Computer Networks 67 (2014) 14–25

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Computer Networks

journal homepage: www.elsevier .com/locate /comnet

Novel methods for virtual network composition

http://dx.doi.org/10.1016/j.comnet.2014.03.0211389-1286/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Tel.: +44 7760900026.E-mail addresses: ahammaa@essex.ac.uk (A. Hammad), reza.nejabati

@bristol.ac.uk (R. Nejabati), dimitra.simeonidou@bristol.ac.uk (D.Simeonidou).

Ali Hammad a,⇑, Reza Nejabati b, Dimitra Simeonidou b

a High Performance Networks Group, University of Essex, Colchester, UKb High Performance Networks Group, University of Bristol, Bristol, UK

a r t i c l e i n f o a b s t r a c t

Article history:Received 11 October 2013Received in revised form 15 February 2014Accepted 24 March 2014Available online 31 March 2014

Keywords:Network virtualizationVirtual network compositionVirtual network mapping

Network virtualization has been proposed as a technology that aims to solve the Internetossification. Central to the network virtualization is a virtual network composition mech-anism providing an efficient mapping of virtual nodes and links onto appropriate physicalresources in the network infrastructure.

This paper proposes a novel backtracking heuristic algorithm for virtual networkcomposition. Based on this algorithm, two approaches with two different objectives arepresented. The first approach (Backtracking-CR) aims to compose a virtual network usingthe least amount of network resources, while the second (Backtracking-LB) applies loadbalancing for virtual network composition. Furthermore, a linear programming approachthat optimizes the virtual network composition with an objective of using the least amountof network resources is presented and used to bench mark the heuristic algorithm.Simulation results show that using less network resources by applying linear programmingor Backtracking-CR does not produce higher number of successfully mapped virtualnetworks when is compared to load balancing approach. Results also show that theproposed heuristic algorithm is scalable to large physical and virtual networks with respectto the computation time.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Future Internet services are characterized by globaldelivery of high-performance applications over a high-capacity dynamic network. This is mainly driven by theemergence of ever more bandwidth demanding, dynamicand heterogeneous e-services such as cloud computing,HD gaming, HD/UHD video on demand streaming, andIPTV. Internet has started to face technical problems andsuffer from ossification in supporting these types ofheterogeneous and network-based applications [1]. A keychallenge for network operators is deployment of dynamic

infrastructures capable of supporting heterogeneous andnetwork-based applications with several network resourceusage patterns. Network virtualization has been proposedas a technology that aims to solve the issue of Internetossification and provide flexibility for future Internet. Itenables infrastructure providers to partition their physicalnetwork infrastructure into multiple application/servicespecific and customized virtual networks without signifi-cant investment or change in the physical infrastructure.In addition to the infrastructure provider, the role of ser-vice provider has emerged in the network virtualizationbusiness model. A service provider can lease a virtual net-work from one or several infrastructure providers and useit to deploy various protocols and offer services to the endusers. [1–4].

The main advantages of applying network virtualizationcan be summarized as below:

A. Hammad et al. / Computer Networks 67 (2014) 14–25 15

� Each Virtual Network (VN) can have different networkarchitecture including network protocols. As a result,network virtualization provides heterogeneity and cansupport the trend to the Internet pluralist model [1].� Dedicated VNs can be used to test the new technologies,

protocols, network architectures and applications bydevelopers and researchers. Therefore, Internet innova-tion is easier with network virtualization [5].� Network virtualization can be used to support QoS over

network by dedicating a separate VN for each serviceclass or application type [6].� Network virtualization can minimize the cost of owning

physical network elements [7].

Network virtualization is defined as composition of iso-lated VNs simultaneously coexisting over a shared physicalinfrastructure. A VN is a set of virtual nodes interconnectedby virtual links. Virtualization of network nodes and linksis achieved by partitioning and/or aggregation of physicalnetwork resources i.e. routers and links capacities.

VN composition is the process of mapping a VN onto aphysical infrastructure, and it comprises two main actions:virtual node mapping where appropriate physical nodesmust be reserved, and virtual link mapping where virtuallinks must be assigned to suitable physical paths. SinceVNs share the same infrastructure resources, an efficientVN mapping approach is essential to accommodate asmany VNs as possible.

This paper introduces a novel heuristic mapping algo-rithm for VN composition suitable for packet networks(e.g. IP network). The important features of the proposedalgorithm are: on demand and real time VN mapping,VN mapping with network constraints on both virtualnodes and links, one stage mapping of nodes and links aswell as VN mapping with arbitrary topology e.g. star,mesh, ring, etc. Furthermore, a new integer linearprogramming (ILP) approach for optimal mapping is pre-sented. Finally, performance of the proposed approachesare compared.

The rest of this paper is organized as follows. Section 2provides an overview of related works. Section 3 describesthe network model used in this paper. In Section 4, the pro-posed heuristic mapping algorithm and its two variationsare presented. Section 5 introduces our new ILP approach.Performance evaluation of the proposed approaches is pre-sented in Section 6. Finally, Section 7 concludes this paper.

2. Contribution and overview of related work

VN mapping problem is considered as NP-hard problem[8–10] and therefore many of the proposed approachesrestrict the solution space and solve part of the problemin order to reduce its complexity. There are two main cat-egories of approaches that deal with VN mapping: (1)approaches with coordinated node and link mapping and(2) approaches with independent mapping of nodes andlinks in different stages. The first category is more flexiblein selecting different node and link mapping options andoptimizing this selection to suit a predefined objective,and it has been proved to be more efficient [8]. However,

many of the existing algorithms apply node mappingbefore link mapping with no coordination between thetwo stages [5,9,11,10].

Very few research works have been published on coor-dinated mapping of virtual nodes and links such as [8,12].Authors in [8] propose an approach with an objective ofimproving the VN acceptance ratio and balancing the traf-fic load on the network. They use a linear program to findan optimal solution for node mapping as first stage.Multi-commodity flow algorithm is used to map the vir-tual links in the second stage. Although node and linkmapping are coordinated, they are still two consecutivestages. Authors in [12] propose an algorithm with thegoal of minimizing the mapping cost. Choosing the virtualnodes and links for mapping is done by an optimizationprocess that considers the constraints and availableresources as inputs and returns a set of preferred map-ping options. Processing capacity of node and data ratecapacity of link are the considered constraints in evaluat-ing this algorithm.

Authors in [13] present a path-based linear program-ming model for solving the VN mapping problem. In thismodel, a set of paths that can be used to accommodateeach virtual link is predefined, which leads to restrictionin the solution space. Therefore, they propose a columngeneration process which attempts to find optimal solu-tions by gradually incorporating new paths into the solu-tion base. Authors in [14] propose a pro-active and ahybrid policy heuristic to solve the survivable VN embed-ding problem which takes into account that the physicalnetwork might not be fully operational all the times. Singlelink failures are considered, and the proposed heuristicimplements backup policies to handle these failures.

Other relevant published research works are mainlybased on using two separate stages for node and link map-ping. For instance, the authors in [5] propose mappingalgorithms with the goal of minimizing congestion at thephysical nodes and links. They address the problem gener-ally without considering constraints like packet processingcapability and geographical location of node, and band-width of link or interface. The proposed mapping approachin [9] uses path splitting by which virtual link can bemapped onto multiple substrate paths. This approachmaps a set of VN requests together by mapping the nodesfirst and then the links. The authors in [10] propose an off-line distributed VN mapping where all VN requests areknown in advance and network resources are unlimited.The VN mapping in [11] is restricted to backbone-star VNtopology. In addition, the possibility of rejecting requestsdue to unavailability of resources is not addressed in[11], and link bandwidth is the only considered constraint.

A framework for VN mapping where various mappingalgorithms can run in a distributed and parallel way isintroduced in [15]. This framework aims to spread thecomputation load across the network while keeping themapping cost comparable to other centralized approaches.Authors in [16] investigate how a VN mapping algorithmcan be modified to consider energy-efficiency with the goalto have minor impact on the performance regarding otheroptimization criteria.

16 A. Hammad et al. / Computer Networks 67 (2014) 14–25

In this paper, we introduce a new backtracking heuristicVN mapping algorithm. The proposed algorithm appliescoordinated mapping of virtual nodes and links in onestage. This leads to a wider solution space and high flexibil-ity in solution optimization. The constraints considered onnodes (e.g. routers) are packet processing capacity/capabil-ity and geographical location, while bandwidth and delayare the constraints on links. The proposed algorithm designis flexible and generic enough and therefore it can beextended to take into account other constraints. Inaddition, we study the influence of changing the optimiza-tion mechanisms applied in this algorithm by branching itinto two approaches with two different objectives. The firstapproach, called Backtracking-CR (cost reduction), aims tominimize the amount of physical resources used for VNmapping. Backtracking-LB (load balancing) is thesecond approach and its objective is to balance the loadover the available network resources. This proposedbacktracking heuristic algorithm is first introduced in ourprevious conference paper [17] with initial set of results.In the current paper, an extended and updated version ofthe algorithm with more details and research results areprovided.

Furthermore, we present in this paper a new integer lin-ear programming (ILP) approach for mapping virtual net-work considering the same constraints mentioned for theheuristic algorithm. This ILP addresses for the first timenode and link mapping in one stage with the objective tofind the mapping solution with the minimum mappingcost. Comparison between performance of the proposedapproaches in terms of VN request acceptance ratio (i.e.successful mapping of VN requests), cost, physical resourceutilization and running time is carried out. We investigatein this paper the scalability of the proposed approaches forlarge scale networks.

3. Network modelling

3.1. Physical and virtual networks

The physical network is modelled as a weighted undi-rected graph denoted as GR ¼ ðNR; LRÞ where NR is set ofphysical nodes and LR is set of physical links. We representa path between a source node ðsRÞ and a destination nodeðdRÞ by PðsR; dRÞ : sR; dR 2 NR. A path is a set of physical linksthat connect source node to destination node. The set ofphysical paths is denoted by PR. VN is also modelled as aweighted undirected graph denoted by GV ¼ ðNV ; LV Þwhere NV is set of required virtual nodes and LV is set ofrequired virtual links. A subgraph of GV is denoted assubGV .

The attributes and constraints of nodes and links (phys-ical/virtual) are denoted as the following:

� CðnRÞ is the packet processing capacity available in aphysical node nRðnR 2 NRÞ. This refers to the packetprocessing capability of a router. CðnV Þ is the required

processing capacity of the virtual node nV ðnV 2 NV Þ,which represents the required packet processing capa-bility of a virtual router.� locXðnRÞ and locYðnRÞ are x and y coordinates that repre-

sent the location of a physical node nRðnR 2 NRÞ. Simi-larly, locXðnV Þ and locYðnV Þ are x and y coordinatesthat represent the required location of a virtual nodenV ðnV 2 NV Þ. We use DisðnV Þ to represent the maximumlocation distance difference between a virtual node nV

and its hosting physical node. DisðnV Þ defines a distancerange within which physical nodes can be selected tohost nV .� BðlRÞ is the available bandwidth in a physical link

lRðlR 2 LRÞ. BðlV Þ is the required bandwidth of a virtuallink lV ðlV 2 LV Þ.� DðlRÞ is the delay of a physical link lR. DðlV Þ is the

required maximum delay of a virtual link lV .

EðlRÞ is used to denote a set of two end points of a phys-ical link lR. nR 2 EðlRÞ if nR is an end point of lR. Similarly,EðlV Þ is used to denote a set of two end points of a virtuallink lV . nV 2 EðlV Þ if nV is an end point of lV .

3.2. VN mapping

The virtual node mapping is defined by the functionMN : NV ! NR; MNðnV Þ ¼ nR : nV 2 NV ; nR 2 NR. This meansthat the virtual node nV is mapped onto the physical nodenR.

The virtual link mapping is defined by the functionML : LV ! PR : MLðlV ðsV ; dV ÞÞ ¼ PðsR; dRÞ : lV ðsV ; dV Þ 2 LV : sV ;

dV 2 NV ; PðsR; dRÞ 2 PR : sR; dR 2 NR; MNðsV Þ ¼ sR;MNðdV Þ ¼dR: This means that the virtual link lV ðsV ; dV Þ ismapped onto the physical path PðsR; dRÞ, and the two endpoint sV ; dV of this virtual link should be mappedonto the two end points sR; dR of the physical pathrespectively.

4. Backtracking mapping algorithm

Algorithm 1. MatchingðGV ;GRÞ

1: for all nV 2 NV do2: Match nV attributes to physical nodes attributes

and find a set of physical nodesS : 8nR 2 S; MðnV Þ ¼ nR is possible

3: if S ¼¼ ; then4: break// VN request cannot be mapped5: else6: candidatePhysicalNodes½nV � ¼ S7: end if8: end for

9: subGV ¼ ;10: result ¼ MappingðGV ;GR; subGV ,

candidatePhysicalNodes½�Þ

A. Hammad et al. / Computer Networks 67 (2014) 14–25 17

Algorithm 2. MappingðGV ;GR; subGV , candidatePhysical ¼

Nodes½�Þ

1: Select unmapped virtual node nV

2: SortðcandidatePhysicalNodes½nV �Þ3: for all nR 2 candidatePhysicalNodes½nV � do

4: for all lV ðnV ; dV Þ connected to nV :

dV 2 subGV;MNðdV Þ ¼ dR do

5: PðnR; dRÞ ¼ mapVirtualLinkðlV ;nR; dR;GR,

maxLinksNumÞ6: if PðnR; dRÞ ¼¼ ; then7: break// go to line 3 to try different physical

node8: end if9: end for

10: if all virtual links connecting nV to subGV havebeen mapped successfully then

11: MNðnV Þ ¼ nR

12: subGV ¼ subGV þ nVþ the mapped virtuallinks

13: if ðsubGV ¼¼ GV Þ then14: return successful mapping15: else

16: Recursive call of MappingðGV ;GR; subGV ,candidatePhysicalNodes½�Þ

17: if previous call is successful then18: return success to the previous stage19: else20: MNðnV Þ ¼ ;21: Remove nR from

candidatePhysicalNodes½nV �22: if candidatePhysicalNodes½nV � ¼¼ ; then23: return failure to the previous stage24: end if25: end if26: end if27: end if28: end for

In this section, we present a new backtracking heuristicalgorithm for virtual network mapping. An initial matchingprocedure (Algorithm 1) is applied first to find a set of can-didate physical nodes for each virtual node. Any physicalnode in this set can be used to map the corresponding vir-tual node. The matching procedure finds all the possiblecandidate physical nodes that satisfy the required virtualnodes attributes (packet processing capacity, location)and store them in a matrix (i.e. candidatePhysicalNodes½�).Then, it calls the mapping algorithm (mapping call:Algorithm 1 line 10).

The proposed backtracking mapping algorithm (Algo-rithm 2) constructs a subgraph gradually by mapping andadding virtual nodes and links to this subgraph until all vir-tual nodes and links are mapped. At each stage, the algo-rithm selects a virtual node that is not mapped, to beadded to the subgraph (Algorithm 2 line 1). The algorithm

selects one of the candidate physical nodes to hostthe selected virtual node. In Algorithm 2 line 2, the candi-date physical nodes are sorted using the procedureSortðcandidatePhysicalNodes½nV �Þ. This process determineswhich physical node will be selected first as a possiblenode for hosting the current virtual node. The sorting crite-rion is related to the main objective of the approach (costreduction or load balancing) as explained later in thissection.

After selecting the physical node, the algorithmattempts to map the virtual links (loop at Algorithm 2 line4) that connect the current virtual node to the virtualnodes that exist in the subgraph. In case those virtual linksdo not exist, the loop terminates and the virtual node willbe added to the subgraph. If a virtual node exits in the sub-graph, this means that the virtual node has been mappedonto a physical node in a previous stage (In Algorithm 2line 4, dV 2 subGV

;MNðdV Þ ¼ dR where dV is a virtual nodemapped onto dR). Therefore, the two end points of therequired path that can be used to map the selected virtuallink (selected in loop at Algorithm 2 line 4) are known. Thealgorithm mapVirtualLink (called at Algorithm 2 line 5, anddescribed in Algorithm 3) that is explained in the next sub-section is used to find a physical path between two physi-cal nodes to map a virtual link.

If the algorithm mapVirtualLink cannot find a path foreach virtual link, different candidate physical node isselected and the same operation is repeated again (loopat Algorithm 2 line 3). If mapping the virtual links is suc-cessful, the algorithm adds the virtual node and links tothe subgraph (Algorithm 2 line 12). Mapping is success-ful if all virtual nodes and links are added to the sub-graph (Algorithm 2 line 13). Otherwise, recursive call isapplied (Algorithm 2 line 16) to map the virtual nodeand links in the next round. If there are no more candi-date physical nodes for mapping the selected virtualnode, the algorithm backtracks to the previous mappedvirtual node and selects different candidate physicalnode for mapping it (Algorithm 2 line 23). As a result,the algorithm is able to try different candidate physicalnodes to host the virtual nodes that represent the endpoints of virtual links, so that it can select the best phys-ical nodes that lead to the best possible physical path tomap the virtual links (using the algorithm mapVirtual-Link). This optimization of physical nodes and links selec-tion in one stage makes the algorithm more flexible insearching for best solution.

mapVirtualLink algorithm description:The algorithm mapVirtualLink is responsible for map-

ping a virtual link onto a physical path that satisfies therequirements of the virtual link. As it was explained inprevious section, this algorithm is called in VN mappingprocess after two candidate physical nodes are identifiedfor mapping the two end points (i.e. virtual nodes) of avirtual link. This algorithm can be called several timesfor each virtual link and with different sources and desti-nations during the recursive process of VN mapping algo-rithm, so that node and path selection is optimized byexamining different candidate physical nodes for each vir-tual node.

18 A. Hammad et al. / Computer Networks 67 (2014) 14–25

Algorithm 3. mapVirtualLinkðlV ; sR; dR;GRðNR; LRÞ;maxLinks

NumÞ

1: for all nR 2 NR do2: numOfLinks½nR� ¼ 13: residualBandwidth½nR� ¼ �14: end for5: numOfLinks½sR� ¼ 06: residualBandwidth½sR� ¼ 17: pathFound ¼ false8: visitedNodesSet ¼ ;9: while !pathFound do10: select current node nR R visitedNodesSet : nR

has the minumum numOfLinks value if the goalis to get the shortest path/ nR has the maximumresidualBandwidth value if the goal is loadbalancing

11: for all mR 2 NR : mR is adjacent to

nR;mR R visitedNodesSet do

12: if ðnumOfLinks½nR� þ 1 <¼ maxLinksNumÞand ðdelay½nR� þ DðlRðnR;mRÞÞ <¼ DðlV ÞÞand ðBðlRðnR;mRÞÞ >¼ BðlV ÞÞ then

13: previous½mR� ¼ nR

14: numOfLinks½mR� ¼ numOfLinks½nR� þ 1

15: residualBandwidth½mR� ¼BðlRðnR;mRÞÞ�BðlV Þ16: delay½mR� ¼ delay½nR� þ DðlRðnR;mRÞÞ17: if mR ¼ dR then18: pathFound ¼ true19: return the path from sR to mR

20: end if21: end if22: end for23: add nR to visitedNodesSet24: end while

The algorithm mapVirtualLink (Algorithm 3) is a modi-fied version of Dijkstra algorithm [18] that is used to findthe shortest path between source and destination. A mainmodification is that mapVirtualLink deals with the fact thatthe returned path should have enough bandwidth to satisfythe required bandwidth of the virtual link, so that the band-width availability in physical links is considered whensearching for possible path. In addition, the required delayof virtual link is considered as the maximum delay over thepath, and the parameter maxLinksNum is considered as themaximum number of cascaded physical links that can beincluded in the path. Furthermore, this algorithm is ableto optimize the selection of physical links by utilizing thetwo different optimization approaches as explained later.

The algorithm mapVirtualLink has five input parame-ters: the virtual link, the source and destination physicalnodes for mapping the two end points of the virtual link,the physical network topology and the parameter max-LinksNum. It explores the network starting from the sourcenode and attempts to reach the destination. When examin-ing the network, a state info is stored at each new explored

node (n) to describe the discovered path (P) connecting thesource node to n. This state info contains the following:

� previous½n�: The previous node of n in P.� numOfLinks½n�: The number of links in P.� delay½n�: The current delay over P.� residualBandwidth½n�: The residual bandwidth in the

physical link connecting n to the previous node.

State info of each node is initialized (Algorithm 3 lines1–8) before start exploring the network and mapping eachvirtual link. Then at each stage, a new node (that is notexamined yet) is selected (Algorithm 3 line 10) startingfrom the source node. This selection is based on the objec-tive of the algorithm i.e. to find the shortest path or to bal-ance the traffic load. After that, the adjacent nodes of thenew examined node are explored. For each adjacent node,the conditions of bandwidth availability, maximum delayand maximum number of physical links in the discoveredpath are checked (Algorithm 3 line 12). State info for theadjacent nodes that satisfy the previous conditions isstored (Algorithm 3 lines 13–16) for using in the nextstages. If the destination node is one of these adjacentnodes, this means that the path is found and the algorithmterminates and returns this path (Algorithm 3 lines 18–19).

Optimization approaches:Two optimization approaches with two different objec-

tives are designed for the proposed backtracking algo-rithm. Each approach applies different mechanisms forphysical nodes and links selection to achieve its objective.The two approaches are described as follows:

(A) Backtracking with cost reduction (Backtracking-CR): The objective of this approach is to map each VN withthe minimum mapping cost (i.e. minimizing amount ofrequired physical resources). The candidate physical nodesfor each virtual node are sorted in descending order basedon the number of their direct connections to other alreadyselected physical nodes in previous rounds of mapping pro-cess. Using this sorting criterion, the selected physicalnodes are more likely to be adjacent. For virtual link map-ping, this approach maps each virtual link onto the shortestpath that satisfies its requirements (bandwidth and delay).For this purpose, the algorithm mapVirtualLink utilizes theleast possible number of physical links when searchingfor the possible path (i.e. the goal is to find the shortest pathwhen selecting the current node at Algorithm 3 line 10).

(B) Backtracking with load balancing (Backtracking-LB): The objective of this approach is to balance the load(link bandwidth and node capacity allocation to VNs) overthe available physical resources. The physical nodes andlinks with more residual available capacities are more pre-ferred for selection. For this purpose, the candidate physi-cal nodes of each virtual node are sorted in descendingorder based on the residual available packet processingcapacity of each physical node. For virtual link mapping,this approach attempts to use the least congested links inthe paths selected for mapping virtual links. The algorithmmapVirtualLink prioritizes the links with more residualavailable bandwidth when searching for a path (i.e. thegoal is to balance the load when selecting the current nodeat Algorithm 3 line 10).

Fig. 1. Example of physical network topology and VN request.

A. Hammad et al. / Computer Networks 67 (2014) 14–25 19

Example of mapping VN request:In this example, we present a scenario for mapping a VN

request onto a physical network to show how the proposedheuristic algorithm works. The physical network and VNrequest are shown in Fig. 1. Each physical node is denotedby ‘pn’ and its ID, and each virtual node is denoted by ‘vn’and its ID. For the sake of simplicity, the capacities andother attributes of physical and virtual resources are notshown. Therefore, this example explains the heuristic algo-rithm without focusing on any specific objective (i.e. loadbalancing or cost reduction). We assume that the matchingprocedure returns candidate physical nodes for each vir-tual node as shown in Table 1. The stages followed bythe algorithm to map the VN request are listed in Table 2.The result of the mapping is shown in Fig. 2.

Table 2Stages of VN composition using the heuristic algorithm.

Stage 1: Mapping vn1 onto pn2Subgraph ¼ fvn1g

Stage 2: Mapping vn2 onto pn4Mapping the virtual link vn1-vn2 onto the physical pathSubgraph ¼ fvn1;vn2g

Stage 3: Mapping vn3 onto pn6Mapping the virtual link vn1-vn3 onto the physical pathMapping the virtual link vn2-vn3 onto the physical pathSubgraph ¼ fvn1;vn2;vn3g

Stage 4: Mapping vn4 onto pn8Failure in mapping the virtual link vn2-vn4, so the algor

Stage 5: Mapping vn3 onto pn7Mapping the virtual link vn1-vn3 onto the physical pathMapping the virtual link vn2-vn3 onto the physical pathSubgraph ¼ fvn1;vn2;vn3g

Stage 6: Mapping vn4 onto pn8Mapping the virtual link vn2-vn4 onto the physical pathMapping the virtual link vn3-vn4 onto the physical pathSubgraph ¼ fvn1;vn2;vn3;vn4g = VN graph (VN Mappin

Table 1Matching procedure output.

Virtual node Candidate physical nodes

vn1 pn1, pn2vn2 pn4vn3 pn6, pn7vn4 pn8

5. ILP approach for optimal VN mapping

In this section, we present our ILP approach for map-ping a VN with the minimum cost. This approach appliesnode and link mapping simultaneously considering thesame aforementioned constraints. In this section, the deci-sion variables used to model the problem are introduced,then the objective function is described and finally theconstraints are explained.

pn2-pn1-pn4

pn2-pn5-pn7-pn6pn4-pn6

ithm backtracks to the state of stage 3 to try different mapping of vn3

pn2-pn5-pn7pn4-pn6-pn7

pn4-pn9-pn8pn7-pn8

g is successful)

Fig. 2. Example result of VN composition.

20 A. Hammad et al. / Computer Networks 67 (2014) 14–25

Decision variables and objective function:The proposed ILP formulation utilizes the decision vari-

ables XðnV ;nRÞ 2 f0;1g; nV 2 NV ; nR 2 NR to indicate whereeach virtual node is located (XðnV ;nRÞ ¼ 1 means that nV is

located at nR). The decision variables YðlV; lRÞ 2 f0;1g;

lV 2 LV ; lR 2 LR are used to indicate which physical links

are used for mapping a virtual link. In addition, ZðlV; nRÞ 2

f0;1g; lV 2 LV ; nR 2 NR indicate if a physical node is usedfor mapping a virtual link (the physical node can be usedfor routing in the selected path or to host an end point of avirtual link). The objective is minimizing the mapping cost:

MinimizeCOST ¼

PnV ;nR XðnV ;nRÞCðnV Þ þ

PlV ;lR YðlV

; lRÞBðlV Þ.

Constraints and their descriptions:

1:P

nR XðnV ;nRÞ ¼ 1; 8nV 2 NV

2:P

nV XðnV ;nRÞ <¼ 1; 8nR 2 NR

3: XðnV ; nRÞ <¼ ZðlV ;nRÞ; 8nR 2 NR; lV 2 LV ; nV 2 EðlV Þ4: XðnV ; nRÞ þ

PlR jnR2EðlRÞYðl

V; lRÞ <¼

Fig. 3. VN acceptance ratio for different average VN request arrival rates:(A) small network scenario and (B) large network scenario.

2ZðlV ;nRÞ; 8nR 2 NR; lV 2 LV ; nV 2 EðlV Þ5:P

nV XðnV ; nRÞCðnV Þ <¼ CðnRÞ; 8nR 2 NR

6: XðnV ;nRÞabs locXðnV Þ � locXðnRÞ� �

<¼ DisðnV Þ,8nV 2 NV ;nR 2 NR

7: XðnV ;nRÞabs locYðnV Þ � locYðnRÞ� �

<¼ DisðnV Þ,8nV 2 NV ; nR 2 NR

8:P

lV YðlV ; lRÞBðlV Þ <¼ BðlRÞ; 8lR 2 LR

9:P

lR YðlV ; lRÞDðlRÞ <¼ DðlV Þ; 8lV 2 LV

Constraint (1) ensures that each virtual node has to bemapped onto a single physical node. Constraint (2) ensuresthat a physical node can accommodate at most one virtualnode from a VN request. This constraint does not restrictany physical node from accommodating several virtualnodes from different VN requests. Constraint (3) and (4)ensure that each virtual link is mapped onto a physicalpath and they refer to flow conservation conditions. Con-straint (5) represents the capacity bound of each physicalnode. Constraints (6) and (7) represent the location con-straints of each virtual node. Constraint (8) representsthe bandwidth bound of each physical link. Constraint (9)represents the delay bound of each virtual link.

The open source GNU Linear Programming Kit (GLPK)library [19] is used to implement our ILP formulation.

6. Performance evaluation

In this section, we describe the simulation environmentfollowed by the performance metrics used for the evalua-tion of the proposed approaches. Then, the main simula-tion results are presented.

6.1. Simulation environment

A main goal of the simulation is to compare the heuris-tic with ILP in some network scenarios where ILP can beexecuted in reasonable time scale. The physical networkin our experiment is randomly generated with consideringtwo network scenarios: (1) small network scenario wherethe physical network has 25 nodes located in 8� 8 geo-graphical grids and (2) large network scenario where thephysical network has 50 nodes located in 15� 15 geo-graphical grids. In both scenarios, the initial packet pro-cessing capacity of each physical node and the initialbandwidth of each physical link are selected to be 100units. Using uniform distribution, the delay of each physi-cal link is randomly selected between 50 and 100 units.The topology of the physical network is defined by a prob-ability to connect each pair of physical nodes, and thisprobability is set to 0.5 as similar to [8]. This is based onthe pure random graph model that is most commonly usedto test networking problems [20].

In each scenario, we simulate 1000 randomly generatedrequests for VNs (A VN request describes the VN topologyand its constraints i.e. delay and bandwidth of each link aswell as packet processing capacity and geographical loca-tion of each node) that arrive in a Poisson process withan average arrival rate that is varied between 2 and 20

A. Hammad et al. / Computer Networks 67 (2014) 14–25 21

VN requests per 100 time units. The VN lifetime is selectedby an exponential distribution with an average of 1000time units. The number of virtual nodes in each VN is uni-formly distributed between 2 and 5 in the small networkscenario and 2 and 10 in the large network scenario.

In both scenarios, each pair of virtual nodes is ran-domly connected with a probability 0.5. The processingcapacity requirements of virtual nodes are uniformly dis-tributed between 1 and 20 units. The required band-width of each virtual link is a random number between1 and 50 units using uniform distribution. This distribu-tion is also used to generate random maximum delayrequirements for virtual links between 100 and 1000units. Each virtual node is assigned randomly a requiredlocation coordinates based on the grids in the corre-sponding network scenario. In addition, an accepted dis-tance difference between the location of a virtual nodeand the location of a physical node that can be usedfor mapping is randomly selected.

The hardware used to run the simulation is Intel Core 2Duo 3.33 GHz with 4 GB RAM.

Fig. 4. Average mapping cost for different average VN request arrival r

6.2. Performance metrics

We use the following metrics to evaluate and comparethe proposed approaches:

� Acceptance ratio: This ratio measures the percentage ofaccepted VN requests (i.e. sucessful mapping of VNrequests).� Mapping cost: The cost measures the amount of physical

resources used to map a VN request. This metric is equalto the total packet processing capacity units and band-width units reserved for the VN [8].� Running time: This measures the time spent by an

approach to map a VN request.� Node and link utilization: This measures the usage of

each physical node/link.

6.3. Evaluation results

The simulation results are recorded for both small andlarge network scenarios. Heuristic algorithm was scalable

ates: (A) small network scenario and (B) large network scenario.

22 A. Hammad et al. / Computer Networks 67 (2014) 14–25

to large network scenario and produced similar conclu-sions in both scenarios with some increase in the runningtime in large network scenario. On the other hand, whileall ILP results in small network scenario are presented, onlyaverage running time considering maximum time of 1 h ispresented for ILP in large network scenario due to scalabil-ity restriction. Based on the recorded simulation results,we summarize our key observations below:

(1) As expected and shown in Fig. 3, increasing the aver-age VN request arrival rate leaded to decrease in theVN request acceptance ratio for all approaches inboth scenarios. This is because the higher the aver-age arrival rate, the more VNs that the network

Fig. 5. Average physical node utilization for different average VN request arr

has to accommodate simultaneously, which leadsto more network resources consumption that canblock future requests.

(2) Performance of all approaches in terms of VNrequest acceptance ratio is very close. However,Backtracking-LB produced slightly better ratio, andthis is more evident in the small network scenarioas depicted in Fig. 3. Backtracking-LB selects physi-cal nodes and links with more residual capacitiesfor mapping virtual nodes and links. It avoids usingphysical resources with high loads when mappinga VN request. As a result, congestion and bottleneckswhich can block future VN requests are less likely tohappen in the network when using this approach.However, this approach uses more network

ival rates: (A) small network scenario and (B) large network scenario.

A. Hammad et al. / Computer Networks 67 (2014) 14–25 23

resources. On the other hand, ILP approach andBacktracking-CR optimize the mapping cost withoutconsidering load balancing or congestion avoidance.Hence, they optimize the network resource alloca-tion for current VN request, and they do not considerthe state of network for future requests.

(3) Backtracking-CR produced mapping cost close to theoptimal cost resulted from the ILP approach asshown in Fig. 4, while Backtracking-LB generatedthe highest mapping cost. Backtracking-CR aims touse the least amount of physical resources for map-ping a VN request by using physical nodes withshortest paths between them. By contrast, applyingload balancing in Backtracking-LB might increasethe mapping cost because this approach prefers along path for mapping a virtual link if the includedphysical links are less congested than the physicallinks in a shorter path.

Fig. 6. Average physical link utilization for different VN request arrival

(4) The results depicted in Fig. 5 show that averagephysical node utilization is almost equivalent forall approaches. Fig. 5 also shows (through thedepicted confidence interval) that the average nodeutilization has less margin of error when using Back-tracking-LB, which means that node utilization ismore uniform and balanced.

(5) As shown in Fig. 6, average link utilization is thehighest when applying Backtracking-LB. The resultsshow that Backtracking-LB method when is com-pared to Backtracking-CR has up to 60% higher aver-age link utilization. ILP approach produced thelowest average link utilization (in small networkscenario). Fig. 6 also shows that average link utiliza-tion has less margin of error when using Backtrack-ing-LB. This indicates that link utilization is moreuniform and balanced when using Backtracking-LB.Backtracking-CR produced the highest margin of

rates: (A) small network scenario and (B) large network scenario.

Table 3Average mapping running time for different average VN request arrivalrates (small network scenario).

Average VN requestarrival rate

ILP Backtracking-CR

Backtracking-LB

Average running time (seconds) (small network scenario)2 0.276 0.044 0.0444 0.247 0.042 0.0446 0.193 0.039 0.1278 0.13 0.038 0.159

10 0.133 0.034 0.13112 0.106 0.032 0.12214 0.104 0.03 0.09516 0.095 0.027 0.11418 0.099 0.027 0.11720 0.097 0.025 0.116

24 A. Hammad et al. / Computer Networks 67 (2014) 14–25

error. In conclusion, the network is less likely tohave highly utilized or underutilized nodes and linkswhen applying Backtracking-LB.

(6) The average running time of both heuristic algo-rithm and ILP for the small network scenario wasvery short and less than one second for all averagearrival rates as shown in Table 3 (considering bothBacktracking-CR and Backtracking-LB). The averagerunning time for Backtracking-CR was the shortestand less than one second for all average arrival ratesin the large network scenario as shown in Table 4. Asa result of more congestion in the network in thecase of Backtracking-CR and ILP when the arrivalrate is high, less mapping options on average exitfor mapping each VN request. This generally pro-duces smaller solution space that leads to shorterrunning time on average as shown in Tables 3 and4. The recorded results for ILP in Table 4 are aver-aged over the successful mapping of VN requeststhat takes less than the maximum specified periodof 1 h. The average number of ILP termination(because running time exceeds 1 h) in each averagearrival rate was in the range [12–19] of the total VNrequests. On the other hand, the average runningtime for Backtracking-LB was few seconds for theaverage arrival rates higher than 6. This is mainlybecause longer paths are utilized to achieve load bal-ancing especially when the load of VN requests isincreased.

Table 4Average mapping running time for different average VN request arrivalrates (large network scenario).

Average VN requestarrival rate

ILP Backtracking-CR

Backtracking-LB

Average running time (seconds) (large network scenario)2 77.762 0.237 0.2074 87.426 0.234 0.2116 103.324 0.228 0.7718 93.543 0.219 2.033

10 102.869 0.21 4.09712 46.358 0.197 4.78214 41.933 0.18 5.86316 46.042 0.169 4.00518 37.972 0.174 4.86920 43.706 0.151 5.157

As part of performance evaluation, scenarios for net-work topology generation with giving higher connectionprobability to the closer nodes as presented in [20] aresimulated. The conclusions in these scenarios are similarto the presented conclusions in this paper with someincrease in the running time on average as an indicationto larger solution space in these scenarios.

7. Conclusion

Network virtualization has been widely recognized asthe most promising solution to support the increasingneeds for flexibility in future Internet and address its ossi-fication problem. In network virtualization, mapping of vir-tual networks onto physical infrastructure is an essentialfunctionality. This paper proposed two novel approachesbased on a backtracking heuristic algorithm for virtualnetwork composition. These approaches are: (1) Back-tracking-CR optimized for cost reduction. (2) Backtracking-LB optimized for load balancing. The former minimizes theallocated resources for each VN request at the time itarrives, while the latter optimizes the state of network byapplying load balancing. Furthermore, we introduced anew ILP approach that can find an optimal mapping of eachVN request with the minimum mapping cost. The proposedalgorithms and models are capable of finding solutions inone stage mapping of nodes and links. They supporton-demand VN request mapping considering networkconstraints i.e. delay and bandwidth of each link as wellas packet processing capacity and geographical locationof each node.

Simulation results indicate that although ILP and Back-tracking-CR approaches use less network resources to mapVN requests, this does not lead to higher VN request accep-tance ratio when compared to Backtracking-LB. Both Back-tracking-CR and ILP approaches do not consider congestionavoidance. On the other hand, Backtracking-LB producedthe highest mapping cost as a result of using longer phys-ical paths. This approach aims to reduce the bottlenecks byavoiding selection of critical and highly utilized physicalnodes and links. Therefore, physical node and link utiliza-tion is more balanced when applying Backtracking-LB. Bycontrast to ILP approach, simulation results have provedthat the proposed heuristic approaches are scalable, whichmakes these approaches feasible for mapping virtual net-works in larger network scenarios where ILP results mightnot be attainable.

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Ali Hammad received the B.Sc. in InformaticsEngineering from Damascus university, Syria,in 2006. He received the M.Sc. degree withdistinction in Communication and Informa-tion Networks from University of Essex, UK, in2010. He is currently working towards thePh.D. degree at university of Essex. His maininterests are network virtualization for bothIP and optical networks, and cross layer IPover optical network virtualization. He iscurrently a researcher in the High Perfor-mance Networks group at University of Bris-

tol.

Reza Nejabati is Lecturer at University ofBristol. His research interest is on the appli-cation of high-speed network technologies,design and control of software-defined, ser-vice-oriented and programmable network,cross-layer network design, network archi-tecture and technologies for e-science andcloud computing. He is author and co-authorof over 150 papers and three standardizationdocuments. He is involved in several national/international projects. He has served as TPCmember, chair and organizer of several IEEE

conferences and workshops.

Dimitra Simeonidou is Professor of HighPerformance Networks group at University ofBristol. Dimitra is a leading academic inOptical Networks, Future Internet Researchand Experimentation (FIRE), Grid and CloudComputing, and a founder of Transport Soft-ware Defined Networking. She has chaired anumber of international conferences andcommittees across these technical fields. Sheis the author and co-author of over 350 pub-lications of which many have received bestpaper awards, 11 patents and standards.