Topology-aware virtual network embedding based on closeness centrality

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<ul><li><p>Front. Comput. Sci., 2013, 7(3): 446457</p><p>DOI 10.1007/s11704-013-2108-4</p><p>Topology-aware virtual network embedding based oncloseness centrality</p><p>Zihou WANG 1, Yanni HAN1, Tao LIN1, Yuemei XU1, Song CI1,2, Hui TANG1</p><p>1 High Performance Network Laboratory, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China</p><p>2 Department of Computer and Electronics Engineering, University of Nebraska-Lincoln, NE 68182, USA</p><p>c Higher Education Press and Springer-Verlag Berlin Heidelberg 2013</p><p>Abstract Network virtualization aims to provide a way toovercome ossification of the Internet. However, making e-</p><p>cient use of substrate resources requires eective techniques</p><p>for embedding virtual networks: mapping virtual nodes and</p><p>virtual edges onto substrate networks. Previous research has</p><p>presented several heuristic algorithms, which fail to consider</p><p>that the attributes of the substrate topology and virtual net-</p><p>works aect the embedding process. In this paper, for the first</p><p>time, we introduce complex network centrality analysis into</p><p>the virtual network embedding, and propose virtual network</p><p>embedding algorithms based on closeness centrality. Due to</p><p>considering of the attributes of nodes and edges in the topol-</p><p>ogy, our studies are more reasonable than existing work. In</p><p>addition, with the guidance of topology quantitative evalua-</p><p>tion, the proposed network embedding approach largely im-</p><p>proves the network utilization eciency and decreases the</p><p>embedding complexity. We also investigate our algorithms</p><p>on real network topologies (e.g., AT&amp;T, DFN) and random</p><p>network topologies. Experimental results demonstrate the us-</p><p>ability and capability of the proposed approach.</p><p>Keywords network virtualization, virtual network embed-ding, complex networks, closeness centrality</p><p>1 Introduction</p><p>Solving the ossification problem of the Internet with network</p><p>Received March 26, 2012; accepted July 31, 2012</p><p>E-mail:</p><p>virtualization has received a lot of attention in the past few</p><p>years [14]. The IP-based architecture makes the Internet</p><p>successful for deploying heterogeneous networks. Neverthe-</p><p>less, there are more and more emerging services on the In-</p><p>ternet which have dierent requirements that the current IP-</p><p>based Internet cannot meet. At the same time, because of the</p><p>multi-ISP environment, large-scale network innovation and</p><p>experiments cannot be tested. Many researchers have tried</p><p>to solve the problem, and a number of solutions and testbeds</p><p>have focused on network virtualization technologies [57].</p><p>In network virtualization environment, the traditional role</p><p>of the internet service provider (ISP) is divided into two roles:</p><p>the infrastructure provider (InP) who maintains the substrate</p><p>network, and the service provider (SP) who creates virtual</p><p>networks. SPs rent the physical resources from InPs to create</p><p>virtual networks and deploy end-to-end services to meet user</p><p>requirements. The principal advantage of network virtualiza-</p><p>tion is that multiple virtual networks will be able to coexist</p><p>on the same substrate network and oer various customized</p><p>services at the same time. For example, in network virtu-</p><p>alization environment, online games and IPTV can perform</p><p>simultaneously on dierent virtual networks without interfer-</p><p>ence.</p><p>Network virtualization research faces many challenges.</p><p>For example, virtual resource description, virtual network in-</p><p>stantiation, and virtual network management. The fundamen-</p><p>tal problem in network virtualization is the virtual network</p><p>embedding problem, i.e., eectively mapping the virtual net-</p><p>work requests to the substrate network with the minimum</p><p>cost of physical resources. Due to multiple objectives and</p></li><li><p>Zihou WANG et al. Topology-aware virtual network embedding based on closeness centrality 447</p><p>multiple constraints, the virtual network embedding problem</p><p>turns out to be NP-hard [3], and several heuristic algorithms</p><p>have been proposed in recent years [816]. Most of them</p><p>map the virtual networks in two independent phases. In the</p><p>first phase, the virtual nodes are mapped with greedy meth-</p><p>ods ignoring topology attributes. Then in the second phase,</p><p>the edges are mapped with shortest path-based algorithms.</p><p>However, separately considering the node and edge map-</p><p>ping processes will restrict the solution space, and lead to de-</p><p>creased utilization of substrate network resources and a lower</p><p>revenue of the InP. In this paper, we jointly consider the two</p><p>node and edge mapping phases by measuring the significance</p><p>of the nodes in the global network topology when mapping</p><p>the nodes in the first phase. And for the first time, we in-</p><p>troduce network centrality analysis into the virtual network</p><p>embedding problem. With the guidance of centrality anal-</p><p>ysis, we develop two novel algorithms to achieve eective</p><p>resource utilization.</p><p>In a network, even nodes with the same available re-</p><p>sources, vary in their importance due to their dierent loca-</p><p>tions. It is reasonable to firstly choose the substrate nodes</p><p>with the same available resources in a more important loca-</p><p>tion. Furthermore, the importance of a node is more com-</p><p>plex when the network is dynamically changing. The current</p><p>states of all the elements in the global network determine the</p><p>importance of a node. Centrality analysis provides eective</p><p>methods for measuring the importance of nodes in a com-</p><p>plex network and it has been widely used in complex network</p><p>analysis, especially in social network analysis. In the scope</p><p>of centrality analysis, the nodes can be characterized by mul-</p><p>tidimensional measures [17, 18].</p><p>To the best of our knowledge, no existing literature has ex-</p><p>plored the relationship between network centrality analysis</p><p>and the virtual network embedding problem. We map vir-</p><p>tual nodes using a fast selective algorithm based on the mea-</p><p>surement of nodes by network centrality. Dierent from ex-</p><p>isting solutions which map the nodes only considering local</p><p>resources, e.g., CPU and bandwidth of the adjacent edges,</p><p>we analyze the characteristics of network topology from a</p><p>global view, and take into consideration the topology prop-</p><p>erty in computing the resource availability, rather than only</p><p>resources of the nodes. The key advantage of this method is</p><p>that the virtual nodes are mapped to the more important sub-</p><p>strate nodes in a preferential manner. The importance of a</p><p>node is jointly determined by its own resources and location</p><p>in the entire topology.</p><p>The major contributions in this paper are summarized in</p><p>the following:</p><p> Introducing network centrality to the virtual networkembedding problem. When embedding the virtual net-</p><p>works, sorting the nodes with the topology-aware close-</p><p>ness centrality method from network centrality analysis.</p><p> Extending the closeness centrality to a new formatwhich is more appropriate for the virtual network em-</p><p>bedding problem. The classical definition of closeness</p><p>only considers the topology. Inspired by field theory, we</p><p>redefine closeness, which consider topology attributes</p><p>with the dynamic states of the nodes and edges at the</p><p>same time.</p><p> Evaluating the proposed algorithms based on networkcentrality. Our results show that, centrality based algo-</p><p>rithms achieve better performance. The acceptance ratio</p><p>of the two proposed algorithms is much higher than the</p><p>benchmark algorithm. The improved algorithm also de-</p><p>creases the cost of the substrate network.</p><p>In Section 2, the network model and the VN embedding</p><p>problem are formally defined. In Section 3, we introduce</p><p>network centrality to analyze the topologies of substrate net-</p><p>works and virtual networks. Two VN embedding algorithms</p><p>based on closeness are proposed in Section 4 and Section 5.</p><p>We evaluate the algorithms using experiments in Section 6.</p><p>In Section 7, we briefly review the related work. The paper</p><p>concludes in Section 8.</p><p>2 Virtual network embedding problem</p><p>In this section, we describe the general virtual network em-</p><p>bedding problem.</p><p>2.1 Network model</p><p>The substrate network topology of the InP is modeled as a</p><p>weighted graph, GS = (NS , ES ), where NS refers to the set</p><p>of nodes of the substrate network, while ES refers to the</p><p>set of edges of the substrate network. Each substrate node</p><p>nS NS is associated with an available CPU capacity valuec(nS ), while each substrate edge eS (i, j) ES between nodesni and n j is associated with an available bandwidth capacity</p><p>value bw(eS ).</p><p>The virtual networks of the SP are defined similarly. The</p><p>ith arriving virtual network request is denoted by GiV =</p><p>(NiV , EiV ), where N</p><p>iV and E</p><p>iV refer to the sets of virtual nodes</p><p>and virtual edges of the ith arriving virtual network request,</p><p>respectively. Each virtual node nV NiV is associated with aCPU requirement value c(nV) and each virtual edge eV (i, j) EiV between nodes ni and n j is associated with a bandwidth re-</p></li><li><p>448 Front. Comput. Sci., 2013, 7(3): 446457</p><p>quirement bw(eV). For each request, it has a lifetime td(GiV ).</p><p>If the VN request has been embedded on the substrate net-</p><p>work, the allocated resources will be dedicated to the VN</p><p>during its lifetime. When the lifetime of the VN is over, the</p><p>allocated substrate resources will be released and can be re-</p><p>allocated to other VNs.</p><p>The embedding of a virtual network refers to completely</p><p>mapping the sets of nodes and edges of a VN request GiV to</p><p>the substrate network GS . When a VN request arrives, the</p><p>InP needs to determine whether to accept it or not. If the</p><p>request is accepted, the substrate network will assign the se-</p><p>lected substrate resources to create the corresponding virtual</p><p>network. Figure 1 depicts the embedding of two VN requests</p><p>to the substrate network. Two virtual networks, Req. 1 and</p><p>Req. 2 coexist on the same substrate network. Nodes A and</p><p>B, and the edge between them are shared by the two virtual</p><p>networks. When both of the virtual networks are embedded,</p><p>the available bandwidth of edge A-B is 502010 = 20 andthe available CPUs of Node A and B are 10 and 5, respec-</p><p>tively.</p><p>Fig. 1 Virtual network embedding</p><p>2.2 Objectives of virtual network embedding</p><p>The embedding problem is a multi-objective optimization</p><p>problem with multiple constraints. Researchers may focus on</p><p>dierent objectives. Similar to the existing methods [11, 16],</p><p>here we define the objective of VN embedding as maximiz-</p><p>ing the acceptance ratio and revenue with the same cost of</p><p>substrate network in the long term.</p><p>An important objective of VN embedding is to achieve a</p><p>high acceptance ratio of the virtual network requests over</p><p>time. In the long term, the acceptance ratio can be defined</p><p>as</p><p>limT</p><p>T</p><p>t=0</p><p>VNRS</p><p>T</p><p>t=0</p><p>VNR</p><p>, (1)</p><p>where VNRS denotes the number of the virtual network re-</p><p>quests that are embedded successfully, and VNR denotes the</p><p>total number of virtual network requests.</p><p>The other two important objectives of VN embedding are</p><p>the revenue and the cost of InPs. Revenue denotes the eco-</p><p>nomic benefit of accepting VN requests. In this paper, the</p><p>revenue of an InP is described as the sum of the total virtual</p><p>resources that are embedded to the substrate network over</p><p>time. Thus, we use the following definition of revenue for a</p><p>request GiV at time t,</p><p>R(GiV , t) =</p><p>eEiVbw(ev) +</p><p>nNiVc(nv), (2)</p><p>where bw(ev) and c(nv) are the bandwidth requirement of the</p><p>virtual edge e and the CPU requirement of the virtual node n,</p><p>respectively.</p><p>Our final objective is to maximize the long-term average</p><p>revenue of the InP, which is defined as:</p><p>limT</p><p>T</p><p>t=0</p><p>R(GiV , t)</p><p>T. (3)</p><p>The cost of an InP denotes the total substrate resources al-</p><p>located to VNs. Similarly, we define the cost for a request GiVat time t,</p><p>C(GiV , t) =</p><p>pP(GiV )hops(p) bws(p,GiV) +</p><p>nNiVc(nv), (4)</p><p>where P(GiV) is the entire set of physical paths allocated for</p><p>virtual edges in GiV , hops(p) is the number of hops in a path</p><p>p, and bws(p,GiV) is the reserved bandwidth over a path p.</p><p>And the long-term average cost of the InP is defined as:</p><p>limT</p><p>T</p><p>t=0</p><p>C(GiV , t)</p><p>T. (5)</p><p>If the long-term average costs of the InPs are the same, the</p><p>higher revenue is preferred. So the long-term revenue to cost</p><p>ratio is also considered to evaluate the eciency of resource</p><p>utilization of the substrate network:</p><p>limT</p><p>T</p><p>t=0</p><p>R(GiV , t)</p><p>T</p><p>t=0</p><p>C(GiV , t)</p><p>. (6)</p><p>3 Network centrality analysis</p><p>In recent years, much research focuses on complex networks.</p><p>Many real world networks that exhibit small world and free</p></li><li><p>Zihou WANG et al. Topology-aware virtual network embedding based on closeness centrality 449</p><p>scale features (WWW, Internet, ecological, cellular, etc.) are</p><p>neither totally random, nor totally regular [19,20]. Measuring</p><p>the topology attributes of real networks is essential in com-</p><p>plex network research. Centrality analysis plays an important</p><p>role in the topology analysis of complex networks. It is pro-</p><p>posed as a measure of the contribution of network position</p><p>to the importance, influence and prominence of a node in a</p><p>network. For example, how influential a person is within a</p><p>social network, or how well a road is used within an urban</p><p>network.</p><p>In the scope of graph theory and network analysis, there are</p><p>several measures of the centrality of a node within a graph</p><p>that determine the relative importance of a node within the</p><p>graph. Four measures of centrality are widely used in net-</p><p>work analysis: degree, betweenness, closeness, and eigen-</p><p>vector centrality [17,18]. These dierent centrality measures</p><p>reflect dierent attributes of the network, and lead to dierent</p><p>results on ranking the nodes.</p><p> Degree centrality measures the local centrality and onlytakes into account the immediate ties to neighbors that</p><p>a node has, rather than indirect ties to all others. One</p><p>node might be eected by a large number of other nodes,</p><p>which might be rather disconnected from the network as</p><p>a whole.</p><p> Betweenness centrality reflects the switching capacityand applies to controlling the trac flow in the event of</p><p>congestion.</p><p> Eigenvector centrality is mainly used to measure thecentrality of directed networks.</p><p> A definition of node centrality on a global scale is basedon how close that the node is to all other nodes. In this</p><p>scale, the idea is that a node is central if it can quickly</p><p>reach all other nodes, not only its neighbors. That is</p><p>closeness centrality.</p><p>The closeness centrality approach emphasizes the distance</p><p>from a node to all other nodes in the network by focusing on</p><p>the distance from each node to all others. We select closeness</p><p>as the centrality measure in the VN embedding problem.</p><p>4 Algorithm based on classical closeness cen-trality</p><p>We propose two topology-aware VN embedding algorithms</p><p>in this paper. One is based on classical closeness [17] which</p><p>only takes into account the topology attributes. The other</p><p>is based on improved closeness which considers both the at-</p><p>tributes of the topology and the resources at the same time.</p><p>In the following, we present the classical notion of closeness</p><p>centrality and the corresponding algorithm. Then in the next</p><p>section, we improve the computing method of the closeness</p><p>value. The improved closeness measure involves the node</p><p>and edge resources.</p><p>4.1 Classical closeness centrality</p><p>In mathematics, clo...</p></li></ul>


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