Research Article MTAD: A Multitarget Heuristic Algorithm for Virtual Machine Placementdownloads.hindawi.com/journals/ijdsn/2015/679170.pdf · 2015. 11. 24. · placement algorithm

Research ArticleMTAD A Multitarget Heuristic Algorithm forVirtual Machine Placement

Lei Chen1 Jing Zhang1 Lijun Cai2 Rui Li2 Tingqin He2 and Tao Meng2

1 College of Electrical and Information Engineering Hunan University Changsha Hunan 410082 China2 College of Computer Science and Electronic Engineering Hunan University Changsha Hunan 410082 China

Correspondence should be addressed to Lijun Cai ljcaihnueducn

Received 20 August 2014 Accepted 11 October 2014

Academic Editor Yu Gu

Copyright copy 2015 Lei Chen et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Cloud data centers are facing increasingly virtual machine (VM) placement problems such as high energy consumptionimbalanced utilization of multidimension resource and high resource wastage rate In order to solve the virtual machine placementproblems in large scale three algorithms are proposed Firstly we propose a physical machine (PM) classification algorithm byanalyzing pseudotime complexity and find out an important factor (the number of physical hosts) that affects the efficiency whichimproves running efficiency through reduction number of physical hosts secondly we present aVMplacement optimizationmodelusingmultitarget heuristic algorithmandfigure out the positive andnegative vectors of three goals usingmatrix transformation so asto provide themapping of VMs to hosts by comparing distance with positive and negative vectors such that the energy consumptionis saved resources wastage of occupied PM is lowered multidimension resource utilization is optimized and the running time isshortened Finally we consider the poor placement efficiency problem of large-scale virtual serial requests and design a concurrentVM classification algorithm using the119870-means method Simulation experiments validate the performance of the algorithm in fouraspects including placement efficiency resources utilization balance rate wastage rate and energy consumption

1 Introduction

Cloud data center is a new development trend of Internetdata center [1] that is a combination of data center andcloud computing Cloud data centers provide varieties for on-demand computing services consisting of three service mod-els including software as a service (SaaS) platform as a ser-vice (PaaS) and infrastructure as a service (IaaS) [2] forusers which is called data center revolution Currently datacenters benefit a lot from virtualization technology and ithas become one of the core technologies of the cloud datacenter However the placement problems of VMs on PMshave always been a huge challenge at the cloud data center

VM placement problems [1 3] in cloud data center are aphysical resources mapping process of VMs to PMs accord-ing to the reasonable allocation rules The whole process-ing services are facing many decision objectives and otherconstraints which is a complex combinatorial optimizationplacement problem and it has no optimal mathematical solu-tion in theory Heuristic algorithm or approximate algorithm

is commonly regarded as the useful choice to solve the VMplacement In recent years a great number ofworks have beendevoted by many scholars to optimize the VM placementalgorithm and they have made some great achievementsHowever the management of cloud data center is still fac-ing many problems such as the VM placement efficiencyenergy consumption of data center the balance of the multi-dimension resources of the physical machine hosts andthe efficiency of serial placement under large-scale virtualrequests

Most traditional VM placement algorithms only considera single target such as physical host resource utilization orenergy consumption while the motivation of this paper is toput forward new heuristic algorithms for improving the VMsplacement efficiency enhancing virtual machine placementperformance increasing the balance rate of dimension physi-cal resources and reducing the resourcewastage rate of physi-cal host under heterogeneous cloud data center environmentFor considering the physical hosts resource utilization wehope to improve the equilibrium degree of multidimensional

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015 Article ID 679170 14 pageshttpdxdoiorg1011552015679170

2 International Journal of Distributed Sensor Networks

resources and reduce resource waste rate of physical hostFor considering energy consumption we need to select thephysical hostswhich have low energy consumption but strongcomputing capacity thus accelerating placement time

The main contributions can be summarized as follows(1) we propose an ISPMC (iterative self-organizing physicalmachine classification) based on ISODATA (iterative self-organizing data analysis techniques algorithm) [4] whichimproves VM placement efficiency of large Internet data cen-ter using the idea of reduction dimensionality The physicalservers can be divided into 119870 classes by ISPMC algorithmaccording to the number of the PMrsquos CPU and memorywhich ensures that the similar physical machines will bedivided into similar classThe algorithm improves the virtualmachine placement efficiency and reduces the PMsrsquo scanningnumber by actual mapping of virtual machine requests toavailable physical machines (2) We design a multitargetheuristic decision algorithm MTAD (multitarget approachdecision) The algorithm considers multiple objectives at thesame time and uses approximate approach to calculate thepositive and negative ideal vectors of three objectives TheMTAD realizes the optimal placement of VM by comparingrealistic and positive and negative ideal solution approachdegree (3) We propose a 119896-means algorithm for balancingresource rate which is called RBRC (resource balance rateclassification) for considering the problem of the large-scaleVM serial placement efficiency RBRC algorithm sorts allvirtual machine requests to queue in nonincreasing order interms of resource balanced degree and divided the virtualmachine requests into 119896 classes according to the request num-ber and balancing degree to improve the placement efficiencyIn addition if the different dimensions VM resources have abetter balance degree themappingworkloadwill be a balancestatus such that improving the PMsrsquo utilization rate

The rest of this paper is organized as follows Section 2presents related work of the VM placement problemSection 3 presents VM placement model in Section 4 wepropose three algorithms for optimizing VM placementSPMC MTAD and RBRC and Section 5 evaluates theperformance of the algorithm Finally Section 6 summarizesthe work and looks forward to the next work

2 Related Work

Currently the majority of existing VM placement algorithmsin cloud data center can be divided into two categoriesaccording to the placement algorithm in terms of serverobject (1) the placement algorithm based on the server-sidelevel It works by using a variety of advanced technologiesto improve the power consumption or performance (2)The placement algorithms based on cluster level mainlyconsider the global optimization and coordination of the VMplacement aiming at using various strategies or theories toreduce the energy consumption and improve performanceFor goals the existing virtual machine placement algorithmcan be allocated into two categories (1) a virtual machineplacement algorithm based on energy consumption andemissions reduction which aims to save energy and reduceCO2emissions so as to achieve ldquogreenrdquo cloud data center

The placement algorithms mainly concentrated on serverlevel such as dynamic voltage FM technology DVFS andnew cooling technique (2) The second category is a virtualmachine placement algorithm based on resource utilizationthe purpose is to maximize the physical resource utilizationfor ensuring application of quality of service (QoS) andmeeting the needs of application service-level constraintsWefocus on the cluster level on the VM placement algorithmThe current common VM placement algorithms include binpacking stochastic [5] integer programming [6] constraintprogramming [7 8] random greedy algorithm [9] simulatedannealing [10] genetic algorithm [11 12] and ant colony opti-mization algorithm At present most of these algorithms aretrying to solve the imbalanced use of multidimension resour-ces utilization problem high energy consumption problemhyperbole resources wastage problem and other issues

The resource utilization rate of PMrsquos different dimen-sions refers to the imbalanced utilization between differentdimensions resources (CPU and memory) in the process ofvirtual machine placement Sun et al [14] build up a two-objective optimization model and propose a virtual machineplacement algorithm based on matrix transformation Two-objective optimization model takes the balance of differentdimensions in minimizing number of physical machines andresource utilization into consideration The two-objectiveoptimization model firstly sets up corresponding virtualmachine requests queue matrix cluster matrix and thecorresponding initialization placement matrix by consider-ing virtual machine placement algorithm based on matrixtransformation and then looks for the best result meeting thetwo goals by the corresponding matrix transformation Wereduce the dimension of physical machine resources by usingthe concept of vector distance However the model doesnot take the heterogeneous of physical servers into accountand complexity of solving balancing rate based on vectordistanceWang et al [15] put forward amultiobjective geneticevolution VM placement algorithm Firstly the algorithmconstructs the model by considering multiobjective such asbalancing utilization rate of PMrsquos different dimensions ormaximizing resource usage and then considers the averageinequality and position constraint conditions to solve thevirtual machine placement problem using the genetic evo-lutionary algorithm by way of heuristic iterative mutationvirtualized allocation However the resource usage algorithmis poor and has low time efficiency with a large number ofVM requests In [16] Lu et al propose a two-stage virtualmachine consolidation placement algorithm In the firststage they use a polynomial approximate load balancescheme PTAS and adjust the different VM placement andthen migration and integration to maximize the maximumresource utilization In the second stage they balance theload differences of physical servers using queuing modeland reduce the imbalance of different dimensions resourcesThe two-stage algorithm is the objective process of virtualmachine migration and integration but the adjustment ofdynamic resource takes a long time and has poor flexibility

Energy saving [3 17] is anothermain developing directionof VM placement algorithm Shi et al [18] put forward a kindof vector packing algorithm PMs can be seen as a box and

International Journal of Distributed Sensor Networks 3

VMs can be seen as items into box using the greedy thoughtto allocate virtual machine placement with the minimumpossible physical machine and shut down the other unusedphysical machine so as to reduce the number of physicalmachines used to achieve the purpose of saving energyHowever the algorithmdoes not take heterogeneous physicalservers constraints and greedy placement methods cannotachieve the optimal global solution In [19] Wu et al firstlyattempt to solve theVMplacement problemby using the sim-ulated annealing to achieve the energy saving On this basisDhingra and Paul [20] use optimized simulated annealingfor VM placement process looking for energy consumptionby random iteration better physical host servers It ensuresvirtual machinersquos SLA server degree increases the resourcesutilization and reduces the energy consumption Tang andPan [13] propose a virtual machine placement algorithmbased on genetic algorithm Such algorithms consider theenergy consumption of data centerrsquos physical host and theenergy consumption of network communication by generat-ing a random initial population and then use multiple genemutations to look for minimum energy consumption ofphysical hosts and network communication However thealgorithm just considers one network structure and has highcomputational complexity and low allocating efficiency In[21] Song et al propose a large-scale convex optimizationalgorithm for virtual machine placement The algorithmimproves the virtual machine placement by using the theoryof convex optimization to convert the VM placement prob-lem into multiobjective optimization problems according tothe actual data center network architecture

Currently most optimization virtual machine placementalgorithms are converting multiple allocation objectives intoseveral single-objectives and rarely simultaneously optimizemultiple targets Therefore most of them just obtain a localsolution rather than the global optimization solution

3 Virtual Machine Placement Model

31 Notation Used in Virtual Machine Placement Before giv-ing themultitarget approximating virtualmachine placementmodel some notations used in subsequent section are listedin Notations section

Notations used in virtual machine placement are shownin Notations section

32 A Multiobjective Approximating Virtual Machine Place-ment Model The VM placement process in multiobjectiveapproach way is as follows According to themultitarget deci-sion-making (wastage rate balance rate energy consump-tion etc) a series of multidimensions (CPU memory etc)of random VM requests conduct periodic optimization ofthe decision-making process to determine the physicalplacement programs Multiobjective approximating virtualmachine placementmodel considers the following objectives

(1) improve placement algorithm efficiency(2) balance physical servers load reduce wastage rate of

cluster resources and improve resource utilization(3) optimize resource balance rate on different dimen-

sions

(4) reduce the number of high-consumption physicalmachines used and improve energy-efficiency andscalability of data centers

321 Improve Placement Algorithm Efficiency Optimal place-ment algorithm efficiency and reducing placement time VMplacement is NP-hard problem which cannot be solved inpolynomial time but in a pseudopolynomial time

Theorem 1 Pseudopolynomial time of virtual machine place-ment problem is119874(119899

2sdot119874(119885

max119901119903119900

)) the time required for themax-imum target solution is 119874(119885

max119901119903119900

)

Assumptions 1 We have the following

The set of virtual machines request is

V1(cpumem) V

2(sdot sdot sdot ) V

119899(sdot sdot sdot ) (1)

The set of physical host servers is

1199011(cpumem) 119901

2(sdot sdot sdot ) 119901


The objective function set of virtual machines place-ment is 119891

1(119909) 1198912(119909) 119891

119897(119909)

Proof The time complexities of virtual machine placementproblem can be expressed as follows

Firstly scan the virtual machine requests 119894 119894 = 1 rarr 119899one by one traversal matched physical machines accordingto decision-making objective function 119895 119895 = 1 rarr 119898 solvedecision-making optimization objective 119891

119896(119909) 119896 = 1 rarr 119897

for physical machines 119895 one by oneLet 119874(119885

maxpro ) be the maximum time required for solv-

ing the objective function 119874(119885maxpro ) = max119874(119891

1(119909))

119874(119891119897(119909))So the maximum time complexity of virtual machine is

allocated as follows 119874(119899 lowast 119898 lowast 119874(119885maxpro )) = 119874(119899

2119874(119885

maxpro )) 119899

is the dimension number of the physical hostAccording toTheorem 1 we can solve the objective func-

tion itself from the beginning and reduce the used numberof physical servers to improve the VM placement algorithmefficiency

322 Balance Physical Servers Load Reduce Wastage Rate ofCluster Resources and Improve Resource Utilization Wastagerate Waste

119901119895refers to the average ratio value between dif-

ferent dimension remaining resources and the whole phys-ical server as shown in (3) Cluster resource wastage raterefers to the average value of different dimensions resources


wastage rate on physical machine servers which carries vir-tual machines Consider

Waste Rate =

WasteCpu119875119895

=

119901119879cpu119895

119901cpu119895

WasteMem119875119895

=

119901119879mem119895

119901mem119895

Waste119901119895

=

(WasteCpu119875119895

+WasteMem119875119895

)

2

Waste119875=

119898

sum

119895=0

Waste119901119895

(3)

Reduce wastage rate of cluster resources on one handwe need to improve resource utilization of single physicalmachines on the other hand we need to strengthen theresource balance rate on different dimensions of physicalservers Optimized cluster resource wastage rate can beexpressed as

min1198911(119909) = minWaste

119875=

119898

sum

119895=0

(119901119879cpu119895

119901cpu119895

+ 119901119879mem119895

119901mem119895

)

2

(4)

323 Optimize Resource Utilization Rate on Different Dimen-sions Considering multidimensional PMrsquos resources (CPUmemory storage etc) resource utilization rate on differentdimensions should be taken into account with placementvirtual machines ensuring similarity load among multidi-mensional resources to maximize improving resource uti-lization of physical servers Resource placement balancingcomparison is shown in Figure 1

As Figure 1(a) shows PMrsquos CPU utilization has been upto 90 with only 22 of memory utilization The virtualmachine requests include (CPU and memory) resources dueto full capacity utilization of the PMrsquos CPU which cause PMnot to carry more virtual machines and 68 of the memoryresources are idle wasted Figure 1(b) shows that CPU andmemory resources are up to 90 utilization all dimensionsresources have a balanced utilization and PMrsquos differentdimensions reached the best benefit As time goes by thevirtual machines demise CPU and memory utilization canmaintain a good balance which ensures the full use ofdifferent dimensions resources and maximizes PM resourceutilization However due to the randomness of the vir-tual machines requests and randomness of the demandfor resources in each dimension which could not ensureaccuracy balancing of different dimension resources There-fore the more the balanced utilization of each dimensionresources is the more PMrsquos resources are fully used

In order to ensure balance utilization of PMrsquos differentdimensions resources the physical server must try to hosta similar virtual machine request with their remainingresources so we use vector angle to measure the similar-ity between virtual machines and physical server With-out considering the physical storage attributes we han-dle virtual machine requests as a two-dimensional vector

V ⟨CPUMEM⟩ The remaining resources of physical hostscan be seen as a two-dimensional vector ⟨CPUMEM⟩ Justmake sure that the two vectors are mutually parallel and keepresources relatively balancing after physical servers hostingvirtual machines Therefore we use vector angle to measureimpact on virtual machine requests to the physical machineresources the smaller the angle is the better balancingof different dimension resources will be after the physicalmachines have hosted virtualmachines Vector angle formulais as follows

cos ⟨V ⟩ =V sdot

|V| sdot 10038161003816100381610038161003816100381610038161003816

(5)

V sdot = Vcpu (119901cpuminus 119901119879cpu

) + Vmem(119901

memminus 119901119879mem

)

(6)

|V|2 = V sdot V = (Vcpu)2 + (Vmem)2

(7)

10038161003816100381610038161003816100381610038161003816

2

= sdot = (119901cpu

minus 119901119879cpu

)2

+ (119901mem

minus 119901119879mem

)2

(8)

Therefore in order to optimize resource balance rate ofphysical machines we need to minimize the vector anglebetween virtual machines and physical machines objectivesare as follows

min1198912(119909) = sum

V119894isin119881sum

119901119895isin119875

cos ⟨V119894 119901119895⟩ (9)

324 Saving the Energy Efficiency Physical hosts in clouddata center present heterogeneous structure usually com-posed by a variety of different structures physical hosts Ifwe only reduce the PM usage number for saving energy con-sumption usually it is inefficient because small amounts ofhigh-performance energy PMs may cause far greater energyconsumption thanmultiple low-power physical hostsThere-fore multiobjective approach model of this paper for energysaving includes two aspects as follows

(1) Reducing the Number of High Energy Physics Hosts Invirtual machine placement process the multitarget approachmodels will choose smaller power consumption physical hostamong the physical hosts that meet virtual machine requestPlacement principles are as follows as far as possible to assignvirtual machines to physical host that already carried othervirtualmachines to achievemultiple virtualmachines sharingphysical host when a new physical host is needed to open tryto select the low power consumption physical hostThereforeenergy savings objective function can be defined as follows

min1198913(119909) = sum

119895isin119875used

119901energy119895

(10)

(2) Extend the Physical Host Opening and Closing Cycle Dueto the randomness of the virtual machine requests and ran-domness of life cycle the frequent switching physical hostswill inevitably lead to additional energy consumption andcause long switching machine cycle seriously affecting theplacement efficiency and performance of virtual machinesTherefore the hosts need a certain degree of extending the


PM

CPU MEM

90

22

PM

MEM

CPU

68

30 2

VM(CPUMEM)

40 15

20 8

(a)

PM

CPU MEM

90

PM

MEM

CPU

20 30

30 45VM

(CPUMEM)

40 15

90

(b)

Figure 1 PM multidimensional resource balance

switching cycles The model proposes a solution by using afixed waiting periodWe the expert database to determine thephysical hostrsquos closing period119879 as a fixedwaiting time so as toavoid frequent switching the servers During the wait periodthe physical host is idle waiting for the arrival and placementof virtual requests

325 The Objective Function Therefore the objective func-tion of multiobjective approach virtual machine placementmodel is as follows

min119891 (119909) = 120572 lowast 1198911(119909) + 120573 lowast 119891

12(119909) + 120574 lowast 119891

3(119909)

= 120572 lowast [

[

119898

sum

119895=0

(119901119879cpu119895

119901cpu119895

+ 119901119879mem119895

119901mem119895

)

2

]

]

+ 120573 lowast [

[

sum


119901119895isin119875

cos ⟨V119894 119901119895⟩]

]

+ 120574 lowast [

[

sum


119895isin119875

119901energy119895

]

]

(11)

4 A Multitarget Heuristic Algorithm forVirtual Machine Placement MTAD

41 Physical Host Classification Algorithm (ISPMC) TheVMplacement problem in cloud data center is NP-hard problemit cannot be solved in polynomial time FromTheorem 1 weknow that pseudopolynomial time of virtual machine place-ment problem is119874(119899

2sdot 119874(119885

maxpro )) and the time complexity of

the maximum target of all solutions is119874(119885maxpro ) In case of not

considering objective function solving time we must reducethe number of physical hosts 119899 to enhance the efficiencyof placement algorithm the smaller 119899 is the faster virtualmachine placement is

Themain function of ISPMC classification algorithm is toclassify the heterogeneous PM hosts according to the clusterresource types So divide the large number of physical hostsinto 119870 set that have similar structure When the virtualmachine is allocated we use a single physical set as targetgroups so as to reduce the number of placement algorithm forcomputing the physical host 119899 and accelerate virtual machinerequests placement rate


Input(1) Read expert parameter database get pre-classificationnumber 119880(2) The set of physical hosts 119875 119901

119894 119901119894isin 119875

Output The category set of physical hostsFor Iterations 119868 do(1) According to the Euclidean distance to get the

nearest neighbor clustering calculate the cluster domain-related information the cluster center and the averagedistance between the category and the global averagedistance

For Initial cluster doIF119863119895gt 119863 and119873

119896gt 2(120579

119899+ 1) then stop splitting

jump out of loopELSE IF 119870 le 1198802 then split jump out of loopELSE IF iterations are even times or 119880 ge 119870 ge 1198802

then merge jump out of loopELSE IF iterations reach I times the last iteration

then 120579119888= 0 then merge jump out of loop

End IFEnd ForEnd For

Algorithm 1 PM classification algorithm ISPMC

Due to the heterogeneous characteristics of the clouddata center physical host the classification parameters ofphysical host will be determined by actual number of physicalmachines Type 119880 and other information and dynamicallyconstruct parameters expert database that managed by thesystem maintenance people Also the number of classifica-tion 119880 in expert library has great subjective and arbitrarywhich may cause to lower actual classification performanceTherefore we propose a physical host classification algo-rithm ISPMC based on the ISODATA clustering algorithmCompared with ISODATA ISPMC algorithm focuses on thefollowing optimization

(1) To achieve PM classification we use the number ofphysical host CPU and memory as clustering properties andcalculate coordinates in ISPMC algorithm The amount ofmem-ory is enormous magnitude units which need to be reducedcorrespond we can divided it by 512 as a clustering criterion

(2) Compared to the ISODATA algorithm ISPMC algo-rithm reduces the input initial parameters according to theactual situation of physical hostsThe reducing initial param-eters are as the following (1) initialize the cluster centerBecause the ISPMC algorithm parameters expert databasehas already stored species quantity119880 of physical host ISPMCalgorithm can randomly obtain different types hosts to com-posite initialize cluster centers (2) Reduce the complexityof the sample standard deviation calculation according tothreshold 120579

119904 In ISODATAalgorithm it uses distance between

the auxiliary samples to judge whether cluster needs splittingaccording to the fluctuation degree (standard deviation) ofsample and the cluster center as we know the numberof samples is huge multidimensional standard deviationcalculation is time consuming and the effectiveness is lowso ISPMC algorithm combined with the actual physical hostclassification requirements using the distance between the

hosts to determine whether a cluster classification is neededshielding the complexity of the sample standard deviationcalculation optimizes the sample standard deviation of thecomplex calculation

(3) Adjust the splitting standard of ISODATA When thenumber of clusters is two times larger than the predictednumber of119880 ISODATAalgorithmwill not conduct data divi-sion for PM classification the actual classification of the datashould not exceed two times the predicted number SPMCalgorithm adjusts the splitting of the original ISODATA algo-rithm standard 2119880 and ensures ISPMC classification number119870 satisfying 1198802 lt 119870 lt 2119880 The optimizing of ISPMC clas-sification algorithm can help to solve virtual machines place-ment problem

(4) ISPMC algorithm improves the classification time byabandoning standard deviation calculation for all clustersbetween samples and classification standards greatly reducesthe classification of computing time and improves the classi-fication efficiency

Table 1 shows the initial parameters of ISPMC algo-rithm which includes four stages through repeatedly self-organization iteration to achieve physical host classification

Pseudocode for ISPMCalgorithm is shown inAlgorithm 1

Stage 1 Initialize the Environment and Calculate ClusteringInformation

Step 1 Initialize the physical environment read expert para-meter database to obtain preclassification number 119880 inputphysical host set119875 119901

119894 119901119894isin 119875 and generate the initial cluster

centers1198851199111 119911

119896 CPU andmemory are two-dimensional

properties of the physical hosts 119880 is equal to the preclassifi-cation number 119870


Table 1 ISPMC placement algorithm parameters

Vars Description

119880The expected number of (physical classificationnumber) classification

120579119899

Theminimum number of physical machines in eachcategory If the physical machine number is less than itthen it is not a classification

120579119888

Theminimum distance between the two clusters If thenumber is smaller than it merge the two clusters

119871Themerger standard maximum clusters number ofeach iteration

119868 Maximum number of iterations

Step 2 According to the Euclidean distance of initial clustercenters classify the physical host

Step 3 According to (12) correct each cluster domain center119911119896 by (13) calculate the distance between various cluster

domain center physical hosts and cluster center field119863119896 cal-

culate the maximum between various cluster domain centerphysical hosts and cluster center field component Differmax

119896

such as the maximum between CPU of various clusterdomain center physical hosts and CPU of cluster center fieldcomponent Differcpu

119896and memory maximum Differmem

119896 by

(14) calculate the total average distance between physical hostand corresponding cluster center as

119911119896=

1

119873119896

sum

119901isin119911119896

119901 119896 = 1 2 119870 (12)

119863119896=

1

119873119896

sum

119901isin119911119896

1003817100381710038171003817119901 minus 119911119896

1003817100381710038171003817 119896 = 1 2 119870 (13)

119863 =1

119873

119870

sum

119896=1

119873119896119863119896 (14)

Stage 2 Splitting Determination and Merging Operations

Step 4 Cluster splitting determination merger and iteration

(1) If the number of iterations has been reached 119894 timesthe last iteration then 120579

119888= 0 go to Step 6

(2) If the host number in cluster119873119896lt 120579119899 stop the classi-

fication 119896 = 119896 minus 1 go to Step 2(3) If 119870 le 1198802 that is half of the clusters center number

is less than or equal to the predicted value go to Step5 and split the existing clustering process

(4) If the number is an even number of times of theiteration or 119880 ge 119870 ge 1198802 then there is no splittinggo to Step 6 Otherwise go to Step 5 Iteration to aneven number is for fair dealing the merger and splitoperations

(5) If it is the last iteration the algorithm ends otherwiseif it is changing the input parameters go to Step 1 ifnot go to Step 2

Stage 3 Cluster Splitting

Step 5 Judge whether the cluster meets one of the followingtwo conditions

(1) 119863119895gt 119863 and 119873

119896gt 2(120579

119899+ 1) such that total number

of 119911119896classification samples exceeds the specified value

more than double(2) 119870 le 1198802If this is true split 119911

119896into two new cluster centers 119911

+

119896

and 119911minus

119896 119870 = 119896 + 1 Each corresponding component of the

cluster centers in 119911+

119896plus Differmax

119896 each corresponding com-

ponent of 119911minus119896is equal to the cluster centersrsquo component minus

Differmax119896

and finishes splitting operations go to Step 2Otherwise go to Step 4

Stage 4 Cluster Merging

Step 6According to formula (15) calculate the distance of allcluster centers as follows

119863119894119895=

10038171003817100381710038171003817119911119894minus 119911119895

10038171003817100381710038171003817 119894 = 1 2 119870 minus 1 119895 = 119894 + 1 119870

(15)

119911lowast

119896=

1

119873119894119896+ 119873119895119896

[119873119894119896119911119894119896+ 119873119895119896119911119895119896] 119896 = 1 2 119871

(16)

Step 7 Compare 119863119894119895with 120579

119888in ascending order by cluster

distance to form a set 11986311989411198951

11986311989421198952

119863119894119871119895119871

that is 11986311989411198951

lt

11986311989421198952

lt sdot sdot sdot lt 119863119894119871119895119871

Step 8 According to formula (16) merge the two clustercenters 119911

119894119896and 119911

119895119896when the distance is 119863

119894119896119895119896and then get

new center 119911lowast119896 The two merged cluster centers vectors were

respectively divided by the number of clustering domainweighted samples ensure 119911

lowast

119896as a real averaging vector

42 A Multitarget Heuristic Algorithm for Virtual MachinePlacement MTAD In Section 3 we present a multitargetheuristic virtual machine placement model MTAD algo-rithm includes three objectives resource wastage rate dif-ferent dimension resource utilization rate of physical hostsand reducing the energy consumption using approximateapproximation method to sort all solutions select the fithighest multiattribute physical host as the mapping entityand complete the virtual machine placement The basic ideaof MTAD algorithm is based on the resources of the virtualmachine requests select hosts which meet the conditionsof physical host and solve the three dimensions targets byforming a raw data matrix According to the different sizesof three targets data normalize the original matrix to get anormalized matrix and work out the best and worst schemesthat have the maximum positive closeness and minimumnegative closeness

Pseudocode forMTAD algorithm is shown in Algorithm 2The basic steps of MTAD algorithm are as follows

Step 1 Traverse the virtual machine placement request queue119881V1 V

119899


Input (1) Virtual Machine request set 119881V1 V

119899

(2) Input the physical host set 119875 119901119894 119901119894isin 119875

Output The set of virtual machines mappingFor virtual machine requests set do(1) According to the virtual machine requests select the

proper physical hosts(2) Form the original decision matrix according to the

three properties of the target(3) Normalize the original decision matrix to form a

matrix of normalized(4) According to the attributes weights to form the

judgment matrix(5) Looking for the positive and negative ideal solution

of multi-attribute(6) Calculate closeness between attributes and ideal

solution to determine the final placementEnd For

Algorithm 2 MTAD multitarget heuristic algorithm for virtual machine placement

Step 2 Select the physical hosts set 1198751198941199011 119901

119898 which

meets the virtual machine requests

Step 3 According to the three decision attributes of multitar-get approach model for physical hosts set 119875119894119901

1 119901

119898 use

the objective attribute function to solve the property values119909119894119895and form an initial judgment matrix as follows

119869matrix = [

[

11990911

11990912

sdot sdot sdot 1199091119899

11990921

11990922


11990931

11990932


]

]

(17)

Step 4 Because the attribute values may have different unitsthe original decision matrix needs to be normalized accord-ing to formula (19) form a normalized matrix 119869matrix1015840 asfollows

119869matrix1015840 = [[

[

1199091015840

111199091015840

12sdot sdot sdot 1199091015840

1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

(18)

where

1199091015840

119894119895=

119909119894119895

radicsum119899

119895=11199092

119894119895

119894 = 1 2 3 (19)

Step 5 Form a weighted judgment matrix 119885 according to thetarget attributes weights as

119885 = 119869matrix1015840119861 = [

[

1199081

0 0

0 1199082

0

0 0 1199083

]

]

[[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

=[[

[

11989111

11989112


11989121

11989122


11989131

11989132


]]

]

(20)

where 1199081+ 1199082+ 1199083= 1

Step 6 Get the positive ideal solution and negative idealsolution which are used for evaluating targets according tothe weighted comparison matrix 119885 as follows

(1) positive ideal solution

119891lowast

119894= max (119891

119894119895) 119894 isin 1 2 3 (21)

(2) negative ideal solution

1198911015840

119894= min (119891

119894119895) 119894 isin 1 2 3 (22)

Step 7 Calculate the Euclidean distance between the idealsolution values of positive and negative solution as

119878lowast

119895= radic

3

sum

119894=1

(119891119894119895minus 119891lowast

119894)2

119895 isin 1 119899

1198781015840

119895= radic

3

sum

119894=1

(119891119894119895minus 1198911015840

119894)2

119895 isin 1 119899

(23)

Step 8 Calculate the relative closeness of each target as

119862lowast

119895=

1198781015840

119895

(119878lowast

119895+ 1198781015840

119895)

119895 = 1 2 119899 (24)

Step 9Use the relative closeness119862lowast119895size to sort and get a final

decision and solve the next virtual machine

43 Virtual Machine Classification Algorithm Based on Bal-ancing Rate RBRC With the continuous development ofcloud computing technology and the expanding size of thecloud data center the virtual machines concurrent place-ment requests are becoming increasingly huge Large-scalevirtual machine placement requests have brought unprece-dented challenges to the traditional serial placement algo-rithm So we propose a 119870-means virtual machine classi-fication algorithm (RBRC) based on balancing utilization


Input Virtual Machine request Set 119881V1 V

119899

Output 119870 virtual machine classification setIF number of 119881 is bigger than 119870 then(1) Convert the virtual requests into two- dimensionalvector V ⟨CPU MEM⟩ with vector ⟨1 1⟩ Calculateangle |V|(2) Ascend order |V| select 119870 initial point as the center

point in stepwise wayWhile 119870 clusters have changed do(3) re-clustering according to the Euclidean distance(4) Calculate the center point of each cluster

End WhileEnd IF

Algorithm 3 Virtual machine classification algorithm based on balancing rate RBRC

rate the algorithm ensures the balancing rate degree ofvirtual machine requests and dynamically divides the virtualmachine requests into 119870-class according to the 119870-classphysical host partition achieved from ISPMC algorithm so asto improve the efficiency of virtual machines placement andload balancing between different classified physical hosts

Definition 2 (119870-means) Input parameter 119896 divide the set of 119899objects into119870 clusters ensure within the clusters having highsimilarity such that the clusters having low similarity

Definition 3 (Euclidean distance) Euclidean distance isdefined as follows

119889 (119894 119895) = radic(100381610038161003816100381610038161199091198941minus 1199091198951

10038161003816100381610038161003816

2

+100381610038161003816100381610038161199091198942minus 1199091198952

10038161003816100381610038161003816

2

+ sdot sdot sdot +10038161003816100381610038161003816119909119894119901

minus 119909119895119901

10038161003816100381610038161003816

2

)

(25)

where 119894 = (1199091198941 1199091198942 119909

119894119901) and 119895 = (119909

1198951 1199091198952 119909

119895119901) are the

two 119901-dimension data objects

RBRC algorithm process is as follows

Step 1 Input the virtual machine requests Set 119881V1 V

119899

and judge whether the number of119881 is less than or equal to119870if true end algorithm otherwise go to Step 2

Step 2 Convert the virtual requests into two-dimensionalvector V ⟨CPUMEM⟩ according to formula (5) and vector⟨1 1⟩ Calculate angle value |V|

Step 3Ascend order |V| and select119870 initial point as the centerpoint in stepwise way

Step 4 Loop from Step 5 to Step 6 until the cycles do notchange in each cluster anymore

Step 5Traverse119881 and performneighbor clustering accordingto the virtual machine requests and Euclidean distance of 119870center point (25) to form 119896 clusters

Step 6 Recalculate the center vector of each cluster eachcomponent of the vector is the average value of all objectsrsquocomponent in cluster

Pseudocode for RBRC algorithm is shown in Algorithm 3

5 Experimental Simulation

In this paper we use cloud computing platform CloudSim35[22] as a simulation tool to compare ISPMC MTAD andRBRC algorithms with several VM placement algorithmsand verify the placement efficiency of ISPMC and RBRCalgorithms At the same time we evaluate the performanceof the MTAD algorithm by considering placement efficiencyresource wastage rate multidimension resources balancerate and physical machine energy consumption simulationresults are illustrated theMTAD algorithm has better perfor-mance than other algorithms

51 Simulation Environment In the CloudSim platformphysicalmachine requests and virtualmachine placement aregenerated in the random way We design multiple classessuch as the data center host VM andDataCenterBroker andimplement the simulation of the VM and PM We optimizeCloudSim simulation so as to submit repeatedly virtualmachine allocation requests in multibatch way by using themultithreadTherefore we can simulate the placement of vir-tual machine requests on more reality environment (becausereal virtual machine placement is a dynamic change processphysical machine hosts may have already loaded some virtualmachine requests) Strategies generated for the physical andvirtual machine placement are listed as follows

511 Physical Machine Random generation is adopted todefine classDataCenterCharacteristics for generating the cor-responding DataCenter andmain physical machine hosts Toapproach more approximately real circumstances four typesof physical hosts are generated to simulate heterogeneousenvironment as shown in Table 2

Again random strategy is applied under the conditionof four-type physical machines to generate multiple physicalhost machines Machines of the first type are equipped withordinary and larger amount of parameters Similarly hostmachines have smaller amount when they are more highlyequipped Main random generation lists are given in Table 3


Table 2 Parameters of physical host machine

Type CPU cores Memory (G) Power (w)G1 2 4 220G2 6 8 260G3 8 14 300G4 16 24 380

Table 3 Random generation lists of physical hosts

Amount Type-G1 Type-G2 Type-G3 Type-G4800 350 200 150 1001200 550 350 200 1002000 900 550 300 2503500 1600 900 600 4005000 2300 1200 1000 5007500 3500 2000 1200 800

Table 4 The description of simulation algorithms

Indicator Algorithm

Gr [9] Comparing VM placement algorithms ofon-demand cloud computing using greedy algorithm

Sa [10] Resource allocation in cloud computing area usingsimulated annealing algorithm

Ga [13] A hybrid genetic algorithm for the energy efficientvirtual machine placement problem in data centers

MTAD Amultitarget heuristic algorithm for virtual machineplacement

ISPMC An iterative self-organizing physical machineclassification algorithm

RBRC A 119870-means virtual machine classification algorithm

512 Virtual Machine Placement Requests Random strategyis used for the second time to generate the placement queueof VM requests based on the number of physical hostsgenerated so as to form VM queue that meets CloudSimand DataCenterBroker In this study random parameters ofplacement requests were chosen from 10 to approximately3500 where CPU cores were generated randomly from 1 to6 and memory from 1 lowast 512M to approximately 15 lowast 512MMemory amount in each generation is equal to multipleintegers of 512M

52 Simulation Result On CloudSim many demonstrationswere given for ISPMCMTAD and RBRC algorithms Exper-iments simulation and performance analysis were shown inTable 4 where placement efficiency wastage rate balancerate and energy consumption were taken as the performanceindexes Table 4 depicts diagram of the six algorithms

521 Simulation Results of ISPMC Algorithm Themain pur-pose of ISPMC algorithm is to classify the physical hosts andnarrow the scanning dimension of physical host machinesOn basis of genetic revolution placement the experimenthas compared the placement efficiency difference by usingISPMC and analyzed its performance In Figures 2 and 3it can be clearly known that ISPMC further accelerates

0 100 200 300 400 500 600 7000

500

1000

1500

2000

2500

3000VM placement acceleration rate(PM-5000)

VM

allo

catio

n tim

e (m

s)

VM number

GaGa-ISPMC

Figure 2 The acceleration rate on genetic algorithm (a)

0 2000 4000 6000 80003500

4000

4500

5000

5500VM acceleration rate(VM-1000)

VM

allo

catio

n tim

e (m

s)

PM number

GaGa-ISPMC

Figure 3 The acceleration rate on genetic algorithm (b)

the placement efficiency rate and improves placement per-formance Figure 2 displays the acceleration condition ofISPMC genetic placement algorithm when the number ofhost machines is 5000 and placement requests are rangingfrom 10 to 700 With the number of virtual machine requestsbeing increased it is more obvious for ISPMC to improvethe placement efficiency In Figure 3 we fixed the numberof virtual machine requests to verify the acceleration per-formance of ISPMC placement efficiency by changing thenumber of the physical hosts As seen fromFigure 3 when thenumbers of physical hosts become larger ISPMC can betteraccelerate the placement efficiencyThrough the classificationof ISPMC algorithm we reduced the physical host dimensionand shortened virtual machine placement time howeverwhen the numbers of physical hosts become smaller theacceleration performance of ISPMC is a bit poorer than thatof the genetic algorithm Because physical hosts dimensionis too small if it is classified again physical host dimensiondecreased slowly Besides the ISPMC algorithm itself needs


0 50 100

200

300

400

500

600

700

800

900

1000

1200

0

1000

2000

3000

4000

5000

6000Host number (5000)

VM

allo

catio

n tim

e (m

s)

VM numberGrSa

GaMTAD

Figure 4 The running time

classification for some time Therefore when the physicalhost number is small the acceleration performance of ISPMCalgorithm is poor In addition the ISPMC algorithm is toclassify the physical hosts so that virtual machine placementrequests will relatively concentrate on mapping on the sametype of physical host which promotes regional balancedperformance and provides convenience for conservation andmanagement of energy consumption

522 Simulation Results of MTAD Algorithm The experi-ment verifies MTAD algorithm in many aspects We verifyperformance between MTAD algorithm and several otheralgorithms including algorithmplacement efficiency wastagerate resource balance rate and energy consumption

Figure 4 shows the placement time difference of variousalgorithms Placement efficiency of MTAD algorithm isbetter than that of other algorithms As shown in Figure 4with the increase of the virtual machine requests placementtime increases gradually Time efficiency ofMTAD algorithmis between greedy algorithm and genetic algorithm the sim-ulated annealing algorithm is the worst because the greedyalgorithm only needs to randomly select the large resourcein physical host set and has the faster time In the physicalhosts MTAD algorithm is required to extract positive andnegative solutions which meet multiple objectives (prop-erties) and then approximately chooses a suitable physicalhost MTAD algorithm is slightly worse than the greedyalgorithm over time aspect When using genetic algorithmand simulated annealing which need many time iterationsin the initial solutions to obtain more optimal physical hostthe longer iteration is the longer time consumption is Inaddition with the number of virtual machine requests beingincreased greedy algorithm needs to traverse longer scopeand time consumption becomes longer with the number ofvirtual machine requests being increased MTAD algorithmsupported by ISPMC will exceed greedy algorithm

The resource utilization rate of PMrsquos different dimensions(balance rate) has been verified in Figure 5 Utilizationbalance rate refers to angle value between CPU and memory

0 50 100

200

300

400

500

600

700

800

900

1000

1100

1200

Host number (5000)

Reso

urce

bal

ance

d ra

te

VM numberGrSa

GaMTAD

03

04

05

06

07

08

09

1

Figure 5 Resource balanced rate

utilization and reflects difference degree on different dimen-sions of physical hosts Balance rate is higher and the availableextended resources of different dimensions are greater whichincrease overall resource utilization of physical hosts As seenfrom Figure 5 the resource utilization of MTAD algorithmis optimal Ga algorithm takes second place and greedyalgorithm is the worst When carrying out virtual machineplacement firstly MTAD algorithm traverses physical hostsset to calculate the physical hosts set which meets virtualmachine requests by using the approach method Then weget the approximate positive and negative solutions in thephysical host set according to multiple targets restrictedFinally we find the suitable physical hosts through theglobal approach degree of multiple targets We fully considervirtual machine placement agent that affects PMrsquos differentdimensions resources balance rate when MTAD algorithmcarries the virtual machine placement and choose smallerdifference balance rate as assignment target and thereforeimprove the overall balance level of PM hosts Ga intelligentplacement algorithm uses self-organizing repeated iterativeit also considers local resource balancing degree Greedyalgorithm does not consider different dimensions resourcesbalance rate so its efficiency is the worst

The resourcewastage rate refers towastage degree averagevalue of different dimensions resources for virtual machineshosted by physical machine (in this paper we only considerCPU and memory) and it is another measure index of theresource utilization rate Figure 6 compares various algorithmdifferences of a PMrsquos resource wastage rate As known fromFigure 6 with the VM requests being increased physicalhost resource wastage rate gradually decreased and stabilizedAmong the algorithms resource wastage rate of MTADalgorithm is the lowest Ga algorithm and Sa algorithm areapproximate and greedy algorithm is the worst From Fig-ure 6 it is not difficult to know that resource wastage rate ofMTAD algorithm is optimal Firstly theMTAD considers thecurrent balance rate approximation degree of virtualmachinerequests and physical host the closer of the degree is themore balancing of the physical host resource utilization will


Host number (5000)

Reso

urce

was

te ra

te

0 50 100

200

300

400

500

600

700

800

900

1000

1200

VM numberGrSa

GaMTAD

03

02

01

04

05

06

07

08

09

1

Figure 6 Resource waste rate

200400540

200400

0

500

200 300 400 500 600 700 800 900 1000 12000

50100

Phys

ical

mac

hine

usa

ge

Virtual machine number

GrGa

SaMTAD

PM-G 4

PM-G 2

(6Core8G260W)

(16Core24G380W)

PM-G 3

(8Core14G300W)

PM-G 1

(2Core4G220W)

Figure 7 Physical machine usage

be the available degree of different dimensions resourcesbecomes larger and the PMrsquos wastage rate will be smallersecondly use ISPMC algorithm to classify virtual machineplacement virtual machines will relatively concentrate on aclassification physical host so as to enhance the physical hostarea utilization rate However through repeated iteration Gaalgorithm and Sa algorithm which take the whole physicalmachine set as the placement area for improving the virtualmachine placement efficiency yet the overall resource rate isweaker than that of MTAD algorithm However the greedyalgorithm does not consider any optimization for virtualmachine placement so the resource waste rate is the highest

Figure 7 shows the energy consumption performance ofdifferent placement algorithms Due to heterogeneous struc-ture of data center physical hosts it is not proper if we simplycompare energy performance according to the physical hostsused number We consider the used number of different typeof physical hosts under the condition that the size of physicalhosts is fixed different virtual machine placement requestsare carried out so as to statistical the quantity of differenttype physical hosts From Figure 7 we can see that four algo-rithms placement 200sim1200 virtual machine requests in5000 physical hosts The used number of four differentphysical hosts can be seen from left to right as follows

(1)The first class physical host with the number of virtualmachine placement requests being increased the used num-ber of physical hosts ofGAalgorithmandMTADalgorithm isrelatively larger Ga algorithm is slightly higher than MTADalgorithm Compared with two previous algorithms the usednumber of Sa algorithm is smaller and the greedy algorithmdoes not have any physical host (2)The second class physicalhost a large number of the second class physical hosts areused by MTAD algorithm followed by Sa algorithm Gaalgorithm and theGR algorithmTheGRalgorithm also doesnot use any second host (3) The third class host among thefour kinds of algorithms Sa algorithm andMTAD algorithmused more physical hosts Ga algorithm and Gr algorithmare less (4) The fourth class host with the number of virtualmachine requests being increased greedy algorithm usedalmost all of the fourth class physical hosts Ga algorithmis the second and Sa algorithm is the medium MTADalgorithm almost does not use any fourth class physical hostFrom Figure 7 we summarize that when MTAD algorithmcarries the virtual machine requests it tends to use lowerenergy consumption (low configuration) physical hosts Saalgorithm and Ga algorithm are the random balancingplacement while greedy algorithm is likely to use the highenergy consumption physical host (high configuration)

523 Simulation Results of RBRC Algorithm With thecontinuous development of the cloud computing modelthe number of virtual machine placement will be gradu-ally expanded the current serial placement will inevitablybecome a bottleneck of virtualmachine placement algorithmWe present RBRC algorithm that aims at solving the aboveproblem the main idea is to use classification thought toclassify resource demand similar to virtual machine basedon large-scale virtual machine requests and achieve theconcurrent placement way We take the demand balancedegree of different dimensions resources as core classificationidea According to ISPMC algorithm physical hosts will bedivided into119870 class by using119870-means classification Figure 8is an assigning time efficiency acceleration diagram of RBRCalgorithm

As shown in Figure 8 with the number of virtualmachines being increased RBRC algorithm can greatlyimprove the placement efficiency of MTAD algorithmBecause of RBRC classification algorithm concurrent place-ment virtual machine requests the algorithm greatly reducesthe whole placement time and improves the performanceHowever when the quantity of virtual machine placement isfew the classification degree of RBRC is relatively small theused time is almost the same and does not change too much

6 Conclusion

We put forward three optimal algorithms for virtual machineplacement by analyzing the related work and defects ofvirtual machine placement algorithms in cloud data center(1) ISPMC is a physical hosts classification algorithm Takingthe heterogeneous nature of the physical host constraints weclassify the physical hosts by clustering so as to reduce thedimensions of the physical hosts and optimize the placement


0 50 1000

100

200


VM

allo

catio

n tim

e (m

s)

VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

200

400


VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

500


VM number

MTADMTAD-RBRC

VM

allo

catio

n tim

e (m

s)

MTADMTAD-RBRC

0 50 1000

500

1000


VM number

Figure 8 Placement time efficiency of RBRC

efficiency of virtual machine requests (2) MTAD is a multi-target heuristic virtual machine placement algorithmMTADconsiders virtual machine placement problems such asldquodifferent dimensions resources imbalancedrdquo ldquohigh wastageraterdquo and ldquohigh energy consumptionrdquo We use multiobjectiveoptimization theory traverse the set of physical hosts and getthe multiple objectives positive and negative ideal solutionsThus we can obtain a reasonable placement solution bycomparison of approach degree between multiple objectivesand positive and negative ideal solutions MTAD algorithmenhances the balance rate of different PMrsquos dimensionsresources and the overall resources utilization it is effective torequest heterogeneous physical hosts with lower energy con-sumption (3) There is a VM classification algorithm RBRCbased on 119870-means We divided the virtual machines intoseveral similar demand groups and used concurrent place-ment model to achieve the goal of rapidly allocating virtualmachines The main target of RBRC algorithm is to solve lowefficiency problem of large-scale virtual machine placementin serial way

All three kinds of optimization algorithms focus on thephysical machine hosts and have no considering of the net-work factors and other special applications (QoS quality etc)which will be the future work

Notations

119881 Random set of virtual machine requests119875 Set of data center physical servers

119875used Set of virtual machines hosted byphysical servers

119881cpu119894

CPU demand for virtual machine 119894V119894isin 119881

119881mem119894

Memory demand for virtual machine 119894V119894isin 119881

119901cpu119895

The total capacity of the physical hostCPU of 119895 119901

119895isin 119875

119901mem119895

The total capacity of the physical hostmemory of 119895 119901

119895isin 119875

119901energy119895

Power consumption per unit time of thephysical host (W)

119901119879cpu119895

The total used number of physical hostCPU of 119895 119901

119895isin 119875

119901119879mem119895

The total used number of physical hostmemory of 119895 119901

119895isin 119875

119881119901119895 Set of virtual machines hosted by

physical host 119901119895 119901119895isin 119875

119901Vcount119895

The number of virtual machines on aphysical server 119895 hosted 119901

119895isin 119875

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Key TechnologySupport Program of China Grant no 2012BAH09B02 and


the Key Science and Technology Project of Changsha CityGrant no K1204006-11-1

References

[1] M F Bari R Boutaba R Esteves et al ldquoData center networkvirtualization a surveyrdquo IEEE Communications Surveys andTutorials vol 15 no 2 pp 909ndash928 2013

[2] T Dillon C Wu and E Chang ldquoCloud computing issues andchallengesrdquo in Proceedings of the 24th IEEE International Con-ference on Advanced Information Networking and Applications(AINA rsquo10) pp 27ndash33 Perth Australia April 2010

[3] R Ranjana and J Raja ldquoA survey on power aware virtualmachine placement strategies in a cloud data centerrdquo inProceed-ings of the IEEE International Conference on Green ComputingCommunication and Conservation of Energy (ICGCE rsquo13) pp747ndash752 2013

[4] E Vintrou D Ienco A Begue and M Teisseire ldquoData mininga promising tool for large-area croplandmappingrdquo IEEE Journalof Selected Topics in Applied Earth Observations and RemoteSensing vol 6 no 5 pp 2132ndash2138 2013

[5] N Bobroff A Kochut and K Beaty ldquoDynamic placement ofvirtual machines for managing SLA violationsrdquo in Proceedingsof the 10th IFIPIEEE International Symposium on IntegratedNetwork Management (IM rsquo07) pp 119ndash128 Munich GermanyMay 2007

[6] S Chaisiri B-S Lee and D Niyato ldquoOptimal virtual machineplacement acrossmultiple cloud providersrdquo inProceeding sof theIEEE Asia-Pacific Services Computing Conference (APSCC rsquo09)pp 103ndash110 IEEE December 2009

[7] H N Van F D Tran and J-M Menaud ldquoAutonomic vir-tual resource management for service hosting platformsrdquo inProceedings of the ICSE Workshop on Software EngineeringChallenges of Cloud Computing (CLOUD rsquo09) pp 1ndash8 IEEEComputer Society May 2009

[8] X Meng V Pappas and L Zhang ldquoImproving the scalabilityof data center networks with traffic-aware virtual machineplacementrdquo in Proceedings of the IEEE Conference on ComputerCommunications (IEEE INFOCOM rsquo10) pp 1ndash9 San DiegoCalif USA March 2010

[9] K Mills J Filliben and C Dabrowski ldquoComparing VM-placement algorithms for on-demand cloudsrdquo in Proceedingsof the 3rd IEEE International Conference on Cloud ComputingTechnology and Science (CloudCom rsquo11) pp 91ndash98 Athens GaUSA December 2011

[10] D Pandit S Chattopadhyay M Chattopadhyay and N ChakildquoResource allocation in cloud using simulated annealingrdquoin Proceedings of the Applications and Innovations in MobileComputing (AIMoC rsquo14) pp 21ndash27 Kolkata India March 2014

[11] H Nakada T Hirofuchi H Ogawa et al ldquoToward virtualmachine packing optimization based on genetic algorithmrdquoin Distributed Computing Artificial Intelligence BioinformaticsSoft Computing and Ambient Assisted Living pp 651ndash654Springer Berlin Germany 2009

[12] S Agrawal S K Bose and S Sundarrajan ldquoGrouping geneticalgorithm for solving the server consolidation problem withconflictsrdquo in Proceedings of the 1st ACMSIGEVO Summit onGenetic and Evolutionary Computation (GEC rsquo09) pp 1ndash8 June2009

[13] M Tang and S Pan ldquoA hybrid genetic algorithm for the energy-efficient virtual machine placement problem in data centersrdquoNeural Processing Letters 2014

[14] M SunWGu X ZhangH Shi andWZhang ldquoAmatrix trans-formation algorithm for virtual machine placement in cloudrdquoin Proceedings of the 12th IEEE International Conference onTrust Security and Privacy in Computing and Communications(TrustCom rsquo13) pp 1778ndash1783 July 2013

[15] S Wang H Gu and G Wu ldquoA new approach to multi-objective virtual machine placement in virtualized data centerrdquoin Proceedings of the 8th IEEE International Conference onNetworking Architecture and Storage (NAS rsquo13) pp 331ndash335 July2013

[16] L Lu H Zhang E Smirni G Jiang and K Yoshihira ldquoPre-dictive VM consolidation on multiple resources beyond loadbalancingrdquo in Proceedings of the IEEEACM 21st InternationalSymposium on Quality of Service (IWQoS rsquo13) pp 83ndash92Montreal Canada June 2013

[17] B Wadhwa and A Verma ldquoEnergy saving approaches forgreen cloud computing a reviewrdquo in Proceedings of the RecentAdvances in Engineering and Computational Sciences (RAECSrsquo14) pp 1ndash6 Chandigarh India March 2014

[18] L Shi J Furlong and R Wang ldquoEmpirical evaluation ofvector bin packing algorithms for energy efficient data centersrdquoin Proceedings of the IEEE Symposium on Computers andCommunications (ISCC rsquo13) Split Croatia July 2013

[19] Y Wu M Tang and W Fraser ldquoA simulated annealingalgorithm for energy efficient virtual machine placementrdquo inProceedings of the IEEE International Conference on SystemsMan and Cybernetics (SMC rsquo12) pp 1245ndash1250 Seoul SouthKorea October 2012

[20] A Dhingra and S Paul ldquoGreen cloud heuristic based BFOtechnique to optimize resource allocationrdquo Indian Journal ofScience and Technology vol 7 no 5 pp 685ndash691 2014

[21] F Song D Huang H Zhou H Zhang and I You ldquoAnOptimization-Based Scheme for Efficient Virtual MachinePlacementrdquo International Journal of Parallel Programming vol42 no 5 pp 853ndash872 2014

[22] R N Calheiros R Ranjan A Beloglazov A F C de Rose andR Buyya ldquoCloudSim a toolkit for modeling and simulationof cloud computing environments and evaluation of resourceprovisioning algorithmsrdquo SoftwaremdashPractice amp Experience vol41 no 1 pp 23ndash50 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



resources and reduce resource waste rate of physical hostFor considering energy consumption we need to select thephysical hostswhich have low energy consumption but strongcomputing capacity thus accelerating placement time

The main contributions can be summarized as follows(1) we propose an ISPMC (iterative self-organizing physicalmachine classification) based on ISODATA (iterative self-organizing data analysis techniques algorithm) [4] whichimproves VM placement efficiency of large Internet data cen-ter using the idea of reduction dimensionality The physicalservers can be divided into 119870 classes by ISPMC algorithmaccording to the number of the PMrsquos CPU and memorywhich ensures that the similar physical machines will bedivided into similar classThe algorithm improves the virtualmachine placement efficiency and reduces the PMsrsquo scanningnumber by actual mapping of virtual machine requests toavailable physical machines (2) We design a multitargetheuristic decision algorithm MTAD (multitarget approachdecision) The algorithm considers multiple objectives at thesame time and uses approximate approach to calculate thepositive and negative ideal vectors of three objectives TheMTAD realizes the optimal placement of VM by comparingrealistic and positive and negative ideal solution approachdegree (3) We propose a 119896-means algorithm for balancingresource rate which is called RBRC (resource balance rateclassification) for considering the problem of the large-scaleVM serial placement efficiency RBRC algorithm sorts allvirtual machine requests to queue in nonincreasing order interms of resource balanced degree and divided the virtualmachine requests into 119896 classes according to the request num-ber and balancing degree to improve the placement efficiencyIn addition if the different dimensions VM resources have abetter balance degree themappingworkloadwill be a balancestatus such that improving the PMsrsquo utilization rate

The rest of this paper is organized as follows Section 2presents related work of the VM placement problemSection 3 presents VM placement model in Section 4 wepropose three algorithms for optimizing VM placementSPMC MTAD and RBRC and Section 5 evaluates theperformance of the algorithm Finally Section 6 summarizesthe work and looks forward to the next work

2 Related Work

Currently the majority of existing VM placement algorithmsin cloud data center can be divided into two categoriesaccording to the placement algorithm in terms of serverobject (1) the placement algorithm based on the server-sidelevel It works by using a variety of advanced technologiesto improve the power consumption or performance (2)The placement algorithms based on cluster level mainlyconsider the global optimization and coordination of the VMplacement aiming at using various strategies or theories toreduce the energy consumption and improve performanceFor goals the existing virtual machine placement algorithmcan be allocated into two categories (1) a virtual machineplacement algorithm based on energy consumption andemissions reduction which aims to save energy and reduceCO2emissions so as to achieve ldquogreenrdquo cloud data center

The placement algorithms mainly concentrated on serverlevel such as dynamic voltage FM technology DVFS andnew cooling technique (2) The second category is a virtualmachine placement algorithm based on resource utilizationthe purpose is to maximize the physical resource utilizationfor ensuring application of quality of service (QoS) andmeeting the needs of application service-level constraintsWefocus on the cluster level on the VM placement algorithmThe current common VM placement algorithms include binpacking stochastic [5] integer programming [6] constraintprogramming [7 8] random greedy algorithm [9] simulatedannealing [10] genetic algorithm [11 12] and ant colony opti-mization algorithm At present most of these algorithms aretrying to solve the imbalanced use of multidimension resour-ces utilization problem high energy consumption problemhyperbole resources wastage problem and other issues

The resource utilization rate of PMrsquos different dimen-sions refers to the imbalanced utilization between differentdimensions resources (CPU and memory) in the process ofvirtual machine placement Sun et al [14] build up a two-objective optimization model and propose a virtual machineplacement algorithm based on matrix transformation Two-objective optimization model takes the balance of differentdimensions in minimizing number of physical machines andresource utilization into consideration The two-objectiveoptimization model firstly sets up corresponding virtualmachine requests queue matrix cluster matrix and thecorresponding initialization placement matrix by consider-ing virtual machine placement algorithm based on matrixtransformation and then looks for the best result meeting thetwo goals by the corresponding matrix transformation Wereduce the dimension of physical machine resources by usingthe concept of vector distance However the model doesnot take the heterogeneous of physical servers into accountand complexity of solving balancing rate based on vectordistanceWang et al [15] put forward amultiobjective geneticevolution VM placement algorithm Firstly the algorithmconstructs the model by considering multiobjective such asbalancing utilization rate of PMrsquos different dimensions ormaximizing resource usage and then considers the averageinequality and position constraint conditions to solve thevirtual machine placement problem using the genetic evo-lutionary algorithm by way of heuristic iterative mutationvirtualized allocation However the resource usage algorithmis poor and has low time efficiency with a large number ofVM requests In [16] Lu et al propose a two-stage virtualmachine consolidation placement algorithm In the firststage they use a polynomial approximate load balancescheme PTAS and adjust the different VM placement andthen migration and integration to maximize the maximumresource utilization In the second stage they balance theload differences of physical servers using queuing modeland reduce the imbalance of different dimensions resourcesThe two-stage algorithm is the objective process of virtualmachine migration and integration but the adjustment ofdynamic resource takes a long time and has poor flexibility

Energy saving [3 17] is anothermain developing directionof VM placement algorithm Shi et al [18] put forward a kindof vector packing algorithm PMs can be seen as a box and










sions




2sdot119874(119885

max119901119903119900


max119901119903119900

)



V1(cpumem) V




1199011(cpumem) 119901




1(119909) 1198912(119909) 119891

119897(119909)



119896(119909) 119896 = 1 rarr 119897




1(119909))



2119874(119885

maxpro )) 119899








Waste Rate =


=

119901119879cpu119895

119901cpu119895


=

119901119879mem119895

119901mem119895

Waste119901119895

=

(WasteCpu119875119895

+WasteMem119875119895

)

2

Waste119875=

119898

sum

119895=0

Waste119901119895

(3)


min1198911(119909) = minWaste

119875=

119898

sum

119895=0

(119901119879cpu119895

119901cpu119895

+ 119901119879mem119895

119901mem119895

)

2

(4)






|V| sdot 10038161003816100381610038161003816100381610038161003816

(5)


) + Vmem(119901


)

(6)


(7)

10038161003816100381610038161003816100381610038161003816

2

= sdot = (119901cpu

minus 119901119879cpu

)2

+ (119901mem

minus 119901119879mem

)2

(8)


min1198912(119909) = sum


119901119895isin119875

cos ⟨V119894 119901119895⟩ (9)



min1198913(119909) = sum


119901energy119895

(10)



PM

CPU MEM

90

22

PM

MEM

CPU

68

30 2

VM(CPUMEM)

40 15

20 8

(a)

PM

CPU MEM

90

PM

MEM

CPU

20 30

30 45VM

(CPUMEM)

40 15

90

(b)





12(119909) + 120574 lowast 119891

3(119909)

= 120572 lowast [

[

119898

sum

119895=0

(119901119879cpu119895

119901cpu119895

+ 119901119879mem119895

119901mem119895

)

2

]

]

+ 120573 lowast [

[

sum


119901119895isin119875

cos ⟨V119894 119901119895⟩]

]

+ 120574 lowast [

[

sum


119895isin119875

119901energy119895

]

]

(11)



2sdot 119874(119885







119894 119901119894isin 119875




119896gt 2(120579




















centers1198851199111 119911





Vars Description


120579119899


120579119888








119896



119896 by


119911119896=

1

119873119896

sum

119901isin119911119896

119901 119896 = 1 2 119870 (12)

119863119896=

1

119873119896

sum

119901isin119911119896

1003817100381710038171003817119901 minus 119911119896

1003817100381710038171003817 119896 = 1 2 119870 (13)

119863 =1

119873

119870

sum

119896=1

119873119896119863119896 (14)




119888= 0 go to Step 6








(1) 119863119895gt 119863 and 119873

119896gt 2(120579





+

119896

and 119911minus






Differmax119896




119863119894119895=

10038171003817100381710038171003817119911119894minus 119911119895

10038171003817100381710038171003817 119894 = 1 2 119870 minus 1 119895 = 119894 + 1 119870

(15)

119911lowast

119896=

1

119873119894119896+ 119873119895119896

[119873119894119896119911119894119896+ 119873119895119896119911119895119896] 119896 = 1 2 119871

(16)




11986311989421198952

119863119894119871119895119871

that is 11986311989411198951

lt

11986311989421198952



119894119896and 119911


119894119896119895119896and then get



lowast





119899



119899











119898 which



1 119901

119898 use


119869matrix = [

[

11990911

11990912


11990921

11990922


11990931

11990932


]

]

(17)


119869matrix1015840 = [[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

(18)

where

1199091015840

119894119895=

119909119894119895

radicsum119899

119895=11199092

119894119895

119894 = 1 2 3 (19)


119885 = 119869matrix1015840119861 = [

[

1199081

0 0

0 1199082

0

0 0 1199083

]

]

[[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

=[[

[

11989111

11989112


11989121

11989122


11989131

11989132


]]

]

(20)

where 1199081+ 1199082+ 1199083= 1



119891lowast

119894= max (119891

119894119895) 119894 isin 1 2 3 (21)


1198911015840

119894= min (119891

119894119895) 119894 isin 1 2 3 (22)


119878lowast

119895= radic

3

sum

119894=1

(119891119894119895minus 119891lowast

119894)2

119895 isin 1 119899

1198781015840

119895= radic

3

sum

119894=1

(119891119894119895minus 1198911015840

119894)2

119895 isin 1 119899

(23)


119862lowast

119895=

1198781015840

119895

(119878lowast

119895+ 1198781015840

119895)

119895 = 1 2 119899 (24)






119899



End WhileEnd IF





119889 (119894 119895) = radic(100381610038161003816100381610038161199091198941minus 1199091198951

10038161003816100381610038161003816

2

+100381610038161003816100381610038161199091198942minus 1199091198952

10038161003816100381610038161003816

2

+ sdot sdot sdot +10038161003816100381610038161003816119909119894119901

minus 119909119895119901

10038161003816100381610038161003816

2

)

(25)

where 119894 = (1199091198941 1199091198942 119909

119894119901) and 119895 = (119909

1198951 1199091198952 119909

119895119901) are the




119899



















Indicator Algorithm










0 100 200 300 400 500 600 7000

500

1000

1500

2000

2500


VM

allo

catio

n tim

e (m

s)

VM number

GaGa-ISPMC


0 2000 4000 6000 80003500

4000

4500

5000


VM

allo

catio

n tim

e (m

s)

PM number

GaGa-ISPMC




0 50 100

200

300

400

500

600

700

800

900

1000

1200

0

1000

2000

3000

4000

5000


VM

allo

catio

n tim

e (m

s)

VM numberGrSa

GaMTAD






0 50 100

200

300

400

500

600

700

800

900

1000

1100

1200

Host number (5000)

Reso

urce

bal

ance

d ra

te

VM numberGrSa

GaMTAD

03

04

05

06

07

08

09

1





Host number (5000)

Reso

urce

was

te ra

te

0 50 100

200

300

400

500

600

700

800

900

1000

1200

VM numberGrSa

GaMTAD

03

02

01

04

05

06

07

08

09

1


200400540

200400

0

500

200 300 400 500 600 700 800 900 1000 12000

50100

Phys

ical

mac

hine

usa

ge


GrGa

SaMTAD

PM-G 4

PM-G 2

(6Core8G260W)

(16Core24G380W)

PM-G 3

(8Core14G300W)

PM-G 1

(2Core4G220W)







6 Conclusion



0 50 1000

100

200


VM

allo

catio

n tim

e (m

s)

VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

200

400


VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

500


VM number

MTADMTAD-RBRC

VM

allo

catio

n tim

e (m

s)

MTADMTAD-RBRC

0 50 1000

500

1000


VM number




Notations



119881cpu119894


119881mem119894


119901cpu119895


119895isin 119875

119901mem119895


119895isin 119875

119901energy119895


119901119879cpu119895


119895isin 119875

119901119879mem119895


119895isin 119875



119901Vcount119895


119895isin 119875



Acknowledgments




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















sions




2sdot119874(119885

max119901119903119900


max119901119903119900

)



V1(cpumem) V




1199011(cpumem) 119901




1(119909) 1198912(119909) 119891

119897(119909)



119896(119909) 119896 = 1 rarr 119897




1(119909))



2119874(119885

maxpro )) 119899








Waste Rate =


=

119901119879cpu119895

119901cpu119895


=

119901119879mem119895

119901mem119895

Waste119901119895

=

(WasteCpu119875119895

+WasteMem119875119895

)

2

Waste119875=

119898

sum

119895=0

Waste119901119895

(3)


min1198911(119909) = minWaste

119875=

119898

sum

119895=0

(119901119879cpu119895

119901cpu119895

+ 119901119879mem119895

119901mem119895

)

2

(4)






|V| sdot 10038161003816100381610038161003816100381610038161003816

(5)


) + Vmem(119901


)

(6)


(7)

10038161003816100381610038161003816100381610038161003816

2

= sdot = (119901cpu

minus 119901119879cpu

)2

+ (119901mem

minus 119901119879mem

)2

(8)


min1198912(119909) = sum


119901119895isin119875

cos ⟨V119894 119901119895⟩ (9)



min1198913(119909) = sum


119901energy119895

(10)



PM

CPU MEM

90

22

PM

MEM

CPU

68

30 2

VM(CPUMEM)

40 15

20 8

(a)

PM

CPU MEM

90

PM

MEM

CPU

20 30

30 45VM

(CPUMEM)

40 15

90

(b)





12(119909) + 120574 lowast 119891

3(119909)

= 120572 lowast [

[

119898

sum

119895=0

(119901119879cpu119895

119901cpu119895

+ 119901119879mem119895

119901mem119895

)

2

]

]

+ 120573 lowast [

[

sum


119901119895isin119875

cos ⟨V119894 119901119895⟩]

]

+ 120574 lowast [

[

sum


119895isin119875

119901energy119895

]

]

(11)



2sdot 119874(119885







119894 119901119894isin 119875




119896gt 2(120579




















centers1198851199111 119911





Vars Description


120579119899


120579119888








119896



119896 by


119911119896=

1

119873119896

sum

119901isin119911119896

119901 119896 = 1 2 119870 (12)

119863119896=

1

119873119896

sum

119901isin119911119896

1003817100381710038171003817119901 minus 119911119896

1003817100381710038171003817 119896 = 1 2 119870 (13)

119863 =1

119873

119870

sum

119896=1

119873119896119863119896 (14)




119888= 0 go to Step 6








(1) 119863119895gt 119863 and 119873

119896gt 2(120579





+

119896

and 119911minus






Differmax119896




119863119894119895=

10038171003817100381710038171003817119911119894minus 119911119895

10038171003817100381710038171003817 119894 = 1 2 119870 minus 1 119895 = 119894 + 1 119870

(15)

119911lowast

119896=

1

119873119894119896+ 119873119895119896

[119873119894119896119911119894119896+ 119873119895119896119911119895119896] 119896 = 1 2 119871

(16)




11986311989421198952

119863119894119871119895119871

that is 11986311989411198951

lt

11986311989421198952



119894119896and 119911


119894119896119895119896and then get



lowast





119899



119899











119898 which



1 119901

119898 use


119869matrix = [

[

11990911

11990912


11990921

11990922


11990931

11990932


]

]

(17)


119869matrix1015840 = [[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

(18)

where

1199091015840

119894119895=

119909119894119895

radicsum119899

119895=11199092

119894119895

119894 = 1 2 3 (19)


119885 = 119869matrix1015840119861 = [

[

1199081

0 0

0 1199082

0

0 0 1199083

]

]

[[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

=[[

[

11989111

11989112


11989121

11989122


11989131

11989132


]]

]

(20)

where 1199081+ 1199082+ 1199083= 1



119891lowast

119894= max (119891

119894119895) 119894 isin 1 2 3 (21)


1198911015840

119894= min (119891

119894119895) 119894 isin 1 2 3 (22)


119878lowast

119895= radic

3

sum

119894=1

(119891119894119895minus 119891lowast

119894)2

119895 isin 1 119899

1198781015840

119895= radic

3

sum

119894=1

(119891119894119895minus 1198911015840

119894)2

119895 isin 1 119899

(23)


119862lowast

119895=

1198781015840

119895

(119878lowast

119895+ 1198781015840

119895)

119895 = 1 2 119899 (24)






119899



End WhileEnd IF





119889 (119894 119895) = radic(100381610038161003816100381610038161199091198941minus 1199091198951

10038161003816100381610038161003816

2

+100381610038161003816100381610038161199091198942minus 1199091198952

10038161003816100381610038161003816

2

+ sdot sdot sdot +10038161003816100381610038161003816119909119894119901

minus 119909119895119901

10038161003816100381610038161003816

2

)

(25)

where 119894 = (1199091198941 1199091198942 119909

119894119901) and 119895 = (119909

1198951 1199091198952 119909

119895119901) are the




119899



















Indicator Algorithm










0 100 200 300 400 500 600 7000

500

1000

1500

2000

2500


VM

allo

catio

n tim

e (m

s)

VM number

GaGa-ISPMC


0 2000 4000 6000 80003500

4000

4500

5000


VM

allo

catio

n tim

e (m

s)

PM number

GaGa-ISPMC




0 50 100

200

300

400

500

600

700

800

900

1000

1200

0

1000

2000

3000

4000

5000


VM

allo

catio

n tim

e (m

s)

VM numberGrSa

GaMTAD






0 50 100

200

300

400

500

600

700

800

900

1000

1100

1200

Host number (5000)

Reso

urce

bal

ance

d ra

te

VM numberGrSa

GaMTAD

03

04

05

06

07

08

09

1





Host number (5000)

Reso

urce

was

te ra

te

0 50 100

200

300

400

500

600

700

800

900

1000

1200

VM numberGrSa

GaMTAD

03

02

01

04

05

06

07

08

09

1


200400540

200400

0

500

200 300 400 500 600 700 800 900 1000 12000

50100

Phys

ical

mac

hine

usa

ge


GrGa

SaMTAD

PM-G 4

PM-G 2

(6Core8G260W)

(16Core24G380W)

PM-G 3

(8Core14G300W)

PM-G 1

(2Core4G220W)







6 Conclusion



0 50 1000

100

200


VM

allo

catio

n tim

e (m

s)

VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

200

400


VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

500


VM number

MTADMTAD-RBRC

VM

allo

catio

n tim

e (m

s)

MTADMTAD-RBRC

0 50 1000

500

1000


VM number




Notations



119881cpu119894


119881mem119894


119901cpu119895


119895isin 119875

119901mem119895


119895isin 119875

119901energy119895


119901119879cpu119895


119895isin 119875

119901119879mem119895


119895isin 119875



119901Vcount119895


119895isin 119875



Acknowledgments




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Waste Rate =


=

119901119879cpu119895

119901cpu119895


=

119901119879mem119895

119901mem119895

Waste119901119895

=

(WasteCpu119875119895

+WasteMem119875119895

)

2

Waste119875=

119898

sum

119895=0

Waste119901119895

(3)


min1198911(119909) = minWaste

119875=

119898

sum

119895=0

(119901119879cpu119895

119901cpu119895

+ 119901119879mem119895

119901mem119895

)

2

(4)






|V| sdot 10038161003816100381610038161003816100381610038161003816

(5)


) + Vmem(119901


)

(6)


(7)

10038161003816100381610038161003816100381610038161003816

2

= sdot = (119901cpu

minus 119901119879cpu

)2

+ (119901mem

minus 119901119879mem

)2

(8)


min1198912(119909) = sum


119901119895isin119875

cos ⟨V119894 119901119895⟩ (9)



min1198913(119909) = sum


119901energy119895

(10)



PM

CPU MEM

90

22

PM

MEM

CPU

68

30 2

VM(CPUMEM)

40 15

20 8

(a)

PM

CPU MEM

90

PM

MEM

CPU

20 30

30 45VM

(CPUMEM)

40 15

90

(b)





12(119909) + 120574 lowast 119891

3(119909)

= 120572 lowast [

[

119898

sum

119895=0

(119901119879cpu119895

119901cpu119895

+ 119901119879mem119895

119901mem119895

)

2

]

]

+ 120573 lowast [

[

sum


119901119895isin119875

cos ⟨V119894 119901119895⟩]

]

+ 120574 lowast [

[

sum


119895isin119875

119901energy119895

]

]

(11)



2sdot 119874(119885







119894 119901119894isin 119875




119896gt 2(120579




















centers1198851199111 119911





Vars Description


120579119899


120579119888








119896



119896 by


119911119896=

1

119873119896

sum

119901isin119911119896

119901 119896 = 1 2 119870 (12)

119863119896=

1

119873119896

sum

119901isin119911119896

1003817100381710038171003817119901 minus 119911119896

1003817100381710038171003817 119896 = 1 2 119870 (13)

119863 =1

119873

119870

sum

119896=1

119873119896119863119896 (14)




119888= 0 go to Step 6








(1) 119863119895gt 119863 and 119873

119896gt 2(120579





+

119896

and 119911minus






Differmax119896




119863119894119895=

10038171003817100381710038171003817119911119894minus 119911119895

10038171003817100381710038171003817 119894 = 1 2 119870 minus 1 119895 = 119894 + 1 119870

(15)

119911lowast

119896=

1

119873119894119896+ 119873119895119896

[119873119894119896119911119894119896+ 119873119895119896119911119895119896] 119896 = 1 2 119871

(16)




11986311989421198952

119863119894119871119895119871

that is 11986311989411198951

lt

11986311989421198952



119894119896and 119911


119894119896119895119896and then get



lowast





119899



119899











119898 which



1 119901

119898 use


119869matrix = [

[

11990911

11990912


11990921

11990922


11990931

11990932


]

]

(17)


119869matrix1015840 = [[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

(18)

where

1199091015840

119894119895=

119909119894119895

radicsum119899

119895=11199092

119894119895

119894 = 1 2 3 (19)


119885 = 119869matrix1015840119861 = [

[

1199081

0 0

0 1199082

0

0 0 1199083

]

]

[[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

=[[

[

11989111

11989112


11989121

11989122


11989131

11989132


]]

]

(20)

where 1199081+ 1199082+ 1199083= 1



119891lowast

119894= max (119891

119894119895) 119894 isin 1 2 3 (21)


1198911015840

119894= min (119891

119894119895) 119894 isin 1 2 3 (22)


119878lowast

119895= radic

3

sum

119894=1

(119891119894119895minus 119891lowast

119894)2

119895 isin 1 119899

1198781015840

119895= radic

3

sum

119894=1

(119891119894119895minus 1198911015840

119894)2

119895 isin 1 119899

(23)


119862lowast

119895=

1198781015840

119895

(119878lowast

119895+ 1198781015840

119895)

119895 = 1 2 119899 (24)






119899



End WhileEnd IF





119889 (119894 119895) = radic(100381610038161003816100381610038161199091198941minus 1199091198951

10038161003816100381610038161003816

2

+100381610038161003816100381610038161199091198942minus 1199091198952

10038161003816100381610038161003816

2

+ sdot sdot sdot +10038161003816100381610038161003816119909119894119901

minus 119909119895119901

10038161003816100381610038161003816

2

)

(25)

where 119894 = (1199091198941 1199091198942 119909

119894119901) and 119895 = (119909

1198951 1199091198952 119909

119895119901) are the




119899



















Indicator Algorithm










0 100 200 300 400 500 600 7000

500

1000

1500

2000

2500


VM

allo

catio

n tim

e (m

s)

VM number

GaGa-ISPMC


0 2000 4000 6000 80003500

4000

4500

5000


VM

allo

catio

n tim

e (m

s)

PM number

GaGa-ISPMC




0 50 100

200

300

400

500

600

700

800

900

1000

1200

0

1000

2000

3000

4000

5000


VM

allo

catio

n tim

e (m

s)

VM numberGrSa

GaMTAD






0 50 100

200

300

400

500

600

700

800

900

1000

1100

1200

Host number (5000)

Reso

urce

bal

ance

d ra

te

VM numberGrSa

GaMTAD

03

04

05

06

07

08

09

1





Host number (5000)

Reso

urce

was

te ra

te

0 50 100

200

300

400

500

600

700

800

900

1000

1200

VM numberGrSa

GaMTAD

03

02

01

04

05

06

07

08

09

1


200400540

200400

0

500

200 300 400 500 600 700 800 900 1000 12000

50100

Phys

ical

mac

hine

usa

ge


GrGa

SaMTAD

PM-G 4

PM-G 2

(6Core8G260W)

(16Core24G380W)

PM-G 3

(8Core14G300W)

PM-G 1

(2Core4G220W)







6 Conclusion



0 50 1000

100

200


VM

allo

catio

n tim

e (m

s)

VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

200

400


VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

500


VM number

MTADMTAD-RBRC

VM

allo

catio

n tim

e (m

s)

MTADMTAD-RBRC

0 50 1000

500

1000


VM number




Notations



119881cpu119894


119881mem119894


119901cpu119895


119895isin 119875

119901mem119895


119895isin 119875

119901energy119895


119901119879cpu119895


119895isin 119875

119901119879mem119895


119895isin 119875



119901Vcount119895


119895isin 119875



Acknowledgments




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










PM

CPU MEM

90

22

PM

MEM

CPU

68

30 2

VM(CPUMEM)

40 15

20 8

(a)

PM

CPU MEM

90

PM

MEM

CPU

20 30

30 45VM

(CPUMEM)

40 15

90

(b)





12(119909) + 120574 lowast 119891

3(119909)

= 120572 lowast [

[

119898

sum

119895=0

(119901119879cpu119895

119901cpu119895

+ 119901119879mem119895

119901mem119895

)

2

]

]

+ 120573 lowast [

[

sum


119901119895isin119875

cos ⟨V119894 119901119895⟩]

]

+ 120574 lowast [

[

sum


119895isin119875

119901energy119895

]

]

(11)



2sdot 119874(119885







119894 119901119894isin 119875




119896gt 2(120579




















centers1198851199111 119911





Vars Description


120579119899


120579119888








119896



119896 by


119911119896=

1

119873119896

sum

119901isin119911119896

119901 119896 = 1 2 119870 (12)

119863119896=

1

119873119896

sum

119901isin119911119896

1003817100381710038171003817119901 minus 119911119896

1003817100381710038171003817 119896 = 1 2 119870 (13)

119863 =1

119873

119870

sum

119896=1

119873119896119863119896 (14)




119888= 0 go to Step 6








(1) 119863119895gt 119863 and 119873

119896gt 2(120579





+

119896

and 119911minus






Differmax119896




119863119894119895=

10038171003817100381710038171003817119911119894minus 119911119895

10038171003817100381710038171003817 119894 = 1 2 119870 minus 1 119895 = 119894 + 1 119870

(15)

119911lowast

119896=

1

119873119894119896+ 119873119895119896

[119873119894119896119911119894119896+ 119873119895119896119911119895119896] 119896 = 1 2 119871

(16)




11986311989421198952

119863119894119871119895119871

that is 11986311989411198951

lt

11986311989421198952



119894119896and 119911


119894119896119895119896and then get



lowast





119899



119899











119898 which



1 119901

119898 use


119869matrix = [

[

11990911

11990912


11990921

11990922


11990931

11990932


]

]

(17)


119869matrix1015840 = [[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

(18)

where

1199091015840

119894119895=

119909119894119895

radicsum119899

119895=11199092

119894119895

119894 = 1 2 3 (19)


119885 = 119869matrix1015840119861 = [

[

1199081

0 0

0 1199082

0

0 0 1199083

]

]

[[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

=[[

[

11989111

11989112


11989121

11989122


11989131

11989132


]]

]

(20)

where 1199081+ 1199082+ 1199083= 1



119891lowast

119894= max (119891

119894119895) 119894 isin 1 2 3 (21)


1198911015840

119894= min (119891

119894119895) 119894 isin 1 2 3 (22)


119878lowast

119895= radic

3

sum

119894=1

(119891119894119895minus 119891lowast

119894)2

119895 isin 1 119899

1198781015840

119895= radic

3

sum

119894=1

(119891119894119895minus 1198911015840

119894)2

119895 isin 1 119899

(23)


119862lowast

119895=

1198781015840

119895

(119878lowast

119895+ 1198781015840

119895)

119895 = 1 2 119899 (24)






119899



End WhileEnd IF





119889 (119894 119895) = radic(100381610038161003816100381610038161199091198941minus 1199091198951

10038161003816100381610038161003816

2

+100381610038161003816100381610038161199091198942minus 1199091198952

10038161003816100381610038161003816

2

+ sdot sdot sdot +10038161003816100381610038161003816119909119894119901

minus 119909119895119901

10038161003816100381610038161003816

2

)

(25)

where 119894 = (1199091198941 1199091198942 119909

119894119901) and 119895 = (119909

1198951 1199091198952 119909

119895119901) are the




119899



















Indicator Algorithm










0 100 200 300 400 500 600 7000

500

1000

1500

2000

2500


VM

allo

catio

n tim

e (m

s)

VM number

GaGa-ISPMC


0 2000 4000 6000 80003500

4000

4500

5000


VM

allo

catio

n tim

e (m

s)

PM number

GaGa-ISPMC




0 50 100

200

300

400

500

600

700

800

900

1000

1200

0

1000

2000

3000

4000

5000


VM

allo

catio

n tim

e (m

s)

VM numberGrSa

GaMTAD






0 50 100

200

300

400

500

600

700

800

900

1000

1100

1200

Host number (5000)

Reso

urce

bal

ance

d ra

te

VM numberGrSa

GaMTAD

03

04

05

06

07

08

09

1





Host number (5000)

Reso

urce

was

te ra

te

0 50 100

200

300

400

500

600

700

800

900

1000

1200

VM numberGrSa

GaMTAD

03

02

01

04

05

06

07

08

09

1


200400540

200400

0

500

200 300 400 500 600 700 800 900 1000 12000

50100

Phys

ical

mac

hine

usa

ge


GrGa

SaMTAD

PM-G 4

PM-G 2

(6Core8G260W)

(16Core24G380W)

PM-G 3

(8Core14G300W)

PM-G 1

(2Core4G220W)







6 Conclusion



0 50 1000

100

200


VM

allo

catio

n tim

e (m

s)

VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

200

400


VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

500


VM number

MTADMTAD-RBRC

VM

allo

catio

n tim

e (m

s)

MTADMTAD-RBRC

0 50 1000

500

1000


VM number




Notations



119881cpu119894


119881mem119894


119901cpu119895


119895isin 119875

119901mem119895


119895isin 119875

119901energy119895


119901119879cpu119895


119895isin 119875

119901119879mem119895


119895isin 119875



119901Vcount119895


119895isin 119875



Acknowledgments




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119894 119901119894isin 119875




119896gt 2(120579




















centers1198851199111 119911





Vars Description


120579119899


120579119888








119896



119896 by


119911119896=

1

119873119896

sum

119901isin119911119896

119901 119896 = 1 2 119870 (12)

119863119896=

1

119873119896

sum

119901isin119911119896

1003817100381710038171003817119901 minus 119911119896

1003817100381710038171003817 119896 = 1 2 119870 (13)

119863 =1

119873

119870

sum

119896=1

119873119896119863119896 (14)




119888= 0 go to Step 6








(1) 119863119895gt 119863 and 119873

119896gt 2(120579





+

119896

and 119911minus






Differmax119896




119863119894119895=

10038171003817100381710038171003817119911119894minus 119911119895

10038171003817100381710038171003817 119894 = 1 2 119870 minus 1 119895 = 119894 + 1 119870

(15)

119911lowast

119896=

1

119873119894119896+ 119873119895119896

[119873119894119896119911119894119896+ 119873119895119896119911119895119896] 119896 = 1 2 119871

(16)




11986311989421198952

119863119894119871119895119871

that is 11986311989411198951

lt

11986311989421198952



119894119896and 119911


119894119896119895119896and then get



lowast





119899



119899











119898 which



1 119901

119898 use


119869matrix = [

[

11990911

11990912


11990921

11990922


11990931

11990932


]

]

(17)


119869matrix1015840 = [[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

(18)

where

1199091015840

119894119895=

119909119894119895

radicsum119899

119895=11199092

119894119895

119894 = 1 2 3 (19)


119885 = 119869matrix1015840119861 = [

[

1199081

0 0

0 1199082

0

0 0 1199083

]

]

[[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

=[[

[

11989111

11989112


11989121

11989122


11989131

11989132


]]

]

(20)

where 1199081+ 1199082+ 1199083= 1



119891lowast

119894= max (119891

119894119895) 119894 isin 1 2 3 (21)


1198911015840

119894= min (119891

119894119895) 119894 isin 1 2 3 (22)


119878lowast

119895= radic

3

sum

119894=1

(119891119894119895minus 119891lowast

119894)2

119895 isin 1 119899

1198781015840

119895= radic

3

sum

119894=1

(119891119894119895minus 1198911015840

119894)2

119895 isin 1 119899

(23)


119862lowast

119895=

1198781015840

119895

(119878lowast

119895+ 1198781015840

119895)

119895 = 1 2 119899 (24)






119899



End WhileEnd IF





119889 (119894 119895) = radic(100381610038161003816100381610038161199091198941minus 1199091198951

10038161003816100381610038161003816

2

+100381610038161003816100381610038161199091198942minus 1199091198952

10038161003816100381610038161003816

2

+ sdot sdot sdot +10038161003816100381610038161003816119909119894119901

minus 119909119895119901

10038161003816100381610038161003816

2

)

(25)

where 119894 = (1199091198941 1199091198942 119909

119894119901) and 119895 = (119909

1198951 1199091198952 119909

119895119901) are the




119899



















Indicator Algorithm










0 100 200 300 400 500 600 7000

500

1000

1500

2000

2500


VM

allo

catio

n tim

e (m

s)

VM number

GaGa-ISPMC


0 2000 4000 6000 80003500

4000

4500

5000


VM

allo

catio

n tim

e (m

s)

PM number

GaGa-ISPMC




0 50 100

200

300

400

500

600

700

800

900

1000

1200

0

1000

2000

3000

4000

5000


VM

allo

catio

n tim

e (m

s)

VM numberGrSa

GaMTAD






0 50 100

200

300

400

500

600

700

800

900

1000

1100

1200

Host number (5000)

Reso

urce

bal

ance

d ra

te

VM numberGrSa

GaMTAD

03

04

05

06

07

08

09

1





Host number (5000)

Reso

urce

was

te ra

te

0 50 100

200

300

400

500

600

700

800

900

1000

1200

VM numberGrSa

GaMTAD

03

02

01

04

05

06

07

08

09

1


200400540

200400

0

500

200 300 400 500 600 700 800 900 1000 12000

50100

Phys

ical

mac

hine

usa

ge


GrGa

SaMTAD

PM-G 4

PM-G 2

(6Core8G260W)

(16Core24G380W)

PM-G 3

(8Core14G300W)

PM-G 1

(2Core4G220W)







6 Conclusion



0 50 1000

100

200


VM

allo

catio

n tim

e (m

s)

VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

200

400


VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

500


VM number

MTADMTAD-RBRC

VM

allo

catio

n tim

e (m

s)

MTADMTAD-RBRC

0 50 1000

500

1000


VM number




Notations



119881cpu119894


119881mem119894


119901cpu119895


119895isin 119875

119901mem119895


119895isin 119875

119901energy119895


119901119879cpu119895


119895isin 119875

119901119879mem119895


119895isin 119875



119901Vcount119895


119895isin 119875



Acknowledgments




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Vars Description


120579119899


120579119888








119896



119896 by


119911119896=

1

119873119896

sum

119901isin119911119896

119901 119896 = 1 2 119870 (12)

119863119896=

1

119873119896

sum

119901isin119911119896

1003817100381710038171003817119901 minus 119911119896

1003817100381710038171003817 119896 = 1 2 119870 (13)

119863 =1

119873

119870

sum

119896=1

119873119896119863119896 (14)




119888= 0 go to Step 6








(1) 119863119895gt 119863 and 119873

119896gt 2(120579





+

119896

and 119911minus






Differmax119896




119863119894119895=

10038171003817100381710038171003817119911119894minus 119911119895

10038171003817100381710038171003817 119894 = 1 2 119870 minus 1 119895 = 119894 + 1 119870

(15)

119911lowast

119896=

1

119873119894119896+ 119873119895119896

[119873119894119896119911119894119896+ 119873119895119896119911119895119896] 119896 = 1 2 119871

(16)




11986311989421198952

119863119894119871119895119871

that is 11986311989411198951

lt

11986311989421198952



119894119896and 119911


119894119896119895119896and then get



lowast





119899



119899











119898 which



1 119901

119898 use


119869matrix = [

[

11990911

11990912


11990921

11990922


11990931

11990932


]

]

(17)


119869matrix1015840 = [[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

(18)

where

1199091015840

119894119895=

119909119894119895

radicsum119899

119895=11199092

119894119895

119894 = 1 2 3 (19)


119885 = 119869matrix1015840119861 = [

[

1199081

0 0

0 1199082

0

0 0 1199083

]

]

[[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

=[[

[

11989111

11989112


11989121

11989122


11989131

11989132


]]

]

(20)

where 1199081+ 1199082+ 1199083= 1



119891lowast

119894= max (119891

119894119895) 119894 isin 1 2 3 (21)


1198911015840

119894= min (119891

119894119895) 119894 isin 1 2 3 (22)


119878lowast

119895= radic

3

sum

119894=1

(119891119894119895minus 119891lowast

119894)2

119895 isin 1 119899

1198781015840

119895= radic

3

sum

119894=1

(119891119894119895minus 1198911015840

119894)2

119895 isin 1 119899

(23)


119862lowast

119895=

1198781015840

119895

(119878lowast

119895+ 1198781015840

119895)

119895 = 1 2 119899 (24)






119899



End WhileEnd IF





119889 (119894 119895) = radic(100381610038161003816100381610038161199091198941minus 1199091198951

10038161003816100381610038161003816

2

+100381610038161003816100381610038161199091198942minus 1199091198952

10038161003816100381610038161003816

2

+ sdot sdot sdot +10038161003816100381610038161003816119909119894119901

minus 119909119895119901

10038161003816100381610038161003816

2

)

(25)

where 119894 = (1199091198941 1199091198942 119909

119894119901) and 119895 = (119909

1198951 1199091198952 119909

119895119901) are the




119899



















Indicator Algorithm










0 100 200 300 400 500 600 7000

500

1000

1500

2000

2500


VM

allo

catio

n tim

e (m

s)

VM number

GaGa-ISPMC


0 2000 4000 6000 80003500

4000

4500

5000


VM

allo

catio

n tim

e (m

s)

PM number

GaGa-ISPMC




0 50 100

200

300

400

500

600

700

800

900

1000

1200

0

1000

2000

3000

4000

5000


VM

allo

catio

n tim

e (m

s)

VM numberGrSa

GaMTAD






0 50 100

200

300

400

500

600

700

800

900

1000

1100

1200

Host number (5000)

Reso

urce

bal

ance

d ra

te

VM numberGrSa

GaMTAD

03

04

05

06

07

08

09

1





Host number (5000)

Reso

urce

was

te ra

te

0 50 100

200

300

400

500

600

700

800

900

1000

1200

VM numberGrSa

GaMTAD

03

02

01

04

05

06

07

08

09

1


200400540

200400

0

500

200 300 400 500 600 700 800 900 1000 12000

50100

Phys

ical

mac

hine

usa

ge


GrGa

SaMTAD

PM-G 4

PM-G 2

(6Core8G260W)

(16Core24G380W)

PM-G 3

(8Core14G300W)

PM-G 1

(2Core4G220W)







6 Conclusion



0 50 1000

100

200


VM

allo

catio

n tim

e (m

s)

VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

200

400


VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

500


VM number

MTADMTAD-RBRC

VM

allo

catio

n tim

e (m

s)

MTADMTAD-RBRC

0 50 1000

500

1000


VM number




Notations



119881cpu119894


119881mem119894


119901cpu119895


119895isin 119875

119901mem119895


119895isin 119875

119901energy119895


119901119879cpu119895


119895isin 119875

119901119879mem119895


119895isin 119875



119901Vcount119895


119895isin 119875



Acknowledgments




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119899











119898 which



1 119901

119898 use


119869matrix = [

[

11990911

11990912


11990921

11990922


11990931

11990932


]

]

(17)


119869matrix1015840 = [[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

(18)

where

1199091015840

119894119895=

119909119894119895

radicsum119899

119895=11199092

119894119895

119894 = 1 2 3 (19)


119885 = 119869matrix1015840119861 = [

[

1199081

0 0

0 1199082

0

0 0 1199083

]

]

[[

[

1199091015840

111199091015840


1119899

1199091015840

211199091015840


2119899

1199091015840

311199091015840


3119899

]]

]

=[[

[

11989111

11989112


11989121

11989122


11989131

11989132


]]

]

(20)

where 1199081+ 1199082+ 1199083= 1



119891lowast

119894= max (119891

119894119895) 119894 isin 1 2 3 (21)


1198911015840

119894= min (119891

119894119895) 119894 isin 1 2 3 (22)


119878lowast

119895= radic

3

sum

119894=1

(119891119894119895minus 119891lowast

119894)2

119895 isin 1 119899

1198781015840

119895= radic

3

sum

119894=1

(119891119894119895minus 1198911015840

119894)2

119895 isin 1 119899

(23)


119862lowast

119895=

1198781015840

119895

(119878lowast

119895+ 1198781015840

119895)

119895 = 1 2 119899 (24)






119899



End WhileEnd IF





119889 (119894 119895) = radic(100381610038161003816100381610038161199091198941minus 1199091198951

10038161003816100381610038161003816

2

+100381610038161003816100381610038161199091198942minus 1199091198952

10038161003816100381610038161003816

2

+ sdot sdot sdot +10038161003816100381610038161003816119909119894119901

minus 119909119895119901

10038161003816100381610038161003816

2

)

(25)

where 119894 = (1199091198941 1199091198942 119909

119894119901) and 119895 = (119909

1198951 1199091198952 119909

119895119901) are the




119899



















Indicator Algorithm










0 100 200 300 400 500 600 7000

500

1000

1500

2000

2500


VM

allo

catio

n tim

e (m

s)

VM number

GaGa-ISPMC


0 2000 4000 6000 80003500

4000

4500

5000


VM

allo

catio

n tim

e (m

s)

PM number

GaGa-ISPMC




0 50 100

200

300

400

500

600

700

800

900

1000

1200

0

1000

2000

3000

4000

5000


VM

allo

catio

n tim

e (m

s)

VM numberGrSa

GaMTAD






0 50 100

200

300

400

500

600

700

800

900

1000

1100

1200

Host number (5000)

Reso

urce

bal

ance

d ra

te

VM numberGrSa

GaMTAD

03

04

05

06

07

08

09

1





Host number (5000)

Reso

urce

was

te ra

te

0 50 100

200

300

400

500

600

700

800

900

1000

1200

VM numberGrSa

GaMTAD

03

02

01

04

05

06

07

08

09

1


200400540

200400

0

500

200 300 400 500 600 700 800 900 1000 12000

50100

Phys

ical

mac

hine

usa

ge


GrGa

SaMTAD

PM-G 4

PM-G 2

(6Core8G260W)

(16Core24G380W)

PM-G 3

(8Core14G300W)

PM-G 1

(2Core4G220W)







6 Conclusion



0 50 1000

100

200


VM

allo

catio

n tim

e (m

s)

VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

200

400


VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

500


VM number

MTADMTAD-RBRC

VM

allo

catio

n tim

e (m

s)

MTADMTAD-RBRC

0 50 1000

500

1000


VM number




Notations



119881cpu119894


119881mem119894


119901cpu119895


119895isin 119875

119901mem119895


119895isin 119875

119901energy119895


119901119879cpu119895


119895isin 119875

119901119879mem119895


119895isin 119875



119901Vcount119895


119895isin 119875



Acknowledgments




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119899



End WhileEnd IF





119889 (119894 119895) = radic(100381610038161003816100381610038161199091198941minus 1199091198951

10038161003816100381610038161003816

2

+100381610038161003816100381610038161199091198942minus 1199091198952

10038161003816100381610038161003816

2

+ sdot sdot sdot +10038161003816100381610038161003816119909119894119901

minus 119909119895119901

10038161003816100381610038161003816

2

)

(25)

where 119894 = (1199091198941 1199091198942 119909

119894119901) and 119895 = (119909

1198951 1199091198952 119909

119895119901) are the




119899



















Indicator Algorithm










0 100 200 300 400 500 600 7000

500

1000

1500

2000

2500


VM

allo

catio

n tim

e (m

s)

VM number

GaGa-ISPMC


0 2000 4000 6000 80003500

4000

4500

5000


VM

allo

catio

n tim

e (m

s)

PM number

GaGa-ISPMC




0 50 100

200

300

400

500

600

700

800

900

1000

1200

0

1000

2000

3000

4000

5000


VM

allo

catio

n tim

e (m

s)

VM numberGrSa

GaMTAD






0 50 100

200

300

400

500

600

700

800

900

1000

1100

1200

Host number (5000)

Reso

urce

bal

ance

d ra

te

VM numberGrSa

GaMTAD

03

04

05

06

07

08

09

1





Host number (5000)

Reso

urce

was

te ra

te

0 50 100

200

300

400

500

600

700

800

900

1000

1200

VM numberGrSa

GaMTAD

03

02

01

04

05

06

07

08

09

1


200400540

200400

0

500

200 300 400 500 600 700 800 900 1000 12000

50100

Phys

ical

mac

hine

usa

ge


GrGa

SaMTAD

PM-G 4

PM-G 2

(6Core8G260W)

(16Core24G380W)

PM-G 3

(8Core14G300W)

PM-G 1

(2Core4G220W)







6 Conclusion



0 50 1000

100

200


VM

allo

catio

n tim

e (m

s)

VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

200

400


VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

500


VM number

MTADMTAD-RBRC

VM

allo

catio

n tim

e (m

s)

MTADMTAD-RBRC

0 50 1000

500

1000


VM number




Notations



119881cpu119894


119881mem119894


119901cpu119895


119895isin 119875

119901mem119895


119895isin 119875

119901energy119895


119901119879cpu119895


119895isin 119875

119901119879mem119895


119895isin 119875



119901Vcount119895


119895isin 119875



Acknowledgments




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Indicator Algorithm










0 100 200 300 400 500 600 7000

500

1000

1500

2000

2500


VM

allo

catio

n tim

e (m

s)

VM number

GaGa-ISPMC


0 2000 4000 6000 80003500

4000

4500

5000


VM

allo

catio

n tim

e (m

s)

PM number

GaGa-ISPMC




0 50 100

200

300

400

500

600

700

800

900

1000

1200

0

1000

2000

3000

4000

5000


VM

allo

catio

n tim

e (m

s)

VM numberGrSa

GaMTAD






0 50 100

200

300

400

500

600

700

800

900

1000

1100

1200

Host number (5000)

Reso

urce

bal

ance

d ra

te

VM numberGrSa

GaMTAD

03

04

05

06

07

08

09

1





Host number (5000)

Reso

urce

was

te ra

te

0 50 100

200

300

400

500

600

700

800

900

1000

1200

VM numberGrSa

GaMTAD

03

02

01

04

05

06

07

08

09

1


200400540

200400

0

500

200 300 400 500 600 700 800 900 1000 12000

50100

Phys

ical

mac

hine

usa

ge


GrGa

SaMTAD

PM-G 4

PM-G 2

(6Core8G260W)

(16Core24G380W)

PM-G 3

(8Core14G300W)

PM-G 1

(2Core4G220W)







6 Conclusion



0 50 1000

100

200


VM

allo

catio

n tim

e (m

s)

VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

200

400


VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

500


VM number

MTADMTAD-RBRC

VM

allo

catio

n tim

e (m

s)

MTADMTAD-RBRC

0 50 1000

500

1000


VM number




Notations



119881cpu119894


119881mem119894


119901cpu119895


119895isin 119875

119901mem119895


119895isin 119875

119901energy119895


119901119879cpu119895


119895isin 119875

119901119879mem119895


119895isin 119875



119901Vcount119895


119895isin 119875



Acknowledgments




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 50 100

200

300

400

500

600

700

800

900

1000

1200

0

1000

2000

3000

4000

5000


VM

allo

catio

n tim

e (m

s)

VM numberGrSa

GaMTAD






0 50 100

200

300

400

500

600

700

800

900

1000

1100

1200

Host number (5000)

Reso

urce

bal

ance

d ra

te

VM numberGrSa

GaMTAD

03

04

05

06

07

08

09

1





Host number (5000)

Reso

urce

was

te ra

te

0 50 100

200

300

400

500

600

700

800

900

1000

1200

VM numberGrSa

GaMTAD

03

02

01

04

05

06

07

08

09

1


200400540

200400

0

500

200 300 400 500 600 700 800 900 1000 12000

50100

Phys

ical

mac

hine

usa

ge


GrGa

SaMTAD

PM-G 4

PM-G 2

(6Core8G260W)

(16Core24G380W)

PM-G 3

(8Core14G300W)

PM-G 1

(2Core4G220W)







6 Conclusion



0 50 1000

100

200


VM

allo

catio

n tim

e (m

s)

VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

200

400


VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

500


VM number

MTADMTAD-RBRC

VM

allo

catio

n tim

e (m

s)

MTADMTAD-RBRC

0 50 1000

500

1000


VM number




Notations



119881cpu119894


119881mem119894


119901cpu119895


119895isin 119875

119901mem119895


119895isin 119875

119901energy119895


119901119879cpu119895


119895isin 119875

119901119879mem119895


119895isin 119875



119901Vcount119895


119895isin 119875



Acknowledgments




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Host number (5000)

Reso

urce

was

te ra

te

0 50 100

200

300

400

500

600

700

800

900

1000

1200

VM numberGrSa

GaMTAD

03

02

01

04

05

06

07

08

09

1


200400540

200400

0

500

200 300 400 500 600 700 800 900 1000 12000

50100

Phys

ical

mac

hine

usa

ge


GrGa

SaMTAD

PM-G 4

PM-G 2

(6Core8G260W)

(16Core24G380W)

PM-G 3

(8Core14G300W)

PM-G 1

(2Core4G220W)







6 Conclusion



0 50 1000

100

200


VM

allo

catio

n tim

e (m

s)

VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

200

400


VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

500


VM number

MTADMTAD-RBRC

VM

allo

catio

n tim

e (m

s)

MTADMTAD-RBRC

0 50 1000

500

1000


VM number




Notations



119881cpu119894


119881mem119894


119901cpu119895


119895isin 119875

119901mem119895


119895isin 119875

119901energy119895


119901119879cpu119895


119895isin 119875

119901119879mem119895


119895isin 119875



119901Vcount119895


119895isin 119875



Acknowledgments




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 50 1000

100

200


VM

allo

catio

n tim

e (m

s)

VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

200

400


VM number

VM

allo

catio

n tim

e (m

s)

0 50 1000

500


VM number

MTADMTAD-RBRC

VM

allo

catio

n tim

e (m

s)

MTADMTAD-RBRC

0 50 1000

500

1000


VM number




Notations



119881cpu119894


119881mem119894


119901cpu119895


119895isin 119875

119901mem119895


119895isin 119875

119901energy119895


119901119879cpu119895


119895isin 119875

119901119879mem119895


119895isin 119875



119901Vcount119895


119895isin 119875



Acknowledgments




References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article MTAD: A Multitarget Heuristic Algorithm for Virtual Machine Placementdownloads.hindawi.com/journals/ijdsn/2015/679170.pdf · 2015. 11. 24. · placement algorithm