Performance evaluation of artificial intelligence algorithms for virtual network embedding

Engineering Applications of Artificial Intelligence ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Engineering Applications of Artificial Intelligence

0952-19http://d

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

Performance evaluation of artificial intelligence algorithms for virtualnetwork embedding$

X.L. Chang a,n, X.M. Mi a, J.K. Muppala b

a School of Computer and Information Technology, Beijing Jiaotong University, Beijing, PR Chinab Department of Computer Engineering, Hong Kong University of Science and Technology, PR China

a r t i c l e i n f o

Article history:Received 11 January 2013Received in revised form19 May 2013Accepted 12 July 2013

Keywords:Cloud computingNetwork virtualizationVirtual network embeddingArtificial Intelligence

76/$ - see front matter & 2013 Published by Ex.doi.org/10.1016/j.engappai.2013.07.007

arlier version of this paper appeared in IEEEescribed in Section V.esponding author. Tel.: +86 1051688490.ail addresses: [email protected] (X.L. [email protected] (J.K. Muppala).

e cite this article as: Chang, X.L., et aAppl. Artif. Intel. (2013), http://dx.do

a b s t r a c t

Network virtualization is not only regarded as a promising technology to create an ecosystem for cloudcomputing applications, but also considered a promising technology for the future Internet. One of themost important issues in network virtualization is the virtual network embedding (VNE) problem, whichdeals with the embedding of virtual network (VN) requests in an underlying physical (substrate network)infrastructure. When both the node and link constraints are considered, the VN embedding problem isNP-hard, even in an offline situation. Some Artificial Intelligence (AI) techniques have been applied to theVNE algorithm design and displayed their abilities. This paper aims to compare the computationaleffectiveness and efficiency of different AI techniques for handling the cost-aware VNE problem. We firstpropose two kinds of VNE algorithms, based on Ant Colony Optimization and genetic algorithm. Then wecarry out extensive simulations to compare the proposed VNE algorithms with the existing AI-based VNEalgorithms in terms of the VN Acceptance Ratio, the long-term revenue of the service provider, and theVN embedding cost.

& 2013 Published by Elsevier Ltd.

1. Introduction

Cloud computing emerges as a new computing paradigm thatoffers IT-related capabilities and resources as dynamically config-urable services, via the Internet and on-demand, to satisfy users’needs. However, the current cloud data center networks have beena barrier to achieve the promise of cloud computing (http://nicira.com/). Network virtualization is regarded as a promising technol-ogy to overcome this barrier and then create an ecosystem forcloud computing applications (http://nicira.com/; Baroncelli et al.,2010). Baroncelli et al. (2010) proposed a network-virtualization-based mediation layer, which is able to provide Network as aService (NaaS) to cloud computing. Moreover, network virtualiza-tion has been regarded as a promising technology for the futureInternet (Anderson et al., 2005). Feamste et al. (2007) talked aboutthe evolution of a future Internet architecture consisting ofinfrastructure providers (InPs) and service providers (SPs).

One of the most important issues in the network virtualizationis the virtual network embedding (VNE) problem, which deals withthe mapping/embedding of VN requests onto specific physicalnodes and paths of the substrate network. When both the node

lsevier Ltd.

PDCAT 2012 (Mi and Chang,

),

l., Performance evaluation oi.org/10.1016/j.engappai.201

and link constraints are considered, the VN embedding problem isNP-hard, even in an offline situation (Zhu and Ammar, 2006).Various solutions to the VNE problems were proposed based onthe different techniques, classified into CPLEX (http://www.ilog.com/products/cplex/)/GLPK (http://www.gnu.org/software/glpk)solver-based exact algorithms and heuristic algorithms. There areat least two advantages of heuristic VNE algorithms: (1) do notimpose requirements on the linearity of the QoS compositionoperators (and thus of objective function and constraints) and(2) scalable. Some authors, such as in Chang et al. (2012) and thereferences therein, have formulated the VNE problem as mixed-integer programs and designed the CPLEX/GLPK-based exact algo-rithms. However, it is generally difficult for an exact algorithm toproduce an optimal solution in a reasonable amount of time formedium or large size problem instances.

Artificial Intelligence (AI) techniques, such as ACO (Ant ColonyOptimization) (Dorigo and Caro, 1999) and PSO (Particles SwarmOptimization) (Eberhart and Kennedy, 1995), have been appliedsuccessfully to design heuristic VNE algorithms. The simulation resultsin Cheng et al. (2011) demonstrated the better performance of PSO-based VNE algorithms in terms of the InP long-term revenue andembedding cost, compared to the existing state-of-the-art algorithms,which are not AI-based. Genetic algorithm (GA) (Goldberg, 2005) isalso an excellent approach to solve the complex optimization pro-blems. To the best of our knowledge, no GA-based VNE algorithm hasbeen presented previously and the existing VNE algorithms based onthe different AI techniques have never been compared to each other.

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X.L. Chang et al. / Engineering Applications of Artificial Intelligence ∎ (∎∎∎∎) ∎∎∎–∎∎∎2

There are two objectives of this paper: (1) Compare thecomputational effectiveness and efficiency of different AI techni-ques for handling the cost-aware VNE problem in the varioussituations of peak resource demands. We focus on three AItechniques, namely ACO, GA and PSO. Each AI technique possessesdistinctive features in their strategies for searching the solutionstate space. This paper only considers the classical versions ofthese AI techniques. (2) Investigate the effect of a node rankingscheme on the performance of an AI-based VNE approach. A noderanking scheme can be used to determine the virtual nodemapping order and to determine the possibility of a physical nodeto host a virtual node, by ranking the relative importance of avirtual/physical node. This paper considers two node rankingmethods (denoted as CB and RW), proposed in (Yu et al. (2008)and Cheng et al. (2011). Note that we consider the cost-aware VNEproblem in the scenarios where the physical resource demands ofeach VN request are certain.

The major contributions are summarized as follows:

(1)

PlEn

We propose two new ACO-based VNE algorithms, named asCB-ACO and RW-ACO. There are some differences between ourACO-based VNE algorithms and the ACO-based VNE algorithmproposed in Fajjari et al. (2011), such as the virtual nodemapping order and the pheromone trail computation method.The detailed differences are described in Section 3. Oursimulation results (unpublished) indicated that the perfor-mance of the VNE algorithm proposed in Fajjari et al. (2011)is even worse than that of the greedy VN mapping method,CB-SP. CB-SP algorithm is described in Section 6. The differ-ence between the two proposed ACO-based algorithms isthe node ranking method. CB-ACO adopts the CB node rank-ing method. RW-ACO uses the RW node ranking method. Inorder to make a fair comparison of the abilities of each AItechnique in handling the cost-aware VNE problem, both theCB-ACO and RW-ACO algorithms apply the simple k-shortest-path link mapping algorithm (Katoh et al., 1982) to mapvirtual links.

(2)
We propose two GA-based VNE algorithms. To the best of ourknowledge, this is the first work of investigating the ability ofGA technique in handling the cost-aware VNE problem. Wedescribe the design of the selection, crossover and mutationoperators used in the proposed GA-based VNE algorithms indetail. Note that there are some similarities between theproposed ACO-based and the proposed GA-based VNE algo-rithms, such as individual representation and the definitions oflocal and global best solutions. Such designs aim to comparethe abilities of the AI techniques in a fair way.
(3)
We perform a comprehensive comparative study of the pro-posed VNE algorithms and the existing state-of-the-art AI-based VNE algorithms in various scenarios, including differentnetwork topologies (flat random topologies and transit-stubtopologies), different sized substrate networks (small-sized,medium-sized and large-sized networks), different physicalnetwork configurations, and different VN configurations. Notethat the existing research on designing AI-based VNE algo-rithms compared their designed algorithms only with the VNEalgorithms which are not designed based on the AI techniques.In addition, these existing evaluations were carried out only inthe small-sized or medium-sized scenarios with a fixed VNarrival rate and a fixed average lifetime. It is possible that oneVNE algorithm performs better in a particular scenario, butmay not work well when there is a change in the settingof environment. Moreover, the existing AI-based VNE algo-rithm evaluations were carried out only under flat randomtopologies.
ease cite this article as: Chang, X.L., et al., Performance evaluation og. Appl. Artif. Intel. (2013), http://dx.doi.org/10.1016/j.engappai.201

1.1. Our simulation results indicate that:

(1)

f art3.0

An AI technique working well in one area may not work wellin the other areas. For example, the authors in Windisch et al.(2007) and the references therein demonstrated that particleswarm optimization is even better than genetic algorithms forsolving a number of test problems. However, GA-based VNEalgorithms proposed in this paper perform better than PSO-based VNE algorithms in terms of Average Revenue (defined inSection 6.2) in all simulations.

(2)
In terms of Average Revenue, the features of an AI techniquehave more impact on the performance of the VNE algorithmbased on this technique, compared to the node rankingmethod employed in the VNE algorithm. We also explain thesimulation results. The simulation results and the resultanalysis presented in this paper not only provide suggestionsfor an infrastructure provider to choose an AI-based VNEapproach, but also provide suggestions for designing a robustVNE algorithm based on the AI techniques.
The rest of the paper is organized as follows: Sections 2 and 3,respectively, present the background knowledge and related workin this area. The details of the ACO-based and GA-based VNEalgorithms are described in Sections 4 and 5, respectively. Weevaluate the AI-based VNE algorithms in Section 6. In Section 7, wesummarize the work presented in the paper.

2. Network model and problem description

2.1. VN embedding

Both the substrate network and the virtual network aremodeled as a weighted undirected graph and are denoted byGS ¼ ðNS; ESÞ and GV ¼ ðNV ; EV Þ, respectively. Here NS=NV is the setof physical/virtual nodes and ES=EV is the set of physical/virtuallinks. Each physical node nS∈NS is associated with CPU resourcescðnSÞ and geographical location lðnSÞ. The system resources of aphysical node include memory, processing power, storage spaceand so on. Without loss of generality, this paper only considers theprocessing power. All the work presented in this paper can beapplied directly to the environment where virtual nodes haveother resource demands besides CPU demand.

Each physical link eSðv;wÞ∈ES between physical nodes (v, w) isassociated with bandwidth capacity. All the physical resources (i.e.bandwidth and CPU) in GS are limited. Usually, a virtual node′s(denoted as nV ) QoS (Quality of Service) requirements include theCPU demand cðnV Þ and a preferred value dn

V

expressing how farthis virtual node can be placed from the specified location lðnV Þ.The QoS requirements of a virtual link eV ðv;wÞ∈EV between virtualnodes (v, w) include the bandwidth requirement bðeV Þ and a delaydemand. Virtual network embedding for a VN request is defined asa mapping from GV to GS with the constraints:

(1)
Each virtual node is mapped to a physical node in a one-to-onemanner, and the virtual node QoS requirements are satisfied.
(2)
Each virtual link eV ðv;wÞ is mapped to a physical path (anunsplittable model) or a flow (a splittable model) in GS betweenphysical nodes which host v and w, with at least two require-ments. One is that the eV ðv;wÞ bandwidth requirement is belowthe total available bandwidth of the physical path or the flow. Thesecond is that the delay constraint of the virtual link is met.
Each VN request has a lifetime. After the VN′s lifetime is ended,the physical resources allocated to this VN must be released.

ificial intelligence algorithms for virtual network embedding.7.007i




X.L. Chang et al. / Engineering Applications of Artificial Intelligence ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 3

The available CPU capacity ANðnSÞ of a physical node nS is definedas ANðnSÞ ¼ cðnSÞ�∑∀nV∈ΩðnSÞcðnV Þ. Here ΩðnSÞ denotes the set of thevirtual nodes, which are hosted on the physical node nS. Theavailable bandwidth AEðeSðv;wÞÞ of a physical link eSðv;wÞ isdefined as bðeSðv;wÞÞ minus the total bandwidth used by virtuallinks that pass through eSðv;wÞ.

2.2. Objective

From the InPs’ point of view, they hope to maximize theirrevenues in the long run while minimizing the embedding cost.Assume that the kth VN (denoted as GVk) is served by InP fromtime tstartGVk

and leaves at time tstartGVkþ Td

GVk. Here, Td

GVkdenotes GVk

lifetime. As in Yu et al. (2008) and Chowdhury et al. (2011), wedefine the revenue RðGVkÞ of serving GVk at unit time as follows:

RðGVkÞ ¼ ∑eV∈EVk

bðeV Þ þ ω ∑nV∈NVk

cðnV Þ ð1Þ

Here ω is the weight to determine the relative importance ofthe CPU and bandwidth resources. The cost of serving GVk may bedefined in terms of the energy consumption or may be defined interms of the consumed physical CPU and link bandwidthresources. This paper focuses on the second definition, which isdefined as follows:

CostðGVkÞ ¼ ∑eS∈ES

∑iηðeS; iÞ⋅f ieS þ ∑

nV∈NVk

cðnV Þ ð2Þ

Here ηðeS; iÞ is weight, f ieS is defined to denote the total amount offlows from physical node v tow on the physical link eSðv;wÞ for theVN’s ith virtual link, i∈f1…jEVkjg.

Assume there are K active VNs in the interval T. For descriptionconvenience, we set T ¼ t2 � t1 and Td

GVk¼ tstartGVk

�tendGVk. The InP′s

Average Revenue over T is defined as follows:

RInpavg ¼

∑k∈K∑Tt ¼ 0RðGVkÞLGVk

Tð3Þ

where

LGVk¼

T ; tstartGVkot1 and t2otendGVk

t2�tstartGVk; tstartGVk

≥t1 and t2otendGVk

tendGVk�t1; tstartGVk

ot1 and t2≥tendGVk

TdGVk

; tstartGVk≥t1 and t2≥tendGVk

8>>>>>><>>>>>>:

ð4Þ

The InP′s average cost over T is defined as follows:

CostInpavg ¼∑k∈K∑T

t ¼ 0CostðGVkÞLGVk

Tð5Þ

Thus, the Average Revenue to cost (R/C) ratio over T is defined asfollows:

R=C Ratio¼ RInpavg

CostInpavg

ð6Þ

Minimizing the embedding cost can advance the embedding offuture VNs. The objective of embedding GVk considered in thispaper is defined as follows:

minimize CostðGVkÞ ð7Þ

3. Related work

In recent years, a lot of work has been done in the area of VNembedding. This paper focuses on the peak demand situations, inwhich the primary concern of InP is how to embed more VNrequests in order to improve InP′s revenue. Thus, we only presentthe existing cost-aware VNE approaches in the following.

Please cite this article as: Chang, X.L., et al., Performance evaluation oEng. Appl. Artif. Intel. (2013), http://dx.doi.org/10.1016/j.engappai.201

Separating the virtual node mapping phase from the linkmapping phase restricts the solution space and may result in poorperformance. The coordination between these two phases can beachieved implicitly or explicitly. Lischka and Karl (2009) andChowdhury et al. (2011) proposed VNE approaches in an explicitlyintegrated method. Lischka and Karl (2009) modeled the topolo-gies of the substrate network and the VN as a directed graph. Thenthey proposed a VNE algorithm based on the subgraph isomorph-ism which mapped virtual nodes and links in the same phase. Theproblem with this algorithm is that it did not consider theembedding cost. Large embedding cost means more physicalresource consumption for embedding and then there may be nosufficient resources for embedding future VN requests. In addition,it is difficult for this algorithm to produce a solution in a reason-able amount of time even for small-size problem instances. Yinand Roscoe (2012) made improvement to this algorithm.

Chowdhury et al. (2011) formulated a Mixed Integer Program-ming (MIP) model for the VNE problem with the assumption thatthe substrate network supports path splitting. The linear program-ming (LP) relaxation and rounding techniques were applied toobtain approximations to their MIP formulation. However, therounding results of their algorithms that correspond to the nodemapping phase may result in an infeasible link embedding solu-tion. Even if the link mapping is feasible, the solution may still befar away from the optimal solution (Cheng et al., 2011).

Some authors achieved the implicit coordination by combingthe link bandwidth resources/demands into the node rank com-putation in the virtual node mapping phase. The node rankingscheme decides the virtual node mapping order and decideswhich physical node is to be used to host a virtual node. Yuet al. (2008) proposed a simple node ranking method (denoted asCB), in which the rank (denoted as NR) for a node u is computed byapplying

NRðuÞ ¼ cðuÞ ∑l∈LðuÞ

bðlÞ ð8Þ

Here u may be a virtual node or a physical node. For a physicalnode u, L(u) is the set of all the outgoing physical links of u in thesubstrate network, c(u) is the available CPU resource of u, and b(l)is the available bandwidth resource of link l∈L(u). For a virtualnode u, L(u) is the set of all the outgoing virtual links of u in thevirtual network, c(u) is the CPU resource demand of u, and b(l) isthe bandwidth resource requirement of link l∈L(u).

Cheng et al. (2011) proposed to apply the Markov RandomWalk (RW) model to rank a network node based on its resourceand topological attributes. We use RW to denote this rankingmethod. In the RW ranking method, the rank of a given node u isnot only determined by its CPU power and its collective bandwidthof outgoing links, but also affected by the ranks of the nodes thatcan be reached from u.

Fajjari et al. (2011) proposed to apply the number of “hanginglinks” (for the definition, refer to Fajjari et al., 2011) to rank thevirtual nodes. Our experiment results (unpublished) indicated thatthis ranking method cannot promote the VN embedding as betteras the first two ranking methods. Thus, this paper only considersCB and RW ranking methods.

GA (genetic algorithms) (Goldberg, 2005), ACO (Ant ColonyOptimization) (Dorigo and Caro, 1999) and PSO (Particles SwarmOptimization) (Eberhart and Kennedy, 1995) are similar in thesense that they are population-based AI techniques and theysearch for the optimal solution by updating generations. Thesetechniques find a solution to a given objective function but employdifferent strategies and computational effort. Some AI techniqueshave been applied to deal with the VNE problem. Note that GA,ACO, and PSO are just a general framework that needs tobe tailored to a specific problem (Bäck et al., 1997). That is, the






AI-based algorithms designed for one problem cannot be directlyused to handle another problem.

Fajjari et al. (2011) proposed an ACO-based VNE algorithm,named VNE-AC. They divided the virtual nodes into access nodesand core nodes (without restriction in geographic locations of thesubstrate core node). VNE-AC mapped access nodes and the virtuallinks between them first. Then VNE-AC mapped core nodes andthe related virtual links. There are at least three differencesbetween VNE-AC and our ACO-based algorithms. Firstly, we mapvirtual links only after all the virtual nodes find their hostingphysical nodes. The uncoupling between node and link mappingsmay degrade the VNE algorithm performance. Our ACO-basedalgorithms overcome this problem by applying the node rankingmethod, which considers the link bandwidth information in thenode rank computation. Secondly, the definition of embeddingcost is different. This may affect the mapping of future VNrequests. Although VNE-AC considers both the node and linkconstraints, its embedding cost only includes link mapping cost.Our algorithms’ embedding cost includes both the node and linkmapping costs, same as in Cheng et al. (2011). Thirdly, thepheromone trail computation method and the probability (in Eq.(11)) of selecting a physical node to host a virtual node aredifferent. VNE-AC uses the information of globe optimal solutionto compute pheromone trail. Our algorithms use the informationof local optimal VN solution in order to improve the exploration ofthe solution space. Note that the virtual node whose location isunknown can be mapped to any place.

Cheng et al. (2011) proposed PSO-based VNE algorithms. PSO isa population based search algorithm where each individual isreferred to as particle and represents a VNE solution. The key ideaof the RW-PSO and CB-PSO proposed in Cheng et al. (2011) is asfollows. The position of each particle represented a possiblemapping solution of the VN′s virtual nodes. A particle is calledas being feasible if all the virtual links find their hosted physicalpaths; otherwise particle is infeasible. The position and velocity offeasible particle i on the dth dimension are computed according tothe following equations:

vdi ¼ P1vdi ⊕P2ðpBestdi Θxdi Þ⊕P3ðgBestdΘxdi Þ ð9Þ

xdi ¼ xdi ⊗vdi ð10ÞHere P1 is the inertia weight, P2 is the cognition weight, and P3 isthe social weight. The feasible position corresponding to the bestfitness of an iteration is denoted as pBest and the overall best outof all the particles in the population is denoted as gBest. Unlessotherwise specified, the fitness function f ðxÞ in the rest of the paperis defined as in Eq. (2), i.e. the objective of the VNE problem. Eachparticle updated its position to achieve a better position accordingto the local and global information. A near-optimal solution of VNembedding can be obtained through the evolution process of theparticles. The difference of CB-PSO from RW-PSO is the rankingmethod. The experiment results in Cheng et al. (2011) indicatedthat the node ranking method affected the performance of a PSO-based algorithm. The readers are referred to Cheng et al. (2011) formore details about PSO-based VNE algorithms (including thedefinitions of the variables in Esq. (9) and (10)).

Network virtualization is an emerging area. The actual char-acteristics of both the substrate networks and the VN requests arestill not well understood (Chowdhury et al., 2011; Zhu and Wolf,2012; Yin and Roscoe, 2012). The existing research used differentsynthetic environments to evaluate their designed VNE algo-rithms. Cheng et al. (2011) used a substrate network with 100nodes and about 500 links in a 100�100 grid, virtual networkrequests’ nodes with uniform distribution between 2 and 20,physical CPU and link data rates with uniform distributionbetween 50 and 100 units, and CPU and link date rate


requirements with uniform distribution between 0 and 50 units.Chowdhury et al. (2011) used a 50-node substrate network in a25�25 grid, CPU and bandwidth requirements uniformly distrib-uted from 0 to 20 and from 0 to 50, respectively. The evaluationparameter settings have an important effect on the VN mappingresults. Thus, it is difficult to make a comparison based on thepublished results. Some VNE algorithms are more suitable forsmall-sized networks with a high node degree. Some VNE algo-rithms may work better in medium-sized networks. In order tomake a fair comparison, this paper compares the proposedalgorithms with the existing algorithms in all the scenarios whichhave been used in Yu et al. (2008), Cheng et al. (2011) andChowdhury et al. (2011). In addition, we vary the parametersettings in these scenarios and do simulation to compare themfurther.

Note that most VNE algorithms were evaluated (Yu et al., 2008;Fajjari et al., 2011) under flat-random topologies. In order to under-stand the performance of VNE algorithms under realistic operationalconditions, Zhu andWolf (2012) proposed a benchmark for evaluatingVNE algorithms, denoted as VNMBench. VNMBench used trans-stubtopology generationmethod to generate substrate topologies and usedthe Waxman method (Waxman, 1991) to generate VN topologies.Trans-stub topologies, different from flat random topologies, cancapture backbone and stub components separately, and producegraphs closely resembling the Internet topology (Zegura et al., 1996).Zhu and Wolf (2012) demonstrated that VNMBench is sufficientlyrealistic through a series of experiments. Yin and Roscoe (2012)evaluated their VNE algorithm using an extensive test workload basedon the analysis of a 5-year trace of experiments submitted to thepopular Emulab testbed and using the substrate topology derivedfrom the current ProtoGENI topology. Note that the existing Emulabtrace did not provide some information necessary to characterize a VNrequest, such as the processing demands and the VN request lifetime.In this paper, we also borrow the parameter settings defined in Zhuand Wolf (2012) and Yin and Roscoe (2012) to construct a bit realisticsimulation environments to make performance evaluation.

4. ACO-based VNE algorithms

Ant Colony Optimization (ACO) is a meta-heuristic inspired bythe behavior of ant colonies (Dorigo and Caro, 1999). SeveralACO variants have been proposed. This section explores theapplication of a classical approach presented in Guntsch andMiddendorf (2002). We present two ACO-based VNE algorithms,namely CB-ACO and RW-ACO in the following.

4.1. CB-ACO algorithm

The CB-ACO algorithm is given in Algorithm 2, which usesAlgorithm 1 to map virtual nodes. Each ant i produces a VNembedding solution and is associated with a vector, which is an |NV|-length integer vector containing the virtual node mapping result,donated by xi ¼ fxi1; xi2:::xiDg. Here hki denotes the physical nodewhich hosts the kth virtual node in the ith ant. Note that Hi onlyrepresents the virtual node mapping. Whenever Hi is updated, itsfeasibility must be checked using the k-shortest-path algorithm to mapall the virtual links in the VN. Hi is called as being feasible if all thevirtual links find their hosted physical paths; otherwise Hi is infeasibleif the f ðiÞ value of this ant is set to +1. At each iteration, compute f ðiÞof each ant and use variable pBest to denote the VNE solutionwith thebest f(x) of this iteration. Variable gBest is defined to denote the VNEsolution with the best f(x) obtained so far.

Each physical node j is associated with a pheromone trail foreach virtual node i, denoted as τij. τij represents the desirability ofassigning virtual node i to physical node j. The initial value of each






pheromone trail is set to a large value (we set to 100 in ourexperiments) in order to increase the exploration space of solu-tions during the first iteration. At each iteration, every ant firstupdates the pheromone trail values in two steps (see Step 3 ofAlgorithm 2): (i) evaporate τij of all the substrate nodes and (ii)reinforce τij of the substrate nodes which contribute to thebuilding of the local best solution (pBest). Then every ant exploresnew solutions according to the new pheromone trails.

Algorithm 1. Input ¼ (GV , GS).

Please citeEng. Appl.

Step 1
Set all physical nodes untouched. Calculate NRðuÞ foreach virtual node and each physical node. NRðuÞ isdefined in Eq. (8).
Step 2
Enqueue all virtual nodes into a priority queue PQ inthe descending order of NRðuÞ.
Step 3
Dequeue the virtual node (denoted as u) with thelargest NRðuÞ. Construct a physical node list CL(u) foru. Each physical node in the list must be untouchedand satisfy the resource requirements of the virtualnode u. Select a physical node (denoted as v) fromCL(u) with its probability puv. puv is defined asfollows:
puv ¼ ðτuvÞα ðNRðvÞÞβ∑w∈CLðuÞððτuwÞαðNRðwÞÞβ Þ

ð11Þ
where α and β are parameters that determine therelative importance of pheromone trail and NRðuÞ.A physical node with lager available resources haspriority to be selected. When a physical node v isselected to host virtual node u, then physical node v
is set to be touched.
Step 4 Repeat Step 3 until PQ is empty.
Algorithm 2. (CB-ACO): Input ¼ (GV , GS).

Step 1
Generate the initial population of ants. Initialize acertain number of ants using Algorithm 1 and checkthe feasibility of each ant′s virtual node mapping.
Step 2
Compute pBest and initialize gBest. Compute f ðxÞof each ant. Compute pBest and set gBest¼pBest.
Step 3
Update the pheromone trail. Before reiterating theprocess from iteration t to t+1, the pheromone trailsof all physical nodes are first evaporated. That is,
τuvðt þ 1Þ ¼ ρ⋅τuvðtÞ, where 0oρo1 and u∈Nv; v∈NS.Then the pheromone trail of each physical nodeparticipating in the construction of pBest isreinforced by the following:
τuvðt þ 1Þ ¼ τuvðt þ 1Þ þ φ
p_bwð12Þ

where p_bw represents the total physical bandwidthused in pBest, and φ is a constant parameter.

Step 4
Evolution. Update each ant solution usingAlgorithm 1 and check the solution feasibility. Wecalculate the fitness function value of each ant andthen update pBest. If f ðgBestÞ4 f ðpBestÞ thengBest¼pBest.
Step 5
Repeat Step 3 and Step 4 until the maximumnumber of iterations is reached. If f ðgBestÞ is +1,output there is no feasible solution. Otherwise, gBestis returned as the VNE solution.
4.2. RW-ACO algorithm

The only difference of the RW-ACO algorithm from the CB-ACOis the definition of NRðuÞ used in Algorithm 1. In the RW-ACOalgorithm, NRðuÞ is defined as in Cheng et al. (2011).

this article as: Chang, X.L., et al., Performance evaluation oArtif. Intel. (2013), http://dx.doi.org/10.1016/j.engappai.201

5. GA-based VNE algorithms

Genetic algorithm (GA) is a randomized search techniquewhich borrows the evolutionary ideas (Goldberg, 2005). Wepresent the CB-GA and RW-GA algorithms in the following.

5.1. CB-GA algorithm

Each chromosome i produces a VN embedding solution and isassociated with two vectors: (1) the host vector Hi ¼ ðh1

i ;h2i ;…;hjN

V ji Þ,

which is a |NV|-length integer vector. hki denotes the physical nodewhich hosts the virtual node k in the ith chromosome, where k∈jNV jand (2) the state vector Si ¼ ðs1i ; s2i ;…; sjN

V ji Þ, which is a |NV|-length bit

vector. If ski ¼ 0, then the corresponding virtual node should be re-mapped. Otherwise, the current mapping of this virtual node remains.Algorithm 4 describes CB-GA, in which Algorithm 3 is applied toinitialize and update each chromosome′s Hi.

In each generation, the elitist selection scheme is applied toguarantee that the fittest member of each generation is copieddirectly into the next generation. The elite strategy retains thegood chromosome and ensures that it is not eliminated throughthe operations of crossover and mutation. Thus, the features of theoffspring chromosomes are at least as good as their parents. Thesimple onepoint crossover is applied to explore the combinationsof the current solution pool. A single crossover site is selected atrandom over the vector length, and the bits on the right side of thesite are exchanged between the two selected chromosomes.Mutation operator is applied to each chromosome but each bit ismutated with a pre-defined probability. Whenever Hi is updated,its feasibility must be checked using the k-shortest-path algorithmto map all the virtual links in the VN. Hi is called as being feasible ifall the virtual links find their hosted physical paths; otherwise Hi

is infeasible. If Hi is unfeasible, the f ðxÞ value of this chromosome isset to +1. The variables pBest and gBest are defined as in ACO-based VNE algorithms. Note that an unfeasible Hi is not involved inthe operation of crossover and mutation. Instead, it is re-initializedand directly put into the next generation.

5.2. RW-GA algorithm

The only difference of the RW-GA algorithm from the CB-GA is thedefinition of NRðuÞ used in Algorithm 3. The RW-GA algorithm appliedthe RW node ranking method proposed in Cheng et al. (2011).

5.3. Time complexity analysis

Runtime complexity is an important concern when designingany heuristic algorithm for real-time applications. Generally algo-rithms with polynomial time complexity are thought to besuitable.

Both the CB ranking method and the RW ranking method canbe solved in polynomial time (Cheng et al., 2011). Thus, Algorithms1 and 3 are both polynomial-time algorithms. In addition, the k-shortest-path based link mapping algorithm is a polynomial-timealgorithm (Katoh et al., 1982). Thus, CB-ACO, RW-ACO, CB-GA andRW-GA are all polynomial-time algorithms.

Algorithm 3. Input¼(Hi, Si, GV , GS).

f artificial int3.07.007i

Step 1
For each physical node v, if v∈Hi and thecorresponding ski is 1, then this physical node is setto touched; otherwise set this physical nodeuntouched.
Step 2
For each virtual node u in the VN request, if thecorresponding value in ski is 0 then enqueue thisvirtual node into a priority queue PQ.
elligence algorithms for virtual network embedding.





Step 3

Please citeEng. Appl.

Calculate NRðuÞ for all the virtual nodes in PQ and forall the untouched physical nodes. NRðuÞ is defined asin Eq. (8). Sort the virtual nodes in PQ in non-increasing order according to their NRðuÞ.

Step 4
Dequeue the virtual node (denoted as u) with thelargest NRðuÞ. Construct a candidate physical nodelist CL(u) for virtual node u. The physical nodes inthe list must be untouched and satisfy the resourceconstraints of the virtual node u. A physical node(denoted as v) in CL(u) is selected with itsprobability pv to host the virtual node u. pv isdefined as follows: pv ¼ NRðvÞ
∑v∈CLðuÞNRðvÞð13Þ

When a physical node is selected to host virtualnode u, this physical node set to touched.

Step 5
If PQ is not empty, go to Step 4. Otherwise, return.
6. Performance evaluation

It is known that network virtualization is not widely deployed.The actual characteristics of both the substrate networks and theVN requests are still not completely understood (Chowdhury et al.,2011; Zhu and Wolf, 2012; Yin and Roscoe, 2012). The existingperformance evaluation of VNE algorithms was mostly done underflat random topologies. This section first presents the existing VNEalgorithms to be compared with the VNE algorithms proposed inthis paper. Then we use the flat random topology and the scenarioconfigurations, which have been used to evaluate the performanceof the existing VNE algorithms, to do simulations in order to makea fair performance evaluation. At last, we do simulations under thetopologies and VN parameter settings used in Zhu and Wolf (2012)and Yin and Roscoe (2012), in order to compare the VNE algo-rithms under realistic operational conditions.

6.1. Details of the algorithms compared and performance metrics

We evaluate the performance of CB-ACO, RW-ACO, CB-GA, RW-GA, CB-PSO (Cheng et al., 2011), RW-PSO (Cheng et al., 2011),R-ViNE, and CB-SP. This R-ViNE applies the R-ViNE proposed inChowdhury et al. (2011) to map the virtual nodes but applies thek-shortest-path-based method to map virtual links. CB-SP is a VNEapproach which applies Algorithm 5 to map virtual nodes andapplies the k-shortest-path-based method to map virtual links. Wemodify the ViNE-Yard simulator (http://www.mosharaf.com/ViNE-Yard.tar.gz) and implement all the eight VNE algorithms.

The metrics considered include

(i)
Acceptance Ratio, which measures the percentage of total VNrequests accepted by an algorithm over a given period.
(ii)
Average Revenue, which measures the generated revenue(defined in Eq. (1)) of an embedding algorithm over time(50,000 time units in Section 6.2 and 25,000 time units inSection 6.3).
(iii)
R/C Ratio (defined in Eq. (6)), which measures the efficiency ofsubstrate resource usage.
The parameters used in CB-PSO and RW-PSO are set as inCheng et al. (2011). In CB-GA and RW-GA, pc ¼ 0:8 and pm ¼ 0:05.In CB-ACO and RW-ACO, φ¼10,000, α¼1, β¼2 and ρ¼80% as inFajjari et al. (2011). In addition, ω used in Eq. (1) and all η used in(2) are set to 1. As in Cheng et al. (2011), we set the maximumnumber of iterations to 20 and individual numbers to 5.

this article as: Chang, X.L., et al., Performance evaluation oArtif. Intel. (2013), http://dx.doi.org/10.1016/j.engappai.201

Algorithm 4. (CB-GA): Input¼(GV , GS).

f artificial int3.07.007i

Step 1
gBest is set to +1. Step 2 Initialize a population of chromosomes. Set all ski
to 0, where 1≤k≤jNV j and the value of i is from 1 tothe population size. Use Algorithm 3 to initializeeach host vector Hi. For each Si, set each ski to1 randomly. For each chromosome i in thepopulation, check the feasibility of its virtual nodemapping and compute its f ðiÞ. Compute pBest andset gBest¼pBest.

Step 3
Generate new population by selection, crossoverand mutation.Selection. Choose the chromosomewith the minimal f ðxÞ and put it in the nextpopulation. Put the left chromosomes in queue TQ.Re-initialization. Dequeue from TQ all thechromosomes whose f ðxÞ is +1. For each unfeasiblechromosome i, set all its ski to 0 and then useAlgorithm 3 to initialize the host vector Hi. After anunfeasible chromosome′s Hi is updated by re-initializing, set all its ski to 1 randomly. At last putthese updated chromosomes in the next population.Crossover and mutation. The left feasiblechromosomes in TQ are first paired randomly andthen the recombination is performed on each pairwith the pre-defined crossover probability pc toobtain two new chromosomes. After crossoveroperation, apply a mutation operation with a pre-defined mutation probability pm to each newchromosome in TQ. At last, put these newchromosomes in the next population.
Step 4
Get pBest and update gBest. Use Algorithm 3 toupdate each Hi and check its feasibility. Computethe fitness f ðiÞ of each chromosome i in thepopulation and update pBest. If f ðgBestÞ4 f ðpBestÞthen gBest¼pBest.
Step 5
Repeat Step 3 and Step 4 until the maximumnumber of iterations is reached.
Step 6
Output the VN embedding solution and stop. Iff ðgBestÞ is +1, output there is no feasible solution.Otherwise, return gBest as the VN embeddingsolution.
Algorithm 5. Input¼(GV , GS).

Step 1
Set all physical nodes untouched. Calculate NRðuÞ forall the physical nodes. Calculate NRðuÞ for all thevirtual nodes. Sort the virtual nodes based on theirNRðuÞ and put in a priority queue PQ. NRðuÞ isdefined as in Eq. (8).
Step 2
Dequeue the virtual node (denoted as u) with thelargest NRðuÞ. Construct a candidate physical nodelist CL(u) for virtual node u. The physical nodes inthe list must be untouched and satisfy the resourceconstraints of the virtual node u. A physical node(denoted as v) with the largest NRðuÞ in CL(u) isselected and set to touched.
Step 3
If PQ is not empty, go to Step 2. Otherwise, return.
6.2. Simulations under flat random topologies

6.2.1. Simulation environmentsTo evaluate in a fair way, we do simulations under the two

simulation environments, which have been commonly used to

elligence algorithms for virtual network embedding.




Small-sized

0.20.250.3

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CB-ACO

RW-ACO

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Fig. 2. Acceptance Ratio over VN lifetime.

Small-sized

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evaluate the performance of the existing VNE approaches. One isthe configurations used in Chowdhury et al. (2011), denoted assmall-sized in the rest of Section 6.2. The other is the configura-tions used in Yu et al. (2008), Cheng et al. (2011), Chowdhury et al.(2011), and Mi and Chang (2012), denoted as medium-sized in therest of Section 6.2.

Small-sized scenarios. The substrate network is configured tohave 50 nodes in (25�25) grid, which are randomly connectedwith probability 0.5. Both the physical node CPU and the linkbandwidth capacities follow a uniform distribution from 50 to 100units. The number of virtual nodes in a VN request is chosenuniformly between 2 and 10. Each pair of virtual nodes israndomly connected with probability 0.5. CPU and bandwidthrequirements are distributed uniformly from 0 to 20 units andfrom 0 to 50 units, respectively. Virtual nodes are also located on(25�25) grids.

Medium-sized scenarios. The substrate network has 100 nodes,which are randomly connected with probability 0.5. Both thephysical node CPU and the link bandwidth capacities follow auniform distribution from 50 to 100 units. The number of virtualnodes in a VN request is chosen uniformly between 2 and 20. Eachpair of virtual nodes is randomly connected with probability 0.5.CPU and bandwidth requirements are distributed uniformlybetween 0 and 50 units.

In both kinds of sized configurations, VN requests arrive in aPoisson process and the lifetimes of the VN requests follow anexponential distribution. As in Yu et al. (2008), Cheng et al. (2011),and Chowdhury et al. (2011), we generate the substrate networktopologies and virtual network topologies using the GT-ITM tool(Zegura et al., 1996).


Fig. 3. R/C over VN lifetime.

Small-sized

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VN Average Arrival Rate (per 100 Time Unit)

Ave

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CB-GA

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CB-SP

Fig. 4. Average Revenue over VN average arrival rate.

Small-sized0.75

6.2.2. Evaluation for online VN requestsWe first do simulations in small-sized scenarios. We fix the VN

request arrival rate to 4 per 100 time units and evaluate the eightalgorithms by varying the average VN request lifetime from 500 to2000 time units. Then we fix the average VN lifetime to 1000 timeunits and evaluate the eight algorithms by varying the VN requestarrival rate from 4 to 8 VN requests per 100 time units. Eachsimulation is run for 50,000 time units. Each experiment isrepeated 10 times and the average value of these repetitions ispresented as the simulation results in the following figures.Figs. 1–6 describe the simulation results.

We then do simulations in medium-sized scenarios. We fix theVN request arrival rate to 5 per 100 time units and evaluate theeight algorithms by varying the average VN request lifetime from500 to 2000 time units. Then we fix the average VN lifetime to1000 time units and evaluate the eight algorithms by varying theVN request arrival rate from 5 to 8 VN requests per 100 time units.Each simulation is run for 50,000 time units. Each experiment isrepeated 10 times and the average value of these repetitions is

Small-sized

1000

2000

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5000

500 1000 1500 2000VN Average Lifetime (Time Unit)

Ave

rage

Rev

enue

CB-ACO

RW-ACO

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CB-SP

Fig. 1. Average Revenue over VN lifetime.

0.2

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CB-ACO

RW-ACO

CB-GA

RW-GA

CB-PSO

RW-PSO

R-ViNE

CB-SP

Fig. 5. Acceptance Ratio over VN average arrival rate.

Please cite this article as: Chang, X.L., et al., Performance evaluation of artificial intelligence algorithms for virtual network embedding.Eng. Appl. Artif. Intel. (2013), http://dx.doi.org/10.1016/j.engappai.2013.07.007i




Small-sized

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R/C

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CB-ACO

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CB-SP

Fig. 6. R/C over VN average arrival rate.

Medium-sized

9000

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rage

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CB-ACO RW-ACO CB-GA RW-GA

CB-PSO RW-PSO R-ViNE CB-SP

Fig. 7. Average Revenue over VN lifetime.

Medium-sized

0.30.35

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0.80.85

0.9


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CB-ACO RW-ACO CB-GA RW-GACB-PSO RW-PSO R-ViNE CB-SP

Fig. 8. Acceptance Ratio over VN lifetime.

Medium-sized

0.45

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500 1000 1500 2000


R/C

Rat

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CB-ACORW-ACOCB-GARW-GACB-PSORW-PSOR-ViNECB-SP

Fig. 9. R/C over VN lifetime.

Medium-sized

14000

CB-ACO RW-ACO CB-GA RW-GACB-PSO RW-PSO R-ViNE CB-SP


presented as the simulation results in the following figures.Figs. 7–12 describe the simulation results.

We summarize the observation from the simulation results asfollows:

13000

Rev

ene

(1)

10000

11000

12000

5 6 7 8

VN Avearge Arrival Rate (per 100 Time Unit)

Ave

rage

Fig. 10. Average Revenue over VN average arrival rate.

PlEn

CB-PSO may not always outperform RW-PSO in terms of AverageRevenue. Our results in all small-sized scenarios indicate thatCB-PSO performs better than RW-PSO in terms of AverageRevenue. The reasons are as follows. It is known that the RWranking method can promote the convergence speed of an AI-based VNE algorithm. Thus, RW-based VNE algorithms con-verge faster than CB-based VNE algorithms under the samenumber of iterations. Fast convergence here means that afterfewer iterations, there is no virtual node needed to be re-mapped. That is, faster convergence means that less of thesolution search space is explored. Thus, compared to RW-based algorithms, CB-based algorithms can explore muchlarger solution space. Moreover, each VN size in small-sizedscenarios is small and then more feasible solutions can befound. The R/C Ratio results in Figs. 3 and 6 show that R/C ratioof CB-PSO is better than that of RW-PSO in small-sizedscenarios. The saved physical resources can be used to embedmore future VNs and then Average Revenue of CB-PSO is betterthan that of RW-PSO in small-sized scenarios.Note that the authors in Cheng et al. (2011) evaluated theperformance of CB-PSO and RW-PSO only in a medium-sizedscenario, where the VN arrival rate is 5 VNs per 100 time units,the VN lifetime is 500 time units and the VN size is [0, 20]. Oursimulation results in all medium-sized scenarios show thatRW-PSO outperforms CB-PSO in terms of Average Revenue,confirming the conclusions obtained in Cheng et al. (2011). Inmedium-sized scenarios, the VN size is large and differentvirtual nodes of a VN cannot be mapped to the same physicalnodes. PSO has the feature of fast convergence. In addition, CB-PSO maps virtual nodes only considering the CPU and band-width of a substrate node. This easily leads to bottleneck nodes

ease cite this article as: Chang, X.L., et al., Performance evaluation of artg. Appl. Artif. Intel. (2013), http://dx.doi.org/10.1016/j.engappai.2013.0

and/or bottleneck links, preventing the successful embeddingof the future VNs of large size. Although the RW rankingmethod can promote the convergence speed, RW-PSO can findmore feasible solutions by considering the topology informa-tion, compared to CB-PSO. Then there are more possibilities forRW-PSO to reduce R/C Ratio. The R/C Ratio results in Figs. 9 and12 show that R/C Ratio of RW-PSO is better than that of CB-PSOin medium-sized scenarios. The saved physical resources can besued to embed more future VNs and then Average Revenue ofRW-PSO is better than that of CB-PSO in medium-sizedscenarios.

(2)
The GA-based algorithms perform better than the PSO-basedalgorithms in terms of Acceptance Ratio and Average Revenueand R/C Ratio in all scenarios. The possible reasons are asfollows. The crossover and mutation operations in GAs canmove a chromosome a relatively large distance in the solutionspace. In addition, each chromosome in GAs has no relation-ship with the current gBest and pBest. Such features help GA-based VNE algorithms search solution in a much larger spacethan using PSO technique. This suggests that GA-based VNEalgorithms are able to find more feasible solutions. Thus, gBest




Medium-sized

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5 6 7 8VN Average Arrival Rate (per 100 Time Unit)

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ioCB-ACO RW-ACO CB-GA RW-GACB-PSO RW-PSO R-ViNE CB-SP


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R/C

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CB-ACORW-ACO

CB-GNRW-GNCB-PSORW-PSO

R-ViNECB-SP



PlEn

in GA-based VNE algorithms is much closer to the optimalsolution. However, in PSO-based VNE algorithms, only the‘best’ particle gives out the information to other particles. Thatis, pBest and gBest in the previous iteration have more impacton the current velocity, especially in the case of P1oP2oP3.This may lead to a bad final solution when gBest is far awayfrom the optimal solution in the first iteration. All the simula-tion results indicate GA-based VNE algorithms outperformPSO-based VNE algorithms in terms of the three metrics. Thebetter performance of two GA-based VNE algorithms over twoPSO-based VNE algorithms suggests that the effect of an AItechnique on the performance is larger than the effect of thenode ranking method.

(3)
CB-GA performs better than RW-GA in terms of Average Revenue.Each chromosome in GAs has less relationship with thecurrent gBest and pBest. In addition, GA-based VNE algorithmsonly re-embed some virtual nodes instead of the whole virtualnodes in each re-embedding. Thus, for a GA-based VNEalgorithm, the larger the solution searching space, the morefeasible solutions. Then, the final solution can be closer to theoptimal, saving more physical resources for embedding futureVN requests. But the fast convergence feature of the RWranking method reduces the solution searching space. Thus,in both the small-sized and medium-sized scenarios, CB-GAperforms better than RW-GA, different from the PSO-basedVNE algorithms. This difference also suggests that the effect ofan AI technique on the performance is larger than the effect ofthe node ranking method.
(4)
In terms of Average Revenue, ACO-based algorithms perform bestin small-sized scenarios and RW-ACO performs best in medium-sized scenarios. Both the PSO and ACO techniques have mem-ories. Such a memory feature leads to the effect of an iterationsolution on the next one and promotes the convergence speed.Note that PSO memorizes the history results due to its two uniquemechanisms: memorizing personal best experiences (pBest) andinformation sharing of global best experiences (gBest). ACO does itdue to applying the pheromone trails. As mentioned above, fasterconvergence may reduce the searching space. ACO technique
ease cite this article as: Chang, X.L., et al., Performance evaluation of artg. Appl. Artif. Intel. (2013), http://dx.doi.org/10.1016/j.engappai.2013.0

overcomes this shortcoming by letting each ant re-embed thewhole VN request in each iteration in order to enlarge thesearching space. Such re-embedding feature can improve R/CRatio. This is demonstrated by the fact that in all simulations R/CRatio of CB-ACO and RW-ACO are better than that of the otherVNE algorithms. Meanwhile, in the simulations of small-sizedscenarios, each VN size is small. Then the failing possibility ofVN re-embedding in each iteration is small. Thus, both the ACO-based algorithms can explore more feasible solutions in small-sized scenarios and then perform better than the PSO-based andGA-based VNE algorithms. In the medium-sized scenarios, thetopology information helps RW-ACO performs best in terms ofAverage Revenue. Although R/C Ratio under CB-ACO is best, thismay cause more bottleneck nodes and/or bottleneck links, pre-venting the successful embedding of the future VNs with largesize. Thus, the simulation results in Figs. 7 and 10 indicate thatAverage Revenue of CB-ACO is less than that of PSO-based VNEalgorithms in some medium-sized scenarios.

(5)
RW-ACO may not always outperform CB-ACO algorithms. Inmedium-sized scenarios, RW-ACO performs better than CB-ACO in terms of Average Revenue, indicated by Figs. 7 and 10.The reason is similar to the reason why RW-PSO is better thanCB-PSO. In small-sized scenarios, the VN size is small and thenthe possibility of successful re-embedding is larger. Then CB-ACO can find more feasible solutions and then produces higherAverage Revenue than that of RW-ACO.
(6)
The metric Acceptance Ratio cannot completely capture theperformance of an algorithm when an InP aims to increase itsrevenue. The simulation results in small-sized scenarios showthat when the VN average arrival rate or VN average lifetime isincreased, Acceptance Ratio of each algorithm is decreased.However, the corresponding Average Revenue is increased.Thus, we cannot simply use Acceptance Ratio to evaluate theperformance of a VNE algorithm. Most of the simulationresults in medium-sized scenarios also confirm this. For exam-ple, in most of the medium-sized scenarios, Acceptance Ratio ofCB-GA is larger than that of RW-ACO. But its Average Revenue isless than that of RW-ACO.
(7)
The metric R/C Ratio cannot completely capture the performanceof an algorithm when an InP aims to increase its revenue. Notethat R/C Ratio is computed based on the information of theVNs which are embedded successfully. The simulation resultsinmedium-sized scenarios indicate that R/C Ratio of R-ViNE andCB-SP is higher than that of CB-PSO and RW-PSO. But AverageRevenue of R-ViNE and CB-SP is less than that of CB-PSO andRW-PSO. The low Average Revenue of CB-SP is as follows. WhenCB-SP is applied to embed virtual nodes, it only considers theCPU and the bandwidth of a substrate node. This easily leadsto bottleneck nodes and/or bottleneck links, preventing thesuccessful embedding of the future VNs.
6.3. Simulations under trans-stub topologies

This section aims to evaluate under realistic operational con-ditions. We first present the operational conditions and thenpresent the simulation results.

6.3.1. Simulation environmentsAs in Zhu and Wolf (2012), we consider two substrate network

sizes: medium size with 100 nodes (e.g., enterprise network) andlarge size with 500 nodes (e.g., city network). Each substrate size isfurther divided into dense and sparse networks, according to thelink density. Dense substrate network has approximated two timesthe number of links of the corresponding sparse substrate net-work. Table 1 gives the parameters of each kind of substrate






networks. Both the physical node CPU and the link bandwidthcapacities follow a uniform distribution from 50 to 100 units.Substrate network topologies are generated by using trans-stubtopology generation method. Note that Yin and Roscoe (2012) didsimulations in large-sized networks.

As mentioned in Section 3, some parameters which arenecessary to characterize a VN request are missing in the Emulabtrace. In addition, the actual characteristics of both the substratenetworks and the VN requests are still not well understood. Thus,we generate a VN request according to the settings in both Zhuand Wolf (2012) and Yin and Roscoe (2012). As in Zhu and Wolf(2012), VN topologies are generated by applying the Waxmanmethod (Waxman, 1991). Parameters α and β used in the Waxmanmethod are uniformly distributed in [0.3, 0.8] and [0.15, 0.25]. CPUand bandwidth requirements are distributed uniformly from 0 to20 units and from 0 to 30 units, respectively. We assume thatvirtual network requests arrive dynamically. As in Yin and Roscoe(2012), VN requests are assumed to arrive in a Poisson process witha mean of four requests per time window. Request duration is

Table 1Parameters of substrate network topology generator.

Topologyparameters

Medium-sizedsparse

Medium-sizeddense

Large-sizedsparse

Large-sizeddense

Number of nodes 100 100 500 500Number of links 129 236 642 1238Scale 100�100 100�100 200�200 200�200Transit domains 2 2 2 2Nodes per transit 2 2 5 5Stubs per transit node 4 4 7 7Nodes per stub 6 6 7 7

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Fig. 13. Results of medium-sized substrate networks with trans-stub top

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Fig. 14. Results of large-sized substrate networks with trans-stub topo


modeled as a Gamma distribution with the parameters: shape¼0.3and scale¼20. Yin and Roscoe (2012) argued the reasonability ofthe settings of VN arrival rate and lifetime.

We use these settings mentioned in the previous paragraph togenerate two VN lists for the simulations in medium-sized net-works and large-sized networks. Note that the virtual nodes in thefirst VN list are located on (100�100) grids, but the virtual nodesin the second VNE list are located on (200�200) grids. Each VNlist includes 1000 VN requests, arriving dynamically in oneexperiment, namely 25,000 time units. The probability of nodenumber between 2 and 10 is around 0.75. The probability of nodenumber between 10 and 20 is around 0.25. As in Zhu and Wolf(2012) and Yin and Roscoe (2012), we use the GT-ITM to generatethe substrate and virtual network topology according to theparameters mentioned above.

6.3.2. Simulation results for online VN requestsWe do simulations in the four scenarios mentioned in Section

6.3.1. Each simulation is repeated 10 times and the average valueof these repetitions is presented as the simulation results in thefollowing figures. Figs. 13 and 14 give the simulation results ofmedium-sized and large-sized scenarios, respectively. Medium-Sparse denotes the results in medium-sized sparse scenario.Medium-Dense denotes the results in medium-sized dense sce-nario. Large-Sparse denotes the results in large-sized sparsescenario. Medium-Dense denotes the results in large-sized densescenario. Note that R-ViNE used GLPK to solve the integer linearprogramming. This solving process cannot be stopped in theexperiment in the large-sized dense scenario. Thus, there are noLarge-Sparse simulation results of R-ViNE in Fig. 14. This alsoindicates that CPLEX/GLPK-based VNE algorithms are not suitablefor large-sized networks.

CB-GA RW-GA

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ology. (a) Average Revenue, (b) Acceptance Ratio, and (c) R/C Ratio.

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logy. (a) Average Revenue, (b) Acceptance Ratio, and (c) R/C Ratio.






The simulation results in Figs. 13 and 14 confirm most of theresults obtained in Section 6.2:

(1)

PlEn

ACO-based VNE algorithms perform best in terms of AverageRevenue. The second is the GA-based VNE algorithms.

(2)
CB-PSO may not always outperform RW-PSO in terms ofAverage Revenue.
(3)
Both the Acceptance Ratio and the R/C Ratio cannot completelycapture the performance of an algorithm when an InP aims toincrease its revenue.
There is an interesting simulation result in Figs. 13 and 14namely that R-ViNE performs better than PSO-based VNE algo-rithms in medium-sized and large-sized sparse substratenetworks. The possible reason is that R-ViNE can utilize physicalresources efficiently, seeing Figs. 13(c) and 14(c). We also observethat R-ViNE consumes too much time to finish an experiment.

7. Conclusion and future work

This paper examines the abilities of both the classical ACO andGA in handling the VNE problem. We first propose two ACO-basedand two GA-based VNE algorithms. Then we compare them withthe existing state-of-the-art VNE algorithms in terms of InP long-term revenue and embedding cost in various scenarios andtopologies. All the simulation results demonstrate that ACOtechnique is a promising AI technique for designing VNE algo-rithms. In addition, the simulation results and the result analysispresented in this paper not only provide suggestions for aninfrastructure provider to choose an AI-based VNE approach, butalso provide suggestions for designing a robust VNE algorithmbased on the AI techniques. Future work includes investigatingwhether the similar results may be obtained when the energyconsumption is the InP major concern in embedding a VN.

Acknowledgment

The work described in this paper has been supported in part byBeijing Municipal Natural Science Foundation (no. 4123103),Program for New Century Excellent Talents in University (NCET-11-0565), and Program for Innovative Research Team in Universityof Ministry of Education of China (IRT201206).

ease cite this article as: Chang, X.L., et al., Performance evaluation og. Appl. Artif. Intel. (2013), http://dx.doi.org/10.1016/j.engappai.201

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Performance evaluation of artificial intelligence algorithms for virtual network embedding