is the highest one among these compared four methods. The main reason is that our method takes into account the multiple metrics of node ranking based on the topological analyses of substrate network and employs comprehensive multiple attribute decision method ELECTRE to measure the node importance of substrate nodes in substrate network. The resource capacity can give a comprehensive node ranking value for each substrate node. The modified resource evaluation value can reduce the failure probability of subsequent link mapping process. The node degree can improve the node ranking of substrate nodes. The CPU utilization ratio can eliminate the bottleneck substrate node to increase the acceptance ratio of VNRs. According to the quantitative analysis from the concrete data, our method ELECTRE-VNE is 10.28% higher than GREEDY-VNE, 8.72% higher than RW-VNE, and 7.10% higher than IC-VNE. In addition, through the vertical comparison Fig. 20.10 vs. Figs. 20.13, 20.11 vs. Fig. 20.14, we can see that our proposed method on increasing demand of CPU capacity performs better than on normal case. The reason is that our proposed five definitions are all associated with the node importance metric.

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20 Virtual Network Embedding Using Node Multiple Metrics Based on Simplified. . .

Fig. 20.14 The VNR acceptance ratio with increasing CPU capacity

20.7 Conclusions VNE is a promising technique to fend off the ossification of the current Internet architecture in NV environments. In this chapter, we introduce six situations to demonstrate the main drawbacks of the classical resource evaluation metric of node ranking and give five definitions to evaluate the node importance with the aim of addressing these issues. We presented a novel VNE algorithm called ELECTREVNE, which uses the simplified ELECTRE method for five evaluation metrics to rank the importance of the substrate nodes and utilizes the shortest path algorithm to perform the link mapping procedure. Two kinds of simulation experiments have shown that our method outperforms the other state-of-the-art methods in terms of the long-term average revenue, the long-term revenue to cost ratio, and the VNR acceptance ratio. Our method mainly uses different node ranking metrics that are jointly considered using simplified ELECTRE decision making method to perform the node mapping process. Therefore, the proposed method has always worked particularly in the case of distributed scientific computation service, where requiring more CPU capacity on nodes to process data but less bandwidth resource on links to transfer the computation results. In our future work, we will focus on the different link ranking metrics with the aim of increasing universality of our method, such as the case of the live network service requiring more bandwidth resources on links to transport

References

371

packets but less CPU capacity on nodes to forward packets. In addition, we will concentrate on the energy-aware, security aware, and QoS-aware VNE algorithms to satisfy diverse kinds of services for virtual networks.

References 1. P. Zhang, H. Yao, C. Qiu, Y. Liu, Virtual network embedding using node multiple metrics based on simplified ELECTRE method. IEEE Access 6, 37314–37327 (2018) 2. Z. Yong, M.H. Ammar, Algorithms for assigning substrate network resources to virtual network components, in Infocom IEEE International Conference on Computer Communications (2006) 3. Z. Zhang, C. Xiang, S. Su, Y. Wang, L. Yan, A unified enhanced particle swarm optimizationbased virtual network embedding algorithm. Int. J. Commun. Syst. 26(8), 1054–1073 (2013) 4. N. Farooq Butt, M. Chowdhury, R. Boutaba, Topology-awareness and reoptimization mechanism for virtual network embedding, in Networking 2010, International IFIP TC6 Networking Conference, Chennai, India (2010), pp. 27–39 5. C. Jiang, X. Ma, C. Chen, J. Ma, Y. Ren, On searching available channels with asynchronous MAC-layer spectrum sensing. IEICE Trans. Commun. E93-B(8), 2113–2125 (2010) 6. H. Cui, S. Tang, X. Huang, J. Chen, Y. Liu, A novel method of virtual network embedding based on topology convergence-degree, in IEEE International Conference on Communications Workshops (2013), pp. 246–250 7. Z. Wang, Y. Han, T. Lin, H. Tang, Virtual network embedding by exploiting topological information, in Global Communications Conference (2012), pp. 2603–2608 8. J. Ding, T. Huang, J. Liu, Y. Liu, Virtual network embedding based on real-time topological attributes. Front. Inform. Technol. Electron. Eng. 16(2), 109–118 (2015) 9. J. Du, C. Jiang, J. Wang, Y. Ren, M. Debbah, Machine learning for 6G wireless networks: carrying forward enhanced bandwidth, massive access, and ultrareliable/low-latency service. IEEE Veh. Technol. Mag. 15(4), 122–134 (2020) 10. A. Fischer, J.F. Botero, M.T. Beck, H.D. Meer, X. Hesselbach, Virtual network embedding: a survey. IEEE Commun. Surv. Tutorials 15(4), 1888–1906 (2013) 11. E. Amaldi, S. Coniglio, A.M.C.A. Koster, M. Tieves, On the computational complexity of the virtual network embedding problem. Electron. Notes Discrete Math. 52(1), 213–220 (2016) 12. J. Lischka, H. Karl, A virtual network mapping algorithm based on subgraph isomorphism detection, in Proceedings of the 1st ACM Workshop on Virtualized Infrastructure Systems and Architectures (2009), pp. 81–88 13. N.M.M.K. Chowdhury, M.R. Rahman, R. Boutaba, Virtual network embedding with coordinated node and link mapping, in Infocom (2009) 14. Y. Wang, Q. Hu, X. Cao, A branch-and-price framework for optimal virtual network embedding. Comput. Netw. 94, 318–326 (2016) 15. M. Melo, S. Sargento, U. Killat, A. Timm-Giel, J. Carapinha, Optimal virtual network embedding: node-link formulation. IEEE Trans. Netw. Serv. Manag. 10(4), 1–13 (2013) 16. M. Melo, Rcio, S. Sargento, U. Killat, A. Timm-Giel, J. Carapinha, Optimal virtual network embedding. Comput. Netw. Int. J. Comput. Telecommun. Netw. 91(C), 184–195 (2015) 17. I. Houidi, W. Louati, W.B. Ameur, D. Zeghlache, Virtual network provisioning across multiple substrate networks. Comput. Netw. 55(4), 1011–1023 (2011) 18. M. Chowdhury, M. Rahman, R. Boutaba, ViNEYard: virtual network embedding algorithms with coordinated node and link mapping. IEEE/ACM Trans. Netw. 20(1), 206–219 (2012) 19. M. Yu, Y. Yi, J. Rexford, M. Chiang, Rethinking virtual network embedding: substrate support for path splitting and migration. ACM SIGCOMM Comput. Commun. Rev. 38(2), 17–29 (2008)

372

20 Virtual Network Embedding Using Node Multiple Metrics Based on Simplified. . .

20. X. Cheng, S. Su, Z. Zhang, H. Wang, F. Yang, Y. Luo, J. Wang, Virtual network embedding through topology-aware node ranking. ACM SIGCOMM Comput. Commun. Rev. 41(2), 38– 47 (2011) 21. F. Juan Botero, X. Hesselbach, Greener networking in a network virtualization environment. Comput. Netw. 57(9), 2021–2039 (2013) 22. T. Wang, M. Hamdi, Presto: towards efficient online virtual network embedding in virtualized cloud data centers. Comput. Netw. 106, 196–208 (2016) 23. X. Hesselbach, J.R. Amazonas, S. Villanueva, J.F. Botero, Coordinated node and link mapping VNE using a new paths algebra strategy. J. Netw. Comput. Appl. 69, 14–26 (2016) 24. S. Gong, J. Chen, S. Zhao, Q. Zhu, Virtual network embedding with multi-attribute node ranking based on TOPSIS, in KSII Transactions on Internet & Information Systems (2016), p. 10 25. M. Feng, J. Liao, J. Wang, S. Qing, Q. Qi, Topology-aware virtual network embedding based on multiple characteristics. KSII Trans. Internet Inform. Syst. 8(1), 2956–2962 (2014) 26. C. Ouyang, S. Wu, C. Jiang, D.W.K. Ng, H. Yang, Secrecy performance for finite-alphabet inputs over fluctuating two-ray channels in FDA communications. IEEE Commun. Lett. 9(10), 1638–1642 (2020) 27. S. Kirkpatrick, C. D. Gelatt Jr., M.P. Vecchi, Optimization by simulated annealing. Science 220(4598), 671 (1983) 28. P. Zhang, H. Yao, M. Li, Y. Liu, Virtual network embedding based on modified genetic algorithm. Peer-to-Peer Netw. Appl. 2, 1–12 (2017) 29. M. Dorigo, Optimization, learning and natural algorithms. Thesis Politecnico Di Milano Italy (1992) 30. I. Fajjari, N. Aitsaadi, G. Pujolle, H. Zimmermann, VNE-AC: virtual network embedding algorithm based on ant colony metaheuristic, in IEEE International Conference on Communications (2011), pp. 1–6 31. P. Zhang, H. Yao, C. Fang, Y. Liu, Multi-objective enhanced particle swarm optimization in virtual network embedding. EURASIP J. Wirel. Commun. Netw. 2016(1), 167 (2016) 32. J. Infhr, G. Raidl, A memetic algorithm for the virtual network mapping problem. J. Heuristics 22(4), 475–505 (2016) 33. W. Wang, B. Wang, Z. Wang, B. Wang, Virtual network embedding algorithm based on analysis of network centrality, in Application Research of Computers (2015) 34. M. Zeleny, P. Nijkamp, A.V. Delft, Multi-criteria analysis and regional decision-making. J. Am. Stat. Assoc. 75(372), 1035 (1977) 35. B. Roy, D. Vanderpooten, An overview on The European School of MCDA: emergence, basic features and current works. Eur. J. Oper. Res. 99(1), 26–27 (1997) 36. C. Hwang, K. Yoon, Multiple Attribute Decision Making Methods and Applications: A Stateof-the-Art Survey (Springer, Berlin, 1981), pp. 1–531 37. C.L. Hwang, A.S.M. Masud, Multiple Objective Decision Making Methods and Applications (Springer, Berlin, 1979), pp. 287–288 38. R. Duan, J. Wang, C. Jiang, H. Yao, Y. Ren, Y. Qian, Resource allocation for multi-UAV aided IoT NOMA uplink transmission systems. IEEE Internet Things J. 6(4), 7025–7037 (2019) 39. C. Jiang, A. Benslimane, M. Dong, E. Hossain, Guest editorial: Introduction to the special section on heterogeneous communications networks. IEEE Trans. Netw. Sci. Eng. 7(4), 2361– 2362 (2020) 40. E.W. Zegura, K.L. Calvert, S. Bhattacharjee, How to model an Internet work. IEEE Infocom 2, 594–602 (1996)

Chapter 21

VNE Strategy Based on Chaotic Hybrid Flower Pollination Algorithm Considering Multi-Criteria Decision Making

Abstract With the development of science and technology and the need for multicriteria decision making (MCDM), the optimization problem to be solved becomes extremely complex. The theoretically accurate and optimal solutions are often difficult to obtain. Therefore, meta-heuristic algorithms based on multi-point search have received extensive attention. The flower pollination algorithm (FPA) is a new swarm intelligence meta-heuristic algorithm that can effectively control the balance between global search and local search through a handover probability and gradually attracts the attention of researchers. However, the algorithm still has problems that are common to optimization algorithms. For example, the global search operation guided by the optimal solution is easy to lead the algorithm into local optimum, and the vector-guided search process is not suitable for solving some problems in discrete space. Moreover, the algorithm does not consider dynamic multi-criteria decision problems well. Aiming at these problems, the design strategy of hybrid flower pollination algorithm for VNE problem is discussed. Combining the advantages of the genetic algorithm and FPA, the algorithm is optimized for the characteristics of discrete optimization problems. The cross operation is used to replace the cross-pollination operation to complete the global search and replace the mutation operation with self-pollination operation to enhance the ability of local search. Moreover, a life cycle mechanism is introduced as a complement to the traditional fitness-based selection strategy to avoid premature convergence. A chaotic optimization strategy is introduced to replace the random sequenceguided crossover process to strengthen the global search capability and reduce the probability of producing invalid individuals. In addition, a 2-layer BP neural network is introduced to replace the traditional objective function to strengthen the dynamic MCDM ability. Simulation results show that the proposed method has good performance in link load balancing, revenue-cost ratio, VNRs acceptance ratio, mapping average quotation, average time delay, average packet loss rate, and the average running time of the algorithm.

Reprinted from ref. [1], with permission of Springer. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Jiang, P. Zhang, QoS-Aware Virtual Network Embedding, https://doi.org/10.1007/978-981-16-5221-9_21

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21.1 Introduction With the coordinated development of multiple technologies such as IoT, big data, cloud computing, and mobile computing, people put forward higher requirements for the service quality and information security of the Internet. In the current research, NV is considered as an effective way to solve the rigid problem of the Internet [2]. Software defined network (SDN) is a new architecture that provides a platform for NV. It implements flexible control of traffic by introducing programmable controllers at the control layer. Being different from the traditional architecture, which needs to communicate and negotiate with the infrastructure providers, the SDN has the advantages of flexible deployment and quick response. In addition, the VNE is one of the key problems in NV, and it has been proved to be an NP-hard optimization problem [3, 4]. The research on optimization problems has been greatly promoted by the rapid development of computer technology. However, the traditional methods have obvious disadvantages when solving complex optimization problems such as objective functions and constraints that cannot be formulated. Therefore, thanks to the actual demand, many meta-heuristic intelligent algorithms based on multi-point search are proposed. However, there are still some unsolved problems in the existing heuristic algorithms [5], such as: (1) parameter tuning is a complex and repeated process when the algorithm has many parameters. (2) The search process guided by the optimal solution is easy to lead the algorithm into a local optimum. (3) The search ability is too low when solving special optimization problems and then leads to premature convergence. (4) The existing methods of calculating fitness cannot meet the requirements of MCDM. In addition, for the VNE problem in discrete space, the optimization process guided by the direction vector is not effective. In view of these problems, a new VNE strategy considering dynamic multi-criteria decision making is proposed [6, 7]. The main contributions and main ideas are summarized as follows: 1. A life cycle mechanism is introduced to limit the number of iterations an individual can survive in a population. This strategy can increase the ability to acquire the lost patterns and thus avoid premature convergence. In addition, the life span dynamically calculated based on fitness can control the death frequency of individuals in the population, so as to avoid the influence of the convergence speed due to the rapid decline of the overall quality of the population. 2. A chaos optimization strategy is introduced to replace the crossover process guided by random sequence. This strategy makes use of the excellent ergodicity of chaos sequences to enhance the global search capability of the algorithm. In addition, compared with the traditional crossover method, it can effectively avoid the generation of invalid individuals. 3. An optimized self-pollination strategy is introduced to improve the local search ability of the algorithm. Moreover, the handover probability in FPA is retained to control the balance between global and local search. In addition, a two-layer BP neural network is introduced to evaluate the performance of solutions with slight differences, which makes the local search phase have more accurate judgment.

21.2 Related Work

375

The remainder of this chapter is organized as follows. Section 21.2 reviews the existing methods for VNE. Section 21.3 introduces the network model and problem statement. Section 21.4 introduces the core strategies used in BP-HFPA method. In Sect. 21.5, we describe our proposed method BP-HFPA in detail. The performance of our method and other methods is evaluated in Sect. 21.6. Section 21.7 concludes this chapter.

21.2 Related Work In [8], the meta-heuristic algorithms are divided into four categories: (1) based on natural evolution, (2) based on biological behavior, (3) based on physical phenomenon, and (4) based on human behavior. This section will analyze the existing meta-heuristic algorithms based on this classification strategy and introduce the research status of VNE problem.

21.2.1 Meta-Heuristic Algorithms (1) Natural evolution. The genetic algorithm is the representative of this kind of algorithm [9–16]. In addition, the mutation based evolutionary strategy and evolutionary planning are not suitable for solving problems with abstract constraints and goals. Genetic planning is a variation of genetic algorithm, and the difference is that the individual of this algorithm is a function. Differential evolution algorithm (DE) [17] has similar iterative steps to genetic algorithm, but it relies on vector operation to guide evolution. (2) Biological behavior. The representative of this kind of algorithm is PSO algorithm based on bird foraging behavior [18–20]. In addition, artificial bee colony algorithm (ABC) can transmit the information of food source to other bees through leading bees [21], ant colony optimization algorithm (ACO) selects new paths through the concentration of pheromones left by other ants [22–24], and Firefly Algorithm (FA) guides the mutual attraction between individuals through brightness [25]. It can be seen that compared with evolutionbased algorithms, individuals of this type of algorithm have certain information interaction capabilities. (3) Physical phenomenon. This kind of algorithm is relatively new. Gravity Search Algorithm (GSA) [26], which is based on Newton’s law of gravity and motion. Big Bang-Big Crunch Algorithm (BBBC) is based on the theory of cosmic explosion [27]. In addition, there is also Black Hole Algorithm (BHA) to simulate black hole phenomenon [28], Lightning Search Algorithm (LSA) to simulate the natural phenomenon of lightning, and the mechanism of step leader propagation [29]. (4) Human behavior. This kind of algorithm simulates human behavior. For example, Harmony Search algorithm (HS) simulates the process of harmony playing [30]. Teaching-Learning-Based Optimization (TLBO) simulates the process of class teaching [31]. Imperialist Competitive Algorithm (ICA) simulates the annexation and competition among countries [32].

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21 VNE Strategy Based on Chaotic Hybrid Flower Pollination Algorithm. . .

According to the no free lunch (NFL) theorem, no single algorithm is suitable for solving all optimization problems. As a result, universality and pertinence cannot be considered at the same time. Therefore, we believe that appropriate algorithms should be selected and optimized for specific problems.

21.2.2 VNE Strategies The authors of [33] divided the VNE methods into two types: optimal algorithms and heuristic algorithms. In recent studies on optimal algorithms, the authors of [34] proposed a dynamic VNE algorithm that can meet the requirements of customized QOS. In the same year, the authors of [35] proposed a VNE algorithm based on five constraints, and the authors of [36] further considered the perception of energy consumption. Moreover, the authors of [37] proposed a candidate set based VNE algorithm considering the time delay and geographical location constraints. The authors of [38] proposed a method comprehensively considered five topology attributes and global network resources. However, in the case of large problem scale, solving the optimal solution often consumes a lot of computing resources. As a result, more researches had focused on the heuristic algorithms with lower computation. In the early research [39], PSO algorithm was used to solve the VNE problem for the first time. In the follow-up studies, the authors of [40] proposed a distributed VNE algorithm (HA-VNE-PSO) that can skip unnecessary iterative steps. The authors of [41] proposed a unified enhanced VNE algorithm (VNEUEPSO) based on PSO. The authors of [42] proposed a VNE algorithm based on a candidate point selection strategy to make up for the shortcomings of heuristic solution was not accurate enough. In addition, there are also many researches based on genetic algorithm. For example, the authors of [43] proposed a VNE algorithm based on cellular genetic mechanism, which further improved the interaction ability of the population. Moreover, the authors of [44] combined the annealing algorithm with genetic algorithm to improve the acceptance rate and reduce the cost, and the authors of [45] discussed the problem of using genetic algorithm to deal with the multi-virtual network embedding (MVNE). It is worth noting that the objective function of the above meta-heuristic algorithm only considers resources or prices and can only preliminarily distinguish the quality of different solutions. Therefore, further optimization is needed.

21.3 Network Model and Problem Statement Figure 21.1 is the process of solving the VNE problem, and it can be simplified as Fig. 21.2. The top left of Fig. 21.2 is a virtual network to be mapped, and the right is a substrate network topology composed of three domains. In this chapter, Fig. 21.2 will be used as references.

21.3 Network Model and Problem Statement

377

Fig. 21.1 Process of solving the VNE problem

21.3.1 Substrate Network and Virtual Network Model In this model, the substrate network is defined as an undirected graph Gs = {N s , Ls }, where N s represents a set of substrate nodes and the Ls represents a set of substrate links. {CP U (ns ), U P (ns ), T D(ns ), P LR(ns )} represents a set of attributes of each substrate node, which, respectively, represent the CPU capacity, the resource unit price, the time delay within substrate nodes, and the packet loss rate. Moreover, {BW (ls ), U P (ls ), AU P (Ps ), T D(ls )} represents a set of attributes of each substrate link, which, respectively, represent the bandwidth, the resource

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21 VNE Strategy Based on Chaotic Hybrid Flower Pollination Algorithm. . .

Fig. 21.2 An substrate network consisting of three domains and a VNR

unit price, the aggregation unit price, and the time delay of substrate links. Therein, the AU P (Ps ) can be expressed as follows: AU P (Ps ) =



U P (ls ),

(21.1)

ls ∈Ps

where Ps represents a substrate path composed of several substrate links. A VN can also be abstracted as an undirected graph Gv = {N v , Lv }, N v represents a set of virtual nodes, and Lv represents a set of virtual links. CP U (nv ) represents the CPU capacity required by the virtual node nv , and BW (lv ) represents the bandwidth required by the virtual link lv .

21.3.2 Virtual Network Embedding Problem Description The process can be modeled as M : Gv {N v , Lv } → Gs {N s , Ls }. Each virtual node nv ∈ N v chooses a substrate node that conforms to the constraint condition as the mapping target. It should be noted that different virtual nodes in the same VNR cannot be mapped repeatedly to the same substrate node. Each virtual link is mapped to a substrate path Ps that conforms to the constraint condition, where the

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379

endpoints of the path are determined during the node mapping phase. In addition, the constraints can be defined as , BW (lv ) ≤ BW (ls ), ∀ls ∈ P s(lv ), (21.2) CP U (nv ) ≤ CP U (ns ), nv ↔ ns , where ↔ represents the process of mapping nv to ns . In addition, a scheme for mapping virtual network can be expressed as M(Gv , N s , P s ), where N s and P s , respectively, represent the set of substrate nodes and the set of substrate paths in this scheme.

21.3.3 Objectives and Evaluation Index The objective function can be expressed as 

OBJ (Gv ) = min

CP U (nv ) × U P (ns )

nv ∈N v

+



(21.3)

BW (lv ) × AU P (Ps ).

lv ∈Lv

The link load balancing can be measured by the variance of consumed resources, and it can be expressed as σ = 2

ls ∈Ls (used

resources f or ls − μ)2 num(Ls )

,

(21.4)

where μ represents the average used resources, and num(Ls ) is the number of links in the substrate network. The revenue–cost ratio can be expressed as (revenue(Gv ) /cost (Gv )), where the revenue and the cost of mapping a virtual network can be expressed as revenue(Gv ) =



CP U (nv ) +

nv ∈N v

cost (Gv ) =

 nv ∈N v

CP U (nv ) +



BW (lv ),

(21.5)

lv ∈Lv



BW (lv )H ops(Ps (lv )),

(21.6)

lv ∈Lv

where H ops(Ps (lv )) represents the number of hops of the substrate path Ps (lv ). The VNR acceptance ratio can be expressed as acceptance ratio =

num(V NRaccept ) , num(V NRref use )

(21.7)

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21 VNE Strategy Based on Chaotic Hybrid Flower Pollination Algorithm. . .

where num(V NRaccept ) represents the number of VNRs that were accepted and successfully mapped to the substrate network, and num(V NRref use ) represents the number of rejections. The average quotation can be expressed as

average quotation =

OBJ (Gv ) . num(V NRaccept )

(21.8)

The total time delay includes the total delay of links and the total delay of nodes, and it can be expressed as 

T D(M(Gv , N s , P s )) =

T D(ns ) +

ns ∈N s

 

T D(ls ).

(21.9)

Ps ∈P s ls ∈Ps

The average time delay can be expressed as average delay =

T D(M(Gv , N s , P s )) . num(V NRaccept )

(21.10)

The total packet loss rate can be expressed as P LR(M(Gv , N s , P s )) =



P LR(ns ).

(21.11)

ns ∈N s

The average packet loss rate can be expressed as average P LR =

P LR(M(Gv , N s , P s )) . num(V NRaccept )

(21.12)

The average running time is the average time consumed by mapping a virtual network, and in milliseconds.

21.4 Strategy Model and Innovation Motivations 21.4.1 Life Cycle Mechanism The authors of [46] explained that the cause of premature convergence is pattern loss. Moreover, due to the search characteristics of genetic algorithm, lost patterns can only be retrieved during the mutation phase. However, the mutation of small probability is not enough to deal with large-scale pattern loss. In addition, because of the characteristics of VNE problem, the lost patterns will be more difficult to obtain, and as shown in Fig. 21.3. The nodes marked in red in Fig. 21.3 are nodes that can be selected as mutation targets. It can be seen that because different virtual nodes

21.4 Strategy Model and Innovation Motivations

381

Fig. 21.3 An substrate network consisting of three domains and a VNR

in the same virtual network cannot be mapped to the same substrate node, there are very few optional nodes. This is especially true when there are fewer resources on the substrate network. Therefore, even if a lost pattern is acquired through mutation, another pattern may be lost because there are too few optional nodes. In order to solve this problem, we introduce a life cycle mechanism to limit the number of iterations for individuals to survive in the population, to avoid obsolete individuals affecting the genetic diversity of the population. Compared to other similar strategies that are aperiodic and random, this strategy can gradually replace the individuals that have existed for a long time. Therefore, it can take into account the overall quality of the population while avoiding premature convergence, thereby ensuring that the convergence rate is not affected. We define the life cycle as the following expression:

lif e cycle =

⎧ ⎨λlif e F (xi ) num(X) × 5, M < 25, F (x ) xi ∈X

i

xi ∈X

i

⎩λlif e F (xi ) num(X) M , M ≥ 25, F (x ) 5

(21.13)

where λlif e represents the life factor, which ranges from 0 to 3, and the default is 1. F (xi ) represents the fitness of the solution xi , num(X) represents the number of individuals in the population X, and M represents the maximum number of iterations. In addition, a method was introduced to further enhance the ability to capture lost patterns. When a new individual is used to replace the old individual, a 0–1 sequence is obtained by bitwise-and operation of new and old individuals. Finally, when a component in the 0–1 sequence is 1, the rest of the substrate nodes

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21 VNE Strategy Based on Chaotic Hybrid Flower Pollination Algorithm. . .

Fig. 21.4 A diagram of single-point crossing

that satisfy the constraint will be randomly selected as the corresponding component in the new individual.

21.4.2 Chaos Strategy After several iterations, it is clear that some nodes that can reduce the fitness of the individuals will repeatedly appear in the descendants that are retained. In which case, the traditional crossover strategy is likely to produce invalid individuals, as shown in Fig. 21.4. Take single-point crossover as an example. If the substrate node N exists simultaneously in a pair of selected individuals A and B to be crossed, invalid individuals will be generated after crossover when the node N is in the same color region. By calculation, the probability of N in the same color region is 50%. Therefore, the probability of producing invalid individuals after crossover is also 50%. This will obviously reduce the search ability of crossover process greatly. To solve this problem, we introduce a chaos optimization strategy [47] into genetic algorithm and use its excellent ergodicity to guide the crossover process. In this chapter, we define a chaos sequence generator based on logistic model and convert the obtained chaos sequence into a mask code for crossover, as follows: xn+1 = uxn (1 − xn ), u ∈ [0, 4], x ∈ (0, 1),

(21.14)

when u is greater than 4, the model will diverge, that is, x is greater than 1. But when it is less than or equal to 4, with the increase of u, the model will appear period doubling bifurcation until it shows a random characteristic, namely chaos. Because we want to get a sequence that is almost random but has chaotic characteristics, we set u to 4 and get the initial x randomly. Define the mask code for crossover as M[m1 , m2 , . . . , mk ], where k is equal to the dimension of the solution, and use the following expression to convert the chaos sequence into the mask code: mi =

, 0, xi < 0.5, 1, xi ≥ 0.5,

(21.15)

therein, when the value is 1, the parents’ genes in this dimension will be crossed, and when the value is 0, the genes will not be crossed.

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383

21.4.3 Self-Pollination Strategy It is well known that traditional mutation process is not enough to deal with the large-scale pattern loss. Moreover, the combination of life cycle strategy and chaos optimization strategy makes the algorithm difficult to fall into local optimal solution. Therefore, the optimized algorithm does not need the traditional mutation operation any more. At the same time, considering that the algorithm with enhanced global search ability has significantly weaker local search ability, we introduce the selfpollination operation from the FPA to replace the traditional mutation operation. Therein, when the number of iterations is t, the self-pollination process can be defined as follows: xit +1 = xit + ε(xjt − xkt ), ε ∈ [0, 1],

(21.16)

where xit represents the individuals to be self-pollinated, xjt and xkt represent a pair of randomly selected individuals, and ε is a random number uniformly distributed in the range of 0 to 1. In view of VNE problem, a common problem is that individuals cannot control the local search within a certain range by adding with an unprocessed vector. For example, define two individuals xjt [1,3,6] and xkt [4,1,2], and an individual xit [4,6,5] to be self-pollinated. Moreover, considering the discrete characteristics of VNE problem, ε is set to 1. According to ε(xjt − xkt ) can get the pollen ν[−3,2,4], then the individual after self-pollination is xit +1[1,8,9]. This process is shown in Fig. 21.5. It can be seen in Fig. 21.5 that the individual xit +1 is far away from the individual xit in geographical location. Therefore, this process does not reflect the characteristics of local search. To solve this problem, we define ε as a process, which is expressed as follows:

dinew =

⎧ ⎪ ⎪ ⎨1, di > 0,

0, d = 0, ⎪ i ⎪ ⎩−1, d < 0, i

(21.17)

where di is the component of pollen vector ν. Because the number of substrate nodes is continuous in the same domain, this method can allow individuals search locally in a small range at the geographic location level, as shown in Fig. 21.4. After being treated by ε, pollen ν[−3,2,4] becomes ν[−1,1,1], while individual xit [4,6,5] becomes xit +1[3,5,4] after pollination. It can be seen that the new strategy can reflect the characteristics of local search. In addition, we use the transfer probability pt to control the switching between global search and local search, p ∈ [0, 1] as shown in Fig. 21.6.

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21 VNE Strategy Based on Chaotic Hybrid Flower Pollination Algorithm. . .

Fig. 21.5 A self-pollination process

Fig. 21.6 A self-pollination process using new strategy

21.4 Strategy Model and Innovation Motivations

385

Fig. 21.7 A two-layer BP neural network for fitness rating

21.4.4 BP Neural Network The evolutionary direction of traditional meta-heuristic algorithms is usually guided by an expression called fitness function (F (xi )), which is usually the objective function multiplied by a conversion coefficient, as follows: F (xi ) = conversion coeff icient × OBJ (Gv ).

(21.18)

However, as the scale of the problem increases, the conventional fitness function based on experience is obviously insufficient to satisfy the consideration of MCDM. In contrast, it is easier to give a fitness rating (poor, average, or good) based on actual use results or experience than to give a specific fitness value. If a set of fitness ratings is regarded as a set of discrete solutions of an undetermined fitness function, it is a problem to be considered to choose an appropriate fitting method to obtain the coefficients of this function. Because ML is a better choice for solving complex fitting problems than manual adjustment [48], a two-layer BP neural network is introduced to assist the calculation of fitness [49–52], as shown in Fig. 21.7. Therein, the input value of each neuron in the input layer and the corresponding calculation method are highlighted in the same color. Moreover, the ReLU proposed in reference [53] is used as the activation function. In addition, the loss function is used to abstract the difference between the output value and the standard value of each neuron into the loss factor, and it can be defined as δoutput = yout × (1 − yout ) × (yout − yt rue ), k δhidden = xki × (1 − xki ) ×

m  n=1

j →i n δk+1 ,

ωk

(21.19) (21.20)

386

21 VNE Strategy Based on Chaotic Hybrid Flower Pollination Algorithm. . .

k where δoutput represents the error factor of neurons feedback in output layer, δhidden represents the error factor of neurons feedback in hidden layer k, yout represents n the output value, yt rue represents the true value, δk+1 represents the error factor of neurons n feedback in the next layer, m is equal to the number of neurons in the next layer, and other information that may be needed is marked in Fig. 21.7. In addition, y represents the output value of the neuron in the output layer, which is calculated by the output value of the neuron in the previous layer, and can be expressed for the following equation:

y = fBP nn (xi )

(21.21)

= ReLU (ω2 · xT 2 + b),

where ωi represents the row vector of the weight of layer i, xi represents the column vector of the neuron output value of layer i, and b represents the threshold (or bias), which measures how easy it is for a neuron to generate excitation. BP neural network can input a set of data samples with known ratings, calculate the loss δ for all neurons, and then adjust the weight and threshold value of the network through the back propagation process, which is called supervised learning. The adjust method can be formulated as i→j

ωk

i→j

= ωk

j

i→j

+ η × δk × ωk

,

bki = bki + η × δki ,

(21.22) (21.23)

where η represents a learning factor, a predefined constant used to adjust the learning j speed, δk represents the loss factor of the reverse output of the neuron j at the k layer, and bki represents the bias of the neuron i at the k layer. Moreover, the initial values of the weights and thresholds follow a normal distribution where the mean is 0 and the variance is 1. In addition, since some steps in the BPHFPA algorithm depend on specific fitness values, so the fitness level should be appropriately processed, and it can be formulated as f itness = λuser

fBP nn (xi ) × F (xi ) + (1 − λuser )F (xi ), n

(21.24)

where λuser represents the importance of the user and ranges from 0 to 1, n is equal to the number of ratings, and the ratings can be expressed as integers 1 to n, and the smaller the better.

21.5 Heuristic Algorithm Design

387

21.5 Heuristic Algorithm Design 21.5.1 Node Mapping Algorithm We use a hybrid algorithm of genetic algorithm and FPA to complete node mapping. The evolution process of traditional genetic algorithms usually includes selection, crossover, and mutation stages. In this model, the elite selection strategy is adopted to retain half of the individuals with lower fitness, a chaotic sequence is used to guide the crossover process, and the mutation phase is replaced by the self-pollination process in the FPA. In addition, the individuals are encoded as 1→j 2→j k→j n→j Xi = {Xi 1 , Xi 2 , . . . Xi k . . . Xi n }. Xi represents the mapping strategy k→j of virtual network with n virtual nodes, and xi k represents the substrate node to which the virtual node k in the virtual network is mapped. Therein, jk is equal to the number of these substrate nodes, and that the substrate node jk should satisfy the constraints of the virtual node k. Moreover, different fitness calculation methods will be used at different phases. In the global search phase, the fitness function F (xi ) is used to calculate the fitness of individuals. In the local search (self-pollination) phase, the trained two-layer BP neural network is used to calculate the fitness. In order to avoid the offsprings generated by crossover that are not feasible solutions of the VNE problem, a feasibility judgment is added. The detailed steps of node mapping algorithm are illustrated in Algorithm 42.

21.5.2 Link Mapping Algorithm The step of weight update in Algorithm 43 refers to updating the weight of the substrate links based on a certain policy. Therein, the weight of the substrate links whose remaining resources are less than the virtual links requirement will be modified to zero. In addition, the weight of the remaining substrate links will be adjusted according to a load balancing strategy. The model uses link resource unit price as link weight, and the load balancing strategy can be expressed for the following equation:  ω(ls ) =

U P (ls )(1 + λweight × ωext ra ) U sed(ls ) > U sed, U P (ls ) U sed(ls ) ≤ U sed.

ωext ra =

U sed(ls ) − U sed max{∀ls ∈ Ls |U sed(ls )} − U sed ls ∈Ls U sed(ls ) , U sed = num(ls ) U sed(ls ) =

 lv ∈M(ls )

BW (lv ),

,

(21.25)

(21.26)

(21.27) (21.28)

388

21 VNE Strategy Based on Chaotic Hybrid Flower Pollination Algorithm. . .

Algorithm 42 The node mapping algorithm based on hybrid flower pollination algorithm. Require: Gs = {N s , Ls } and Gv = {N v , Lv }. Ensure: M(Gv , N s , P s ), where P s is not determined. 1: Pt ← transfer probability; 2: Pc ← cross probability; 3: X ← maximum population capacity; 4: M ← maximum iterations; 5: Randomly generate X individuals; 6: for not reached M iterations do 7: Life judgment and add new individuals; 8: if random decimal > Pt then 9: Select X2 individuals; 10: while the number of individuals is less than X do 11: Select a pair of individual at random; 12: if random decimal < Pc then 13: Crossing this two individuals; 14: end if 15: Feasibility judgment; 16: end while 17: Reduced parental lifespan; 18: else 19: Self-pollination for the whole population; 20: Reduces the lifespan of unrenewed individuals; 21: Resets the lifespan of the updated individuals; 22: end if 23: end for 24: return The individual with the lowest fitness;

Algorithm 43 The link mapping algorithm based on shortest path algorithm. Require: Virtual network node mapping scheme. Ensure: Virtual network link mapping scheme. 1: Sort the virtual links by the required bandwidth in nonincreasing order; 2: for all the unmapped virtual links in VNR do 3: if the existing scheme of this lv can be mapped then 4: Store the existing scheme; 5: else 6: Gets the corresponding two substrate endpoints; 7: Update the weight of each substrate link; 8: Obtain the shortest path between the two endpoints; 9: Restoring weight; 10: end if 11: end for 12: return Link mapping scheme;

21.6 Performance Evaluation

389

where the range of λweight is (0,2], num(ls ) represents the number of substrate links, and M(ls ) represents a collection of mapped virtual links on a substrate link ls .

21.6 Performance Evaluation This section compared the performance of four VNE methods, including VNECGA, MD-PSO, CAN-A, and BP-HFPA. The first two and our methods are meta-heuristics, and the third is the optimal algorithm. Therein, the VNE-CGA algorithm used the genetic algorithm optimized by cellular automata to obtain the node mapping scheme. The MD-PSO algorithm used the PSO algorithm to obtain the node mapping scheme, and a candidate point selection strategy was introduced to initially screen the substrate nodes. Both algorithms used the shortest path algorithm to obtain the link mapping scheme. In addition, the CAN-A algorithm will obtain the optimal solution based on the objective function in the substrate node set and the substrate link set after preliminary screening.

21.6.1 Environment Settings and Algorithm Parameters The substrate network topology and VNR topology are generated by the GT-ITM [54] tool. The number of domains is 4, the number of nodes in a domain is 30, the CPU range of substrate nodes is 100–300, the TD of links and nodes is 1–5, the PLR range of nodes is 0.01–0.5, the UP range of BW and CPU is 1–10, the BW range of inter-domain links is 1000–3000, the BW range of cross-domain links is 3000– 6000, the connection probability between nodes is 0.5, the number range of virtual nodes in a VN is 5–10, the requested CPU and BW range is 1–10, the number of VNRs in 100 time units obeys the Poisson distribution with a mean value of 10, and the lifetime of a virtual network is 1000. In addition, about algorithm parameters, the life weight λlif e is set to 1, the transfer probability p is set to 0.7, the conversion coefficient of fitness function is set to 1, the user factor λuser is set to 0.7, and the intervention weight λweight of link load balancing strategy is set to 2.

21.6.2 Evaluation Results As can be seen from Fig. 21.8, the BP-HFPA algorithm has the best performance in average mapping quotation. This is because the BP-HFPA algorithm has excellent global search ability in the crossover process guided by chaotic sequence, while the algorithm has precise local search ability in the self-pollination process guided by neural network. Therefore, the algorithm can approximate the optimal solution within a limited number of iterations and finally obtain excellent and stable results.

390

21 VNE Strategy Based on Chaotic Hybrid Flower Pollination Algorithm. . .

Fig. 21.8 The diagram of the average quotation

Fig. 21.9 The diagram of load balancing of the substrate links

As can be seen from Fig. 21.9, the BP-HFPA algorithm performs best in link load balancing. This is because although the four algorithms all use shortest path algorithm in link mapping, BP-HFPA algorithm considers load balancing. In addition,

21.6 Performance Evaluation

391

Fig. 21.10 The diagram of revenue–cost ratio

although the CAN-A algorithm takes link load balancing into consideration when generating the candidate path set, however, because time delay is also taken into account, the load balancing situation after comprehensive consideration is not as good as our algorithm. As can be seen from Fig. 21.10, the BP-HFPA algorithm performs best in terms of the revenue–cost ratio. This is because the BP-HFPA algorithm is able to obtain solutions that take into account a variety of indicators, so it also takes into account resource consumption. The CAN-A algorithm focuses on delay and load balancing, and the MD-PSO focuses on quotation, so they perform relatively poorly. It can be seen from Fig. 21.11 that the BP-HFPA algorithm performs best in the VNRs acceptance rate. This is because the BP-HFPA algorithm adds a weight update operation and a re-mapping operation, thus avoiding most mapping failures. As can be seen from Figs. 21.12 and 21.13, the BP-HFPA algorithm has the best performance in terms of average packet loss rate and average delay. This is because the BP-HFPA algorithm can comprehensively score the scheme, and its excellent search ability enables it to approach the current optimal solution every time. In addition, although delay optimization [55, 56] is considered in the objective function of the CAN-A algorithm, its ability to reduce delay is still lower than that of BP-HFPA algorithm. This is because CAN-A removes a large number of solutions through screening, and then better solutions may be missed. In addition, the BPHFPA algorithm has excellent search capabilities, so it can approximate the optimal solution in a wide solution space as much as possible. Therefore, the BP-HFPA algorithm has more advantages.

392

21 VNE Strategy Based on Chaotic Hybrid Flower Pollination Algorithm. . .

Fig. 21.11 The diagram of the VNR acceptance ratio

Fig. 21.12 The diagram of the average time delay

It can be seen from Fig. 21.14 that the average running time of the BP-HFPA algorithm is not much different from the VNE-CGA and CAN-A algorithm, which shows that although our algorithm increases a variety of search strategies, the running time is still within the acceptable range.

21.6 Performance Evaluation

Fig. 21.13 The diagram of the average packet loss rate

Fig. 21.14 The diagram of the average running time

393

394

21 VNE Strategy Based on Chaotic Hybrid Flower Pollination Algorithm. . .

21.7 Conclusion Since VNE is an NP-hard problem, a large number of researches focus on metaheuristic algorithms. However, the existing meta-heuristic algorithms still need to be optimized when solving a VNE problem with discrete characteristics. For example, (1) the global search guided by the global optimal solution is easy to fall into the local optimal solution. (2) The search process guided by the vector cannot reflect the directionality of the vector, and it is easy to produce a large number of invalid individuals. (3) The conventional local search method by controlling step length is not suitable for VNE problem. In addition, MCDM is also worth considering. To solve these problems, this chapter discusses the design of hybrid meta-heuristic algorithm. Combining the advantages of genetic algorithm and FPA algorithm, a chaos optimization strategy is introduced to further enhance the search ability of the algorithm. In addition, a life cycle mechanism is introduced to avoid premature convergence. In addition, a method of fitness calculation based on two-layer BP neural network is proposed, which takes into account multiple targets and makes the comparison of similar individuals more accurate during the local search process. Simulation results show that this method has good performance in many aspects. In future work, we will make efforts to solve the VNE problem in some complex cases and comprehensively consider the divisibility of nodes and links and information security issues.

References 1. P. Zhang, F. Liu, G.S. Aujla, S. Vashisht, VNE strategy based on chaos hybrid flower pollination algorithm considering multi-criteria decision making. Neural Comput. Appl. 33, 10673–10684 (2021) 2. K. Tutschku, T. Zinner, A. Nakao, T.G. Phuoc, Network virtualization: implementation steps towards the future internet. J. Hum. Behav. Soc. Environ. 22(4), 463–478 (2009) 3. J. Wang, C. Jiang, H. Zhang, Y. Ren, K.-C. Chen, L. Hanzo, Thirty years of machine learning: the road to Pareto-optimal wireless networks. IEEE Commun. Surv. Tutorials 22(3), 1472– 1514 (2020) 4. C. Jiang, H. Chen, P. Zhao, N. He, C. Chen, Y. Ren, Adaptive channel sensing for asynchronous cooperative spectrum sensing scheme. IEICE Trans. Commun. E96-B(3), 918–922 (2013) 5. X. Yin, K. Zhang, B. Li, A.K. Sangaiah, J. Wang, A task allocation strategy for complex applications in heterogeneous cluster–based wireless sensor networks. Int. J. Distrib. Sensor Netw. 14(8), 1550147718795355 (2018) 6. P. Zhang, C. Wang, N. Kumar, C. Jiang, Q. Lu, K.-K.R. Choo, J.J.P.C. Rodrigues, Artificial intelligence technologies for COVID-19-like epidemics: methods and challenges. IEEE Netw. 35(3), 27–33 (2021) 7. P. Zhang, C. Wang, C. Jiang, Z. Han, Deep reinforcement learning assisted federated learning algorithm for data management of IIoT. IEEE Trans. Ind. Inform. (2021) 8. M.H. Sulaiman, Z. Mustaffa, M. Saari, H. Daniyal, M. Daud, S. Razali, A.I. Bin Mohamed, Barnacles Mating Optimizer: A Bio-Inspired Algorithm for Solving Optimization Problems (2018), pp. 265–270

References

395

9. C. Ouyang, S. Wu, C. Jiang, J. Cheng, H. Yang, Approximating ergodic mutual information for mixture gamma fading channels with discrete inputs. IEEE Commun. Lett. 24(4), 734–738 (2020) 10. W. Liu, Y. Tang, F. Yang, Y. Dou, J. Wang, A multi-objective decision-making approach for the optimal location of electric vehicle charging facilities. Comput. Mater. Continua 60(2), 813–834 (2019) 11. H. Yang, J. Yi, J. Zhao, Z. Dong, Extreme learning machine based genetic algorithm and its application in power system economic dispatch. Neurocomputing 102, 154–162 (2013) 12. H.M. Pandey, A. Chaudhary, D. Mehrotra, A comparative review of approaches to prevent premature convergence in GA. Appl. Soft Comp. 24, 1047–1077 (2014) 13. H.M. Pandey, A. Shukla, A. Chaudhary, D. Mehrotra, Evaluation of genetic algorithms selection methods, in Information Systems Design and Intelligent Applications (2016), pp. 731–738 14. H.M. Pandey, A. Chaudhary, D. Mehrotra, Grammar induction using bit masking oriented genetic algorithm and comparative analysis. Appl. Soft Comput. 38, 453–468 (2016) 15. H.M. Pandey, A. Chaudhary, D. Mehrotra, G. Kendall, Maintaining regularity and generalization in data using the minimum description length principle and genetic algorithm: Case of grammatical inference. Swarm Evol. Comput. 31, 11–23 (2016) 16. P. Zhang, C. Jiang, X. Pang, Y. Qian, STEC-IoT: a security tactic by virtualizing edge computing on IoT. IEEE Internet Things J. 8(4), 2459–2467 (2021) 17. Z. Huang, C. Wang, J. Chen, H. Tian, Optimal design of aeroengine turbine disc based on kriging surrogate models. Comput. Struct. 89(1–2), 27–37 (2011) 18. G. Venter, S.-S. Jaroslaw, Particle swarm optimization. AIAA J. 41, 129–132 (2002) 19. J. Wang, C. Ju, Y. Gao, A.K. Sangaiah, G.-J. Kim, A PSO based energy efficient coverage control algorithm for wireless sensor networks. Comput. Mater. Contin 56(3), 433–446 (2018) 20. J. Wang, Y. Gao, W. Liu, A.K. Sangaiah, G.-J. Kim, An improved routing schema with special clustering using PSO algorithm for heterogeneous wireless sensor network. Sensors 19(3), 671 (2019) 21. D. Karaboga, B. Basturk, A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J. Global Optim. 39, 459–471 (2007) 22. M. Dorigo, C. Blum, Ant colony optimization theory: a survey. Theor. Comput. Sci. 344(2–3), 243–278 (2005) 23. J. Wang, Y. Gao, K. Wang, A.K. Sangaiah, S.-J. Lim, An affinity propagation-based selfadaptive clustering method for wireless sensor networks. Sensors 19(11), 2579 (2019) 24. J. Wang, C. Jiang, L. Kuang, B. Yang, Iterative Doppler frequency offset estimation in satellite high-mobility communications. IEEE J. Sel. Areas Commun. 38(12), 2875–2888 (2020) 25. X. Yang, X. He, Firefly algorithm: recent advances and applications. Int. J. Swarm Intell. 1(1), 36 (2013) 26. E. Rashedi, N.-P. Hossein, S. Saeid, GSA: a gravitational search algorithm. Inform. Sci. 179(13), 2232–2248 (2009) 27. O. Erol, I. Eksin, A new optimization method: Big Bang Big Crunch. Adv. Eng. Softw. 37(2), 106–111 (2006) 28. S. Kumar, D. Datta, S.K. Singh, Black hole algorithm and its applications. Stud. Comput. Intell. 575, 147–170 (2015) 29. H. Shareef, A. Ibrahim, A. Mutlag, Lightning search algorithm. Appl. Soft Comput. 36, 315– 333 (2015) 30. Z. Geem, Music-inspired harmony search algorithm. Stud. Comput. Intell. 191, 163–172 (2009) 31. R. Venkata Rao, V. Savsani, J. Balic, Teaching-learning-based optimization algorithm for unconstrained and constrained real-parameter optimization problems. Eng. Optim. 44, 1–16 (2012)

396

21 VNE Strategy Based on Chaotic Hybrid Flower Pollination Algorithm. . .

32. E. Atashpaz-Gargari, C. Lucas, Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition, 2007 IEEE Congress on Evolutionary Computation, CEC, vol. 7 (2007), pp. 4661–4667 33. H. Cao, H. Han, Z. Qu, L. Yang, Heuristic solutions of virtual network embedding: a survey. China Commun. 15(3), 186–214 (2018) 34. H. Cao, S. Wu, G. Aujla, Q. Wang, L. Yang, H. Zhu, Dynamic embedding and quality of service driven adjustment for cloud networks. IEEE Trans. Ind. Inform. 16(2), 1406–1416 (2019) 35. H. Cao, Y. Guo, S. Wu, Z. Qu, H. Zhu, L. Yang, Location aware and node ranking value driven embedding algorithm for multiple substrate networks, in 2019 IEEE International Conference on Communications, ICC 2019, Shanghai, China (2019), pp. 1–6 36. H. Cao, S. Wu, Y. Hu, R. Mann, Y. Liu, L. Yang, H. Zhu, An efficient energy cost and mapping revenue strategy for inter-domain NFV-enabled networks. IEEE Internet Things J. 7(7), 5723– 5736 (2019) 37. H. Cao, Y. Zhu, G. Zheng, L. Yang, A novel optimal mapping algorithm with less computational complexity for virtual network embedding. IEEE Trans. Netw. Serv. Manag. 15(1), 356–371 (2018) 38. H. Cao, L. Yang, H. Zhu, Novel node-ranking approach and multiple topology attributes-based embedding algorithm for single-domain virtual network embedding. IEEE Internet Things J. 5(1), 108–120 (2018) 39. X. Cheng, S. Su, Z. Zhang, H. Wang, F. Yang, Y. Luo, J. Wang, Virtual network embedding through topology-aware node ranking. ACM SIGCOMM Comput. Commun. Rev. 41(2), 38– 47 (2011) 40. A. Song, W. Chen, T. Gu, H. Yuan, J. Zhang, Distributed virtual network embedding system with historical archives and set-based particle swarm optimization, in IEEE Transactions on Systems, Man, and Cybernetics: Systems (2019), pp. 1–16 41. Z. Zhang, C. Xiang, S. Su, Y. Wang, L. Yan, A unified enhanced particle swarm optimizationbased virtual network embedding algorithm. Int. J. Commun. Syst. 26(8), 1054–1073 (2013) 42. Y. Ni, G. Huang, S. Wu, C. Li, P. Zhang, H. Yao, A PSO based multi-domain virtual network embedding approach. China Commun. 16(4), 105–119 (2019) 43. L. Zhuang, G. Wang, M. Wang, K. Zhang, A virtual network embedding algorithm based on cellular automata genetic mechanism. MATEC Web Conf. 232(4), 01019 (2018) 44. J. Yu, Solution for virtual network embedding problem based on simulated annealing genetic algorithm, in 2012 2nd International Conference on Consumer Electronics, Communications and Networks (CECNet) (2012), pp. 579–582 45. Z. Zhou, X. Chang, Y. Yang, L. Li, Resource-aware virtual network parallel embedding based on genetic algorithm, in 2016 17th International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT) (2016), pp. 81–86 46. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs (Springer, Berlin, 1996), p. 387 47. F. Kuang, S. Zhang, Z. Jin, W. Xu, A novel SVM by combining kernel principal component analysis and improved chaotic particle swarm optimization for intrusion detection. Soft Comput. 19(5), 1187–1199 (2015) 48. C. Jiang, H. Zhang, Y. Ren, Z. Han, K. Chen, L. Hanzo, Machine learning paradigms for nextgeneration wireless networks. IEEE Wirel. Commun. 24(2), 98–105 (2017) 49. D.E. Rumelhart, G.E. Hinton, R.J. Williams, learning representations by back-propagating errors. Nature 323(10), 533–536 (1986) 50. J. Wang, Y. Gao, W. Liu, A.K. Sangaiah, H.-J. Kim, An intelligent data gathering schema with data fusion supported for mobile sink in wireless sensor networks. Int. J. Distrib. Sensor Netw. 15(3), 1550147719839581 (2019) 51. C. Yin, S. Ding, J. Wang, Mobile marketing recommendation method based on user location feedback. Hum. Centric Comput. Inform. Sci. 9(1), 14 (2019) 52. R. Duan, J. Du, C. Jiang,. Y. Ren, Value-based hierarchical information collection for AUVenabled Internet of Underwater Things. IEEE Internet Things J. 7(10), 9870–9883 (2020)

References

397

53. A. Krizhevsky, I. Sutskever, G.E. Hinton, ImageNet classification with deep convolutional neural networks. Adv. Neural Inform. Process. Syst. 25, 1097–1105 (2012) 54. E.W. Zegura, K.L. Calvert, S. Bhattacharjee, How to model an Internet work. IEEE Infocom 2, 594–602 (1996) 55. H.M. Pandey, Jaya a novel optimization algorithm: what, how and why, in 2016 6th International Conference-Cloud System and Big Data Engineering (2016), pp. 728–730 56. H.M. Pandey, A Modified whale optimization algorithm with multi-objective criteria for optimal robot path planning (2019)

Part VI

Conclusion

Chapter 22

Conclusion

The research of virtual network embedding (VNE) algorithm is a classic problem. On the basis of introducing the classic VNE, this book focuses on the problem of differentiated Quality of Service (QoS) requirements in this field. With the increase of Internet users, the demand for differentiated QoS is becoming more and more urgent. It is a reliable idea to provide solutions for users’ differentiated QoS demand from the perspective of VNE. This book aims to provide a comprehensive VNE solution for differentiated QoS requirements. Therefore, this book provides a more comprehensive VNE algorithm from the four aspects of security requirements, service requirements, energy consumption requirements, and load balancing requirements. In the virtual network mapping algorithm for differentiated QoS requirements, we provide a variety of solutions from different perspectives, including heuristic-based VNE algorithm, machine learning-based VNE algorithm, single-domain VNE algorithm, and multi-domain VNE algorithm. In the introduction of each VNE algorithm, we have a comprehensive description from the application background, research status, model design, algorithm design, and experimental simulation. This book gives a systematic and comprehensive introduction to the VNE algorithm for differentiated QoS requirements, which can provide reliable research ideas and directions for relevant personnel. In the future, we will continue to explore the potential user QoS requirements and carry out more in-depth research on VNE algorithm combined with cutting-edge technology.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 C. Jiang, P. Zhang, QoS-Aware Virtual Network Embedding, https://doi.org/10.1007/978-981-16-5221-9_22

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