Research ArticleA Green Strategy for Federated and Heterogeneous Clouds withCommunicating Workloads

Jordi Mateo1 Jordi Vilaplana1 Lluis M Plagrave2 Josep Ll Leacuterida1 and Francesc Solsona1

1 Department of Computer Science amp INSPIRES University of Lleida Jaume II 69 25001 Lleida Spain2Department of Mathematics University of Lleida Jaume II 73 25001 Lleida Spain

Correspondence should be addressed to Francesc Solsona francescdieiudlcat

Received 28 July 2014 Accepted 10 September 2014 Published 11 November 2014

Academic Editor Wei-Chiang Hong

Copyright copy 2014 Jordi Mateo et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Providers of cloud environments must tackle the challenge of configuring their system to provide maximal performance whileminimizing the cost of resources used However at the same time they must guarantee an SLA (service-level agreement) to theusers The SLA is usually associated with a certain level of QoS (quality of service) As response time is perhaps the most widelyused QoS metric it was also the one chosen in this work This paper presents a green strategy (GS) model for heterogeneous cloudsystemsWe provide a solution for heterogeneous job-communicating tasks and heterogeneous VMs that make up the nodes of thecloud In addition to guaranteeing the SLA the main goal is to optimize energy savings The solution results in an equation thatmust be solved by a solver with nonlinear capabilities The results obtained from modelling the policies to be executed by a solverdemonstrate the applicability of our proposal for saving energy and guaranteeing the SLA

1 Introduction

In cloud computing SLA (service-level agreement) is anagreement between a service provider and a consumer wherethe former agrees to deliver a service to the latter underspecific terms such as time or performance In order tocomply with the SLA the service provider must monitor thecloud performance closely Studying and determining SLA-related issues are a big challenge [1 2]

GS is designed to lower power consumption [3] as muchas possible The main objective of this paper is to developresource scheduling approaches to improve the power effi-ciency of data centers by shutting down and putting idlesservers to sleep as Intelrsquos Cloud Computing 2015 Vision [4]does

At the same time GS is aimed at guaranteeing a nego-tiated SLA and power-aware [3] solutions leaving asidesuch other cloud-computing issues as variability [2] systemsecurity [3] and availability [5] Job response time is perhapsthemost importantQoSmetric in a cloud-computing context[1]That is also why theQoS parameter is chosen in this workIn addition despite good solutions having been presented

by some researchers in the literature dealing with QoS [6 7]and power consumption [8 9] the model presented aims toobtain the best scheduling taking both criteria into account

This paper is focused on proposing a static green alter-native to solving the scheduling problem in cloud environ-ments Many of the cited solutions consist of creating dynam-ically ad hoc VMs depending on the workload made up ofindependent tasks or a parallel job composed of communi-cating or noncommunicating tasks This implies constantlycreating deleting or moving VMsThese processes consumelarge amounts of time Low ratios for return times and VMmanagement should lead to proposingmore static schedulingmethods between the existingVMsThe solution described inthis paper goes on this direction However this solution canbe merged and complemented with dynamic proposals

Our additional contribution with respect to [10] is thatour solution tries to optimize 2 criteria at the same timescheduling tasks to VMs saving energy and consolidatingVMs to the nodes Providing an efficient NLP solution forthis problem is a novelty challenge in the cloud computingresearch field

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 273537 9 pageshttpdxdoiorg1011552014273537

2 The Scientific World Journal

Another important contribution of this paper is methodused to model the power of the virtual machines in functionof their workload Relying on the work done in [11] wherethe authors formulate the problem of assigning people fromvarious groups to different jobs and who may complete themin the minimum time as a stochastic programming problemthe job completion times were assumed to follow a Gammadistribution To model the influence of the workload thecomputing power of the virtual machine is weighted by aload factor determined by an Erlang distribution (equivalentto a Gamma) Finally a stochastic programming problem isobtained and transformed into an equivalent deterministicproblem with a nonlinear objective function

The remainder of the paper is organized as follows Ourcontribution is based on the previous work presented inSection 2 In the GS section (Section 3) we present our maincontributions a sort of scheduling policy These proposalsare arranged by increasing complexity The experimentationshowing the good behavior of our cloud model is presentedin the Results section (Section 4) Finally the Conclusionsand Future Work section outlines the main conclusions andpossible research lines to explore in the near future

2 Related Work

There is a great deal of work in the literature on linearprogramming (LP) solutions and algorithms applied toscheduling like those presented in [12 13] Another notablework was performed in [14] where authors designed a GreenScheduling Algorithm that integrated a neural network pre-dictor in order to optimize server power consumption incloud computing Also the authors in [15] proposed a geneticalgorithm that takes into account both makespan and energyconsumption

Shutting down servers when they are not being used isone of the most direct methods to reduce the idle powerHowever the authors in [16] state that a power-off requiresan additional setup cost resulting in long system delaysShutting down servers may sacrifice quality of service (QoS)levels thus violating the SLA They put the server workat a lower service rate rather than completely stoppingwork during idle periods This drawback can be reduced ifscheduling is performed for a large enough number of tasksas in our case

In [17] the authors treat the problem of consolidatingVMs in a server by migrating VMs with steady and stablecapacity needsThey proposed an exact formulation based ona linear program described by too small a number of validinequalities Indeed this description does not allow solvingin a reasonable time or an optimal way problems involvingthe allocation of a large number of items (or VMs) to manybins (or servers)

In [18] the authors presented a server consolidation(Sercon) algorithmwhich consists ofminimizing the numberof used nodes in a data center and minimizing the numberof migrations at the same time to solve the bin (or server)packing problem They show the efficiency of Sercon forconsolidating VMs and minimizing migrations Despite our

proposal (based on NLP) always finding the best solutionSercon is a heuristic that cannot always reach or find theoptimal solution

The authors in [19] investigated resource optimizationservice quality and energy saving by the use of a neural net-work These actions were specified in two different resourcemanagers which sought to maintain the applicationrsquos qualityservice in accordance with the SLA and obtain energy savingsin a virtual serversrsquo cluster by turning them off when idleand dynamically redistributing the VMs using livemigrationSaving energy is only applied in the fuzzy-term ldquointermediateloadrdquo using fewer resources and still maintaining satisfactoryservice quality levels Large neural network training timesand their nonoptimal solutions could be problems that canbe overcome by using other optimization techniques such asthe NLP one used in this paper

In [10] the authors modelled an energy aware alloca-tion and consolidation policies to minimize overall energyconsumption with an optimal allocation and a consolidationalgorithm The optimal allocation algorithm is solved as abin-packing problem with a minimum power consumptionobjective The consolidation algorithm is derived from alinear and integer formulation of VM migration to adapt toplacement when resources are released

The authors of [20] presented an effective load-balancinggenetic algorithm that spreads the multimedia service taskload to the servers with the minimal cost for transmittingmultimedia data between server clusters and clients forcentralized hierarchical cloud-based multimedia systemsClients can change their locations and each server clusteronly handled a specific type of multimedia task so that twoperformance objectives (aswe do)were optimized at the sametime

In [21] the authors presented an architecture able tobalance load into different virtual machines meanwhile pro-viding SLA guarantees The model presented in that workis similar to the model presented in this paper The maindifference is in the tasks considered Now a more complexand generalized model is presented In addition commu-nicating and heterogeneous tasks as well as nondedicatedenvironments have been taken into account

Our proposal goes further than the outlined literatureInstead of designing a single criteria scheduling problem(LP) we design an NLP scheduling solution which takes intoaccount multicriteria issues In contrast to the optimizationtechniques of the literature our model ensures the best solu-tion available We also want to emphasize the nondedicatedfeature of the model meaning that the workload of the cloudis also considered This also differentiates from the relatedwork This consideration also brings the model into realityproviding more reliable and realistic results

3 GS Model

The NLP scheduling solution proposed in this paper mod-els a problem by giving an objective function (OF) Theequation representing the objective function takes variousperformance criteria into account

The Scientific World Journal 3

GS tries to assign as many tasks as possible to the mostpowerful VMs leaving the remaining ones aside As we willconsider clouds made up of various nodes at the end ofthe scheduling process the nodes all of whose VMs are notassigned any task can then be turned off As SLA based ontheminimization of the return time is also applied themodelalso minimizes the computing and communication time ofthe overall tasks making up a job

31 General Notation Let a jobmade up of119879 communicatingtasks (119905119894 119894 = 1 119879) and a cloud made up of 119873 heteroge-neous nodes (Node

1 Node

119873)

The number of VMs can be different between nodes soweuse notation V

119899(119907119899= 1 119881

119899 where 119899 = 1 119873) to rep-

resent the number of VMs located to Node119899 In other words

each Node119899will be made up by VMs VM

1198991 VM

119899119881119899

Task assignments must show the node and the VM inside

the nodes task 119905119894 is assigned to In doing so Boolean variableswill also be used The notation 119905

119894

119899V119899

is used to represent theassignment of task 119905119894 to Node

119899VM VM

119899V119899

The notation 119872

119894

119899V119899

represents the amount of Memoryallocated to task 119905119894 in VM VM

119899V119899

It is assumed that Memoryrequirements do not change between VMs so 119872

119894

119899V119899

=

119872119894

119899V1015840119899

forall119899 le 119873 and V119899 V1015840119899

le 119881119899 The Boolean variable 119905

119894

119899V119899

represents the assignment of task 119905119894 to VM

119899V119899

Once thesolver is executed the 119905

119894

119899V119899

variables will inform about theassignment of tasks to VMsThis is 119905119894

119899V119899

= 1 if 119905119894 is assigned toVM119899V119899

and 119905119894

119899V119899

= 0 otherwise

32 Virtual Machine Heterogeneity The relative computingpower (Δ

119899V119899

) of a VM119899V119899

is defined as the normalized scoreof such a VM Formally consider

Δ119899V119899

=120575119899V119899

sum119881

119894=1sum119881119894

119896=1120575119894V119896

(1)

wheresum119881119894=1

sum119881119894

119896=1Δ119894V119896

= 1 120575119899V119899

is the score (ie the computingpower) of VM

119899V119899

Although 120575119899V119899

is a theoretical conceptthere are many valid benchmarks it can be obtained with(ie Linpack (Linpack httpwwwnetliborglinpack) orSPEC (SPEC httpwwwspecorg)) Linpack (available in CFortran and Java) for example is used to obtain the numberof floating-point operations per second Note that the closerthe relative computing power is to one (in other words themore powerful it is) the more likely it is that the requests willbe mapped into such a VM

33 Task Heterogeneity In order tomodel task heterogeneityeach task 119905

119894 has its processing cost 119875119894

119899V119899

representing theexecution time of task 119905

119894 in VM119899V119899

with respect to theexecution time of task 119905119894 in the least powerful VM

119899V119899

(in otherwords with the lowest Δ

119899V119899

) It should be a good choice to

maximize 119905119894

119899V119899

119875119894

119899V119899

to obtain the best assignment (in otherwords the OF) as follows

max(119873

sum

119899=1

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

119875119894

119899V119899

) (2)

However there are still a few criteria to consider

34 Virtual MachineWorkload The performance drop expe-rienced by VMs due to workload saturation is also taken intoaccount If a VM is underloaded its throughput (tasks solvedper unit of time) will increase as more tasks are assigned toit When the VM reaches its maximum workload capacityits throughput starts falling asymptotically towards zeroThisbehavior can be modeled with an Erlang distribution densityfunction Erlang is a continuous probability distribution withtwo parameters 120572 and 120582 The 120572 parameter is called the shapeparameter and the 120582 parameter is called the rate parameterThese parameters depend on the VM characteristics When120572 equals 1 the distribution simplifies to the exponentialdistribution The Erlang probability density function is

119864 (119909 120572 120582) = 120582119890minus120582119909 (120582119909)

120572minus1

(120572 minus 1)forall119909 120582 ge 0 (3)

We consider that the Erlang modelling parameters ofeach VM can easily be obtained empirically The Erlangparameters can be obtained by means of a comprehensiveanalysis of all typical workloads being executed in the serversupercomputer or data center to be evaluated In the presentwork a common PC server was used To carry out thisanalysis we continuously increased the workload until theserver was saturated We collected measurements about themean response times at eachworkload variation By empiricalanalysis of that experimentation we obtained the Erlang thatbetter fitted the obtained behaviour measurements

The Erlang is used to weight the Relative computingpower Δ

119899V119899

of each VM119899V119899

with its associated workloadfactor determined by an Erlang distribution This optimalworkload model is used to obtain the maximum throughputperformance (number of task executed per unit of time) ofeach VM

119899V119899

In the case presented in this paper the 119909-axis(abscisas) represents the sum of the Processing cost 119875119894

119899V119899

ofeach 119905

119894 assigned to every VM119899V119899

Figure 1 shows an example in which we depict an Erlang

with 120572 = 76 and 120582 = 15 The Erlang reaches its maximumwhen 119883 = 5 Provided that the abscissas represent theworkload of a VM a workload of 5 will give the maximumperformance to such a VM in terms of throughput So we arenot interested in assigning less or more workload to a specificVM119899V119899

because otherwise this would lead us away from theoptimal assignment

Given an Erlang distribution function with fixed param-eters 120572 and 120582 it is possible to calculate the optimal workloadin which the function reaches the maximum by using itsderivative function

119864 (119909 120572 120582)1015840= 119890minus120582minus1lowast119909

lowast 119909 (120582 minus 1 lowast 119909 minus 120572 minus 1) forall119909 120582 ge 0

(4)

4 The Scientific World Journal

0010203040506070809

1

0 5 10 15 20

120572 = 76 120582 = 15

Figure 1 Erlang plots for different 120572 and 120582 values

Accordingly the optimal workload of the Erlang examplein Figure 1 with 120572 = 76 and 120582 = 15 is

119864 (119909 76 15)1015840= 119890minus14lowast119909

lowast 119909 (14119909 minus 75) = 0

119909 =75

14

(5)

Finally in our case provided that the VM workloaddefined as the sum of the processing costs (119875119894

119899V119899

) of the tasksassigned to a particular VM must be an N number theoptimal workload (119909) is

119909 = round(7514

) = 5 (6)

Provided that Boolean variable 119905119894

119899V119899

= 1 is a booleanvariable informing of the assignment of 119905119894 to VM

119899V119899

and119905119894

119899V119899

= 0 if not the Erlang-weighted Δ119899V119899

would be

Δ119899V119899

119864(

119879

sum

119894=1

119875119894

119899V119899

119905119895

V 120572 120582) (7)

35 Task Communication and VM Selection In this sectionthe VM selection is also considered In doing so eachVM can be selected from a range of 119873 nodes forming afederated cloud We want to obtain an OF that considersthe scheduling of heterogeneous and communicating tasksto 119873 heterogeneous nodes made up of different numbers ofheterogeneous VMs

The communication cost (in time) between tasks 119905119894 and119905119895 when in the same VM is denoted by 119862

119894119895 and shouldbe passed to the solver as an argument For reasons ofsimplicity all communication links are considered to havethe same bandwidth and latency Notation119862119894119895

119899V119899

represents thecommunication cost between task 119905

119894 residing in VM119899V119899

withanother task 119905

119895 (located in the same VM or elsewhere) Pro-vided equivalent bandwidth between any two VMs 119862119894119895

119899V119899

=

119862119895119894

119899V1015840119899

forallV V1015840 le 119881 In other words the communication cost doesnot depend on the VM or the links used between the VMs

VM communication links are considered with the samebandwidth capacity Depending on its location we multiplythe communication cost between tasks 119905119894 and 119905

119895 by a givencommunication slowdown If 119905

119894and 119905119895are located in the same

VM the communication slowdown (denoted by Cs119899V119899

) is 1If 119905119895 is assigned to another VM in the same node than 119905

119894

(119905119895119899V119899

= 1 the Communication slowdown (Cs119899V119899

) will bein the range [0 1] Finally if 119905119895 is assigned to anotherVM located in another node (119905119895

119899V119899

= 1) the correspondingcommunication slowdown term (Cs

119899V119899

) will also be in therange [0 1] Cs

119899V119899

and Cs119899V119899

should be obtained withrespect to Cs

119899V119899

In other words Cs119899V119899

and Cs119899V119899

are therespective reduction (in percentage) in task communicationbetween VMs located in the same and different nodescompared with task communication inside the same VM Tosum up Cs

119899V119899

= 1 ge Cs119899V119899

ge Cs119899V119899

ge 0According to task communication the idea is to add a

component in the OF that penalizes (enhances) the com-munications performed between different VMs and differentnodes Grouping tasks inside the same VM will dependon not only their respective processing cost (119875119894

119899V119899

) but alsothe communication costs 119862119894119895

119899V119899

and communication slowdownsCs119899V119899

Cs119899V119899

and Cs119899V119899

We reward the communications donein the same VM but less so the ones done in differentVMs while still in the same node Finally communicationsbetween nodes are left untouched without rewarding orpenalizing

In the same way if we modelled the OF in function of thetak heterogeneity in (2) the communication component willbe as follows (only the communication component of the OFis shown)

max(119873

sum

119899=1

119881119899

sum

V119899=1

119879

sum

119894=1

(119905119894

119899V119899

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

(8)

And the OF function will be

max(119873

sum

119899=1

119881119899

sum

V119899=1

((

119879

sum

119894=1

119905119894

119899V119899

(119875119894

119899V119899

+

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

times Δ119899V119899

119864(

119879

sum

119895=1

119905119895

119899V119899

119875119895

119899V119899

120572 120582)))

(9)

36 Choosing SLA or Energy Saving It is important tohighlight that the optimization goal is two criteria (SLAand energy in our case) Thus the user could prioritize

The Scientific World Journal 5

the criteria Assignments are performed starting from themost powerful VM When this becomes saturated taskassignment continues with the next most powerful VMregardless of the node it resides in When this VM residesin another node (as in our case) the energy-saving criteriawill be harmed It would be interesting to provide a means ofincreasing criteria preferences in the model presented

In order to highlight specific criteria (ie energy saving)one more additional component must be added to the OFThis component must enhance the assignment of tasks to thesame node by assigning tasks to the most powerful nodesand not only to the most powerful VMs as before This is thenatural procedure to follow because the OF is a maximumThus the likelihood of less powerful nodes becoming idleincreases and this gives the opportunity to power them offhence saving energy

The additional component can be defined in a similar wayas for the relative VM computing power (Δ

119899V119899

) of a VM119899V119899

Instead we obtain the relative node computing power of aNode119899(Θ119899) as the normalized summatory of their forming

VMs Θ119899will inform about the computing power of Node

119899

For119873 nodes Θ119899is formally defined as

Θ119899=

sum119881119899

V119899=1Δ119899V119899

sum119873

119899=1sum119881119899

V119899=1Δ119899V119899

(10)

wheresum119873119899=1

Θ119899= 1 To obtainΘ

119899 the parallel Linpack version

(HPL high performance Linpack) can be used It is the oneused to benchmark and rank supercomputers for the TOP500list

Depending on the importance of the energy savingcriteria a weighting factor should be provided to Θ

119899 We

simply call this factor energy Energy Ξ The Ξ will be in therange (0 1] For an Ξ0 our main criteria will be energysaving and forΞ = 1 our goal is only SLAThus the resultingenergy component will beΘ

119899Ξ Thus for a given Node

119899with

Θ119899 we must weigh the energy saving criteria of such a node

by the following factor

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ (11)

The resulting OF function will be

max(119873

sum

119899=1

(

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ)

times

119881119899

sum

V119899=1

((

119879

sum

119894=1

119905119894

119899V119899

(119875119894

119899V119899

+

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

times Δ119899V119899

119864(

119879

sum

119895=1

119905119895

119899V119899

119875119895

119899V119899

120572 120582)))

(12)

37 Enforcing SLA For either prioritized criteria SLA orenergy saving there is a last consideration to be taken intoaccount

Imagine the case where tasks do not communicate Oncethey are assigned to a node one would expect them to beexecuted in the minimum time In this case there is alreadyno need to group tasks in the VM in decreasing order ofpower in the same node because this node is no longereligible to be switched off A better solution in this case wouldbe to balance the tasks between the VMs of such a nodein order to increase SLA performance Note that this notapply in the communicating tasks due to the communicationslowdown between VMs

To implement this we only need to assign every noncom-municating tasks without taking the relative computing power(Δ119899V119899

) of each VM into accountWe only need to replace Δ

119899V119899

in (12) by Δ defined as

Δ = if (

119879

sum

119895lt119894

119862119894119895

119899V119899

ge 0)Δ119899V119899

else 1

(13)

For the case of noncommunicating tasks by assigning aΔ = 1 all the VMs have the same relative computing powerΔ119899V119899

Thus tasks are assigned in a balanced way

38 Model Formulation Finally the OF function and theirconstraints are presented The best task scheduling assign-ment to VMs which takes all the features into account(GS policy) is formally defined by the following nonlinearprogramming model

max(119873

sum

119899=1

(

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ)

times

119881119899

sum

V119899=1

((

119879

sum

119894=1

119905119894

119899V119899

(119875119894

119899V119899

+

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

times Δ119864(

119879

sum

119895=1

119905119895

119899V119899

119875119895

119899V119899

120572 120582)))

(14a)

st119879

sum

119894=1

119872119899V119899

119894le 119872119899V

119899forall119899 le 119873 V

119899le 119881119899

(14b)

119873

sum

119899=1

119881

sum

V119899=1

119905119894

119899V119899

= 1 forall119894 le 119879 (14c)

6 The Scientific World Journal

Equation (14a) is the objective function (OF) to be max-imized Note that OF is an integer and nonlinear problemInequality in (14b) and equality in (14c) are the constraints ofthe objective function variables Given the constants 119879 (thetotal number of requests or tasks) and 119872V for each VM

119899V119899

the solution that maximizes OF will obtain the values of thevariables 119905119894

119899V119899

representing the number of tasks assigned toVM119899V119899

Thus the 119905119899V119899119894obtained will be the assignment found

by this modelOF takes into account the processing costs (119875119894

119899V119899

) and thecommunication times (119862119894119895

119899V119899

) of the tasks assigned to eachVM119899V119899

and the communication slowdownsbetweenVMsCs119899V119899

and nodes Cs119899V119899

Cs119899V119899

= 1 Δ is defined in Section 37 And119864(sum119879

119895=1119905119895

119899V119899

119875119895

119899V119899

120572 120582) represents the power slowdown of eachVM due to its workload (defined in Section 34)

To sum up for the case when the workload is made up ofnoncommunicating tasks if we are interested in prioritizingthe SLA criteria OF 35 should be applied If on the contrarythe goal is to prioritize energy savingOF (14a) should be usedinstead

4 Results

In this section we present the theoretical results obtainedfrom solving the scheduling problems aimed at achievingbest task assignment Two representative experiments wereperformed in order to test the performance of GS

The experiments were performed by using the AMPL(AMPL A Mathematical Programming Language httpamplcom) language and the SCIP (SCIP Solving ConstraintInteger Programs httpscipzibde) solver AMPL is analgebraic modeling language for describing and solving high-complexity problems for large-scale mathematical computa-tion supported by many solvers Integer and nonlinear (ourmodel type) problems can be solved by SCIP one of thesolvers supported by AMPL

Throughout all the experimentation the Erlang argu-ments were obtained empirically by using the strategyexplained in Section 34

As the objective of this section is to prove the correctnessof the policy only a small set of tasks VMs and nodes waschosen The size of the experimental framework was chosento be as much representative of actual cases as possible butat the same time simple enough to be used as an illustrativeexample So the experimental framework chosen was madeup of 2 different nodes one of them comprised 3VMs and theother 1 VM see Figure 2The objective of this simulation wasto achieve the best assignment for 3 tasks Table 1 shows theprocessing cost 119875119894

119899V119899

relating the execution times of the tasks ineach VM To show the good behavior of themodel presentedeach task has the same processing cost independently of theVM The model presented can be efficiently applied to realcloud environments The only weak point is that the modelis static That means that homogenous and static workloadconditions must be stable in our model Job executions indifferent workload sizes can be saved in a database system

Node 2Node 1

VM2VM3 VM1

VM3

Cloud

Figure 2 Cloud architecture

Table 1 Task processing costs

Task 119905119894 Processing costs 119875119894119899V119899

Value1199051

1198751

11 1198751

12 1198751

13 1198751

211

1199052

1198752

1 1198752

12 1198752

13 1198752

215

1199053

1198753

11 1198753

12 1198753

13 1198753

211

Total processing cost (sum119894119875119894

119899V119899

) 7

providing a means for determining the SLA of such a job infuture executions

41 Without Communications In this section a hypotheticalsituation without communication between tasks is evaluatedIn this situation our scheduling policy tends to assign thetasks to the most powerful set of virtual machines (ie withthe higher relative computing power Δ

119899V119899

considering theirindividual saturation in this choice)This saturation becomescritical when more and more tasks are added Here the mostimportant term is the Erlang function since it models thebehaviour of every virtual machine Thus taking this intoaccount our scheduler knows the exact weight of tasks it canassign to the VMs in order to obtain the best return timesThis phenomenon is observed in the following examples

411 Without Communications and High Optimal ErlangTable 2 shows the parameters used in the first example Theamount ofMemory allocated to each task 119905119894 in every VM119872

119899V119899

(as we supposed this amount to be equal in all the VMs wesimply call it119872119894)The relative computing power (Δ

119899VV) of eachVMand finally the120572 and 120582 Erlang arguments Note that all theVMs have the same Erlang parameters The parameters werechosen this way because any VM saturates with the overallworkload assigned In other words the total processing cost 7is lower than the optimal Erlang workload 16

Table 3 shows the solver assignment results The bestscheduling assigns all the tasks to the same VM (VM

21 the

only VM in node 2) because this VM has the biggest relative

The Scientific World Journal 7

Table 2 Without communications High optimal Erlang VM con-figurations

Node VM119899V119899

119872119894

Δ119899VV Erlang

1 VM11 10 075 120572 = 3 120582 = 8

1 VM12 10 035 120572 = 3 120582 = 8

1 VM13 10 01 120572 = 3 120582 = 8

2 VM21 10 085 120572 = 3 120582 = 8

Table 3 Without communications High optimal Erlang Solverassignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

computing power (Δ119899VV) This result is very coherent Due to

the lack of communications the model tends to assign tasksto the most powerful VMwhile its workload does not exceedthe Erlang optimum (a workload of 10 tasks) As in our casethe total workload is 7 and VM

21could host evenmore tasks

412 Without Communications Low Optimal Erlang andPreserving SLA In this example (see Table 4) the VMs haveanother Erlang However the task processing costs do notchange so they remain the same as in Table 1 In this caseeach VM becomes saturated when the assignment workloadweight is higher than 5 (because 5 is the optimal workload)

The best assignment in this case is the one formed bythe minimum set of VMs with the best relative computingpower Δ

119899VV (see Table 5 column Task Assignment SLA) Theassignment of the overall tasks to only one VM (although itwas the most powerful one) as before will decrease the returntime excessively due to its saturation

413 Without Communications Low Optimal Erlang andPreserving Energy Saving Provided that the most importantcriterion is the energy saving the assignment will be some-what different (seeTable 5 columnTaskAssignment Energy)In this case OF (14a) with Ξ = 1was usedThen as expectedall the tasks were again assigned to VM

21of Node

2

42 With Communications Starting from the same VMconfiguration shown on Table 4 in this section we presenta more real situation where the costs of communicationsbetween tasks are also taken into account It is important tohighlight that in some situations the best choice does notinclude the most powerful VMs (ie with the highest relativecomputing powerΔ

119899V119899

)Thus the results shown in this sectionmust show the tradeoff between relative computing powerof VM workload scheduling impact modeled by the Erlangdistribution and communication efficiency between tasks

421 High Communication Slowdown This example showsthe behaviour of the model under large communication costs

Table 4Without communications Low optimal Erlang PreservingSLA VM configurations

Node VM119899V119899

119872119894

Δ119899VV Erlang

1 VM11 10 075 120572 = 5 120582 = 1

1 VM12 10 035 120572 = 5 120582 = 1

1 VM13 10 01 120572 = 5 120582 = 1

2 VM21 10 085 120572 = 5 120582 = 1

Table 5Without communications Low optimal Erlang PreservingSLA Solver assignment

Node VM119899V119899

SLA EnergyTask assignment Task assignment

1 VM11 1199051 1199053 119905

2

1 VM12 0 1199051 1199053

1 VM13 0 02 VM21 119905

2 0

Table 6 High slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

02119862119904119899V119899

01

between VMs (see Table 6) This table shows the commu-nication costs between tasks (119862119894119895) and the communicationslowdown when communications are done between VMsin the same node (Cs

119899V119899

) and the penalty cost when com-munications are performed between different nodes (Cs

119899V119899

)Note that the penalties are very high (02 and 01) when thecommunications are very influential

The solver assignment is shown in Table 7 In orderto avoid communication costs due to slowdowns the bestassignment tends to group tasks first in the same VM andsecond in the same node Although VM

21should become

saturated with this assignment the high communication costcompensates the loss of SLA performance allowing us toswitch off node 1

422 Low Communication Slowdown Now this exampleshows the behaviour of our policy under more normal com-munication conditions Here the communication penaltiesbetween the different VMs or nodes are not as significantas in the previous case because Cs

119899V119899

and Cs119899V119899

are higherTable 8 shows the communication costs between tasks andthe penalty cost if communications are performed betweenVMs in the same node (Cs

119899V119899

) or between different nodes(Cs119899V119899

)In this case the solver got as a result two hosting VMs

(see Table 9) formed by the VM11(with the assigned tasks 1199052

and 1199053) and VM

21with task 119905

1 In this case due to the low

8 The Scientific World Journal

Table 7 High slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

Table 8 Low slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

08

Table 9 Low slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 119905

1 1199053

1 VM12 01 VM13 02 VM21 119905

2

differences between the different communication slowdownstask assignment was distributed between the two nodes

423 Moderate Communication Slowdown We simulated amore normal situation where the communication slowdownbetween nodes is higher than the other ones From the sameexample it was only reduced Cs

119899V119899

to 04 (see Table 10)As expected the resulting solver assignment was differentfrom that in the previous case Theoretically this assignmentshould assign tasks to the powerful unsaturated VMs but asmuch as possible to the VMs residing on the same node Thesolver result was exactly what was expected Although themost powerful VM is in node 2 the tasks were assigned tothe VMs of node 1 because they all fit in the same nodeThatis the reason why a less powerful node like node 1 but onewith more capacity is able to allocate more tasks than node 2due to the communication slowdown between nodes Theseresults are shown in Table 11

5 Conclusions and Future Work

This paper presents a cloud-based system scheduling mech-anism called GS that is able to comply with low powerconsumption and SLA agreements The complexity of themodel developed was increased thus adding more factorsto be taken into account The model was also tested usingthe AMPL modelling language and the SCIP optimizer Theresults obtained proved consistent over a range of scenariosIn all the cases the experiments showed that all the tasks wereassigned to the most powerful subset of virtual machines bykeeping the subset size to the minimum

Table 10 Moderate slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

04

Table 11 Moderate slowdown Solver assignment

Node VM119899V119899

Tasks assignment1 VM11 119905

2 1199053

1 VM12 1199051

1 VM13 02 VM21 0

Although our proposals still have to be tested in real sce-narios these preliminary results corroborate their usefulness

Our efforts are directed towards implementing thosestrategies in a real cloud environment like the OpenStack[22] or OpenNebula [23] frameworks

In the longer term we consider using some statisticalmethod to find an accurate approximation of the workloadusing well-suited Erlang distribution functions

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 MEYC under ContractsTIN2011-28689-C02-02 The authors are members of theresearch groups 2009-SGR145 and 2014-SGR163 funded bythe Generalitat de Catalunya

References

[1] RAversa BDiMartinoMRak S Venticinque andUVillanoPerformance Prediction for HPC on Clouds Cloud ComputingPrinciples and Paradigms John Wiley amp Sons New York NYUSA 2011

[2] A Iosup N Yigitbasi and D Epema ldquoOn the performancevariability of production cloud servicesrdquo in Proceedings of the11th IEEEACM International Symposium on Cluster Cloud andGrid Computing (CCGrid rsquo11) pp 104ndash113 May 2011

[3] J Varia Architection for the Cloud Best Practices Amazon WebServices 2014

[4] Intel cloud computing 2015 vision httpwwwintelcomcon-tentwwwusencloud-computing

[5] M Martinello M Kaaniche and K Kanoun ldquoWeb serviceavailabilitymdashimpact of error recovery and traffic modelrdquo Relia-bility Engineering amp System Safety vol 89 no 1 pp 6ndash16 2005

[6] J Vilaplana F Solsona F Abella R Filgueira and J Rius ldquoThecloud paradigm applied to e-Healthrdquo BMCMedical Informaticsand Decision Making vol 13 no 1 article 35 2013

The Scientific World Journal 9

[7] J Vilaplana F Solsona I Teixido JMateo F Abella and J RiusldquoA queuing theory model for cloud computingrdquo The Journal ofSupercomputing vol 69 no 1 pp 492ndash507 2014

[8] A Beloglazov and R Buyya ldquoOptimal online deterministicalgorithms and adaptive heuristics for energy and performanceefficient dynamic consolidation of virtual machines in Clouddata centersrdquo Concurrency Computation Practice and Experi-ence vol 24 no 13 pp 1397ndash1420 2012

[9] D Kliazovich P Bouvry and S U Khan ldquoGreenCloud apacket-level simulator of energy-aware cloud computing datacentersrdquoThe Journal of Supercomputing vol 62 no 3 pp 1263ndash1283 2012

[10] C Ghribi M Hadji and D Zeghlache ldquoEnergy efficientVM scheduling for cloud data centers exact allocation andmigration algorithmsrdquo in Proceedings of the 13th IEEEACMInternational SymposiumonCluster Cloud andGridComputing(CCGrid rsquo13) pp 671ndash678 May 2013

[11] M F Khan Z Anwar and Q S Ahmad ldquoAssignment of per-sonnels when job completion time follows gamma distributionusing stochastic programming techniquerdquo International Journalof Scientific amp Engineering Research vol 3 no 3 2012

[12] J L Lerida F Solsona P Hernandez F Gine M Hanzichand J Conde ldquoState-based predictions with self-correction onEnterprise Desktop Grid environmentsrdquo Journal of Parallel andDistributed Computing vol 73 no 6 pp 777ndash789 2013

[13] A Goldman and Y Ngoko ldquoA MILP approach to scheduleparallel independent tasksrdquo in Proceedings of the InternationalSymposium on Parallel and Distributed Computing (ISPDC rsquo08)pp 115ndash122 Krakow Poland July 2008

[14] T Vinh T Duy Y Sato and Y Inoguchi ldquoPerformanceevaluation of a green scheduling algorithm for energy savingsin cloud computingrdquo in Proceedings of the IEEE InternationalSymposium on Parallel amp Distributed Processing Workshops andPhd Forum (IPDPSW rsquo10) pp 1ndash8 Atlanta Ga USA April 2010

[15] M Mezmaz N Melab Y Kessaci et al ldquoA parallel bi-objectivehybrid metaheuristic for energy-aware scheduling for cloudcomputing systemsrdquo Journal of Parallel and Distributed Com-puting vol 71 no 11 pp 1497ndash1508 2011

[16] Y C Ouyang Y J Chiang C H Hsu and G Yi ldquoAnoptimal control policy to realize green cloud systems with SLA-awarenessrdquo The Journal of Supercomputing vol 69 no 3 pp1284ndash1310 2014

[17] T C Ferreto M A S Netto R N Calheiros and C AF de Rose ldquoServer consolidation with migration control forvirtualized data centersrdquo Future Generation Computer Systemsvol 27 no 8 pp 1027ndash1034 2011

[18] A Murtazaev and S Oh ldquoSercon server consolidation algo-rithm using live migration of virtual machines for greencomputingrdquo IETE Technical Review (Institution of Electronicsand Telecommunication Engineers India) vol 28 no 3 pp 212ndash231 2011

[19] A F Monteiro M V Azevedo and A Sztajnberg ldquoVirtualizedWeb server cluster self-configuration to optimize resource andpower userdquo Journal of Systems and Software vol 86 no 11 pp2779ndash2796 2013

[20] C-C Lin H-H Chin and D-J Deng ldquoDynamic multiserviceload balancing in cloud-based multimedia systemrdquo IEEE Sys-tems Journal vol 8 no 1 pp 225ndash234 2014

[21] J Vilaplana F Solsona J Mateo and I Teixido ldquoSLA-awareload balancing in a web-based cloud system over OpenStackrdquoin Service-Oriented ComputingmdashICSOC 2013 Workshops vol

8377 of Lecture Notes in Computer Science pp 281ndash293 SpringerInternational Publishing 2014

[22] OpenStack httpwwwopenstackorg[23] OpenNebula httpwwwopennebulaorg

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

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RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

2 The Scientific World Journal

Another important contribution of this paper is methodused to model the power of the virtual machines in functionof their workload Relying on the work done in [11] wherethe authors formulate the problem of assigning people fromvarious groups to different jobs and who may complete themin the minimum time as a stochastic programming problemthe job completion times were assumed to follow a Gammadistribution To model the influence of the workload thecomputing power of the virtual machine is weighted by aload factor determined by an Erlang distribution (equivalentto a Gamma) Finally a stochastic programming problem isobtained and transformed into an equivalent deterministicproblem with a nonlinear objective function

The remainder of the paper is organized as follows Ourcontribution is based on the previous work presented inSection 2 In the GS section (Section 3) we present our maincontributions a sort of scheduling policy These proposalsare arranged by increasing complexity The experimentationshowing the good behavior of our cloud model is presentedin the Results section (Section 4) Finally the Conclusionsand Future Work section outlines the main conclusions andpossible research lines to explore in the near future

2 Related Work

There is a great deal of work in the literature on linearprogramming (LP) solutions and algorithms applied toscheduling like those presented in [12 13] Another notablework was performed in [14] where authors designed a GreenScheduling Algorithm that integrated a neural network pre-dictor in order to optimize server power consumption incloud computing Also the authors in [15] proposed a geneticalgorithm that takes into account both makespan and energyconsumption

Shutting down servers when they are not being used isone of the most direct methods to reduce the idle powerHowever the authors in [16] state that a power-off requiresan additional setup cost resulting in long system delaysShutting down servers may sacrifice quality of service (QoS)levels thus violating the SLA They put the server workat a lower service rate rather than completely stoppingwork during idle periods This drawback can be reduced ifscheduling is performed for a large enough number of tasksas in our case

In [17] the authors treat the problem of consolidatingVMs in a server by migrating VMs with steady and stablecapacity needsThey proposed an exact formulation based ona linear program described by too small a number of validinequalities Indeed this description does not allow solvingin a reasonable time or an optimal way problems involvingthe allocation of a large number of items (or VMs) to manybins (or servers)

In [18] the authors presented a server consolidation(Sercon) algorithmwhich consists ofminimizing the numberof used nodes in a data center and minimizing the numberof migrations at the same time to solve the bin (or server)packing problem They show the efficiency of Sercon forconsolidating VMs and minimizing migrations Despite our

proposal (based on NLP) always finding the best solutionSercon is a heuristic that cannot always reach or find theoptimal solution

The authors in [19] investigated resource optimizationservice quality and energy saving by the use of a neural net-work These actions were specified in two different resourcemanagers which sought to maintain the applicationrsquos qualityservice in accordance with the SLA and obtain energy savingsin a virtual serversrsquo cluster by turning them off when idleand dynamically redistributing the VMs using livemigrationSaving energy is only applied in the fuzzy-term ldquointermediateloadrdquo using fewer resources and still maintaining satisfactoryservice quality levels Large neural network training timesand their nonoptimal solutions could be problems that canbe overcome by using other optimization techniques such asthe NLP one used in this paper

In [10] the authors modelled an energy aware alloca-tion and consolidation policies to minimize overall energyconsumption with an optimal allocation and a consolidationalgorithm The optimal allocation algorithm is solved as abin-packing problem with a minimum power consumptionobjective The consolidation algorithm is derived from alinear and integer formulation of VM migration to adapt toplacement when resources are released

The authors of [20] presented an effective load-balancinggenetic algorithm that spreads the multimedia service taskload to the servers with the minimal cost for transmittingmultimedia data between server clusters and clients forcentralized hierarchical cloud-based multimedia systemsClients can change their locations and each server clusteronly handled a specific type of multimedia task so that twoperformance objectives (aswe do)were optimized at the sametime

In [21] the authors presented an architecture able tobalance load into different virtual machines meanwhile pro-viding SLA guarantees The model presented in that workis similar to the model presented in this paper The maindifference is in the tasks considered Now a more complexand generalized model is presented In addition commu-nicating and heterogeneous tasks as well as nondedicatedenvironments have been taken into account

Our proposal goes further than the outlined literatureInstead of designing a single criteria scheduling problem(LP) we design an NLP scheduling solution which takes intoaccount multicriteria issues In contrast to the optimizationtechniques of the literature our model ensures the best solu-tion available We also want to emphasize the nondedicatedfeature of the model meaning that the workload of the cloudis also considered This also differentiates from the relatedwork This consideration also brings the model into realityproviding more reliable and realistic results

3 GS Model

The NLP scheduling solution proposed in this paper mod-els a problem by giving an objective function (OF) Theequation representing the objective function takes variousperformance criteria into account

The Scientific World Journal 3

GS tries to assign as many tasks as possible to the mostpowerful VMs leaving the remaining ones aside As we willconsider clouds made up of various nodes at the end ofthe scheduling process the nodes all of whose VMs are notassigned any task can then be turned off As SLA based ontheminimization of the return time is also applied themodelalso minimizes the computing and communication time ofthe overall tasks making up a job

31 General Notation Let a jobmade up of119879 communicatingtasks (119905119894 119894 = 1 119879) and a cloud made up of 119873 heteroge-neous nodes (Node

1 Node

119873)

The number of VMs can be different between nodes soweuse notation V

119899(119907119899= 1 119881

119899 where 119899 = 1 119873) to rep-

resent the number of VMs located to Node119899 In other words

each Node119899will be made up by VMs VM

1198991 VM

119899119881119899

Task assignments must show the node and the VM inside

the nodes task 119905119894 is assigned to In doing so Boolean variableswill also be used The notation 119905

119894

119899V119899

is used to represent theassignment of task 119905119894 to Node

119899VM VM

119899V119899

The notation 119872

119894

119899V119899

represents the amount of Memoryallocated to task 119905119894 in VM VM

119899V119899

It is assumed that Memoryrequirements do not change between VMs so 119872

119894

119899V119899

=

119872119894

119899V1015840119899

forall119899 le 119873 and V119899 V1015840119899

le 119881119899 The Boolean variable 119905

119894

119899V119899

represents the assignment of task 119905119894 to VM

119899V119899

Once thesolver is executed the 119905

119894

119899V119899

variables will inform about theassignment of tasks to VMsThis is 119905119894

119899V119899

= 1 if 119905119894 is assigned toVM119899V119899

and 119905119894

119899V119899

= 0 otherwise

32 Virtual Machine Heterogeneity The relative computingpower (Δ

119899V119899

) of a VM119899V119899

is defined as the normalized scoreof such a VM Formally consider

Δ119899V119899

=120575119899V119899

sum119881

119894=1sum119881119894

119896=1120575119894V119896

(1)

wheresum119881119894=1

sum119881119894

119896=1Δ119894V119896

= 1 120575119899V119899

is the score (ie the computingpower) of VM

119899V119899

Although 120575119899V119899

is a theoretical conceptthere are many valid benchmarks it can be obtained with(ie Linpack (Linpack httpwwwnetliborglinpack) orSPEC (SPEC httpwwwspecorg)) Linpack (available in CFortran and Java) for example is used to obtain the numberof floating-point operations per second Note that the closerthe relative computing power is to one (in other words themore powerful it is) the more likely it is that the requests willbe mapped into such a VM

33 Task Heterogeneity In order tomodel task heterogeneityeach task 119905

119894 has its processing cost 119875119894

119899V119899

representing theexecution time of task 119905

119894 in VM119899V119899

with respect to theexecution time of task 119905119894 in the least powerful VM

119899V119899

(in otherwords with the lowest Δ

119899V119899

) It should be a good choice to

maximize 119905119894

119899V119899

119875119894

119899V119899

to obtain the best assignment (in otherwords the OF) as follows

max(119873

sum

119899=1

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

119875119894

119899V119899

) (2)

However there are still a few criteria to consider

34 Virtual MachineWorkload The performance drop expe-rienced by VMs due to workload saturation is also taken intoaccount If a VM is underloaded its throughput (tasks solvedper unit of time) will increase as more tasks are assigned toit When the VM reaches its maximum workload capacityits throughput starts falling asymptotically towards zeroThisbehavior can be modeled with an Erlang distribution densityfunction Erlang is a continuous probability distribution withtwo parameters 120572 and 120582 The 120572 parameter is called the shapeparameter and the 120582 parameter is called the rate parameterThese parameters depend on the VM characteristics When120572 equals 1 the distribution simplifies to the exponentialdistribution The Erlang probability density function is

119864 (119909 120572 120582) = 120582119890minus120582119909 (120582119909)

120572minus1

(120572 minus 1)forall119909 120582 ge 0 (3)

We consider that the Erlang modelling parameters ofeach VM can easily be obtained empirically The Erlangparameters can be obtained by means of a comprehensiveanalysis of all typical workloads being executed in the serversupercomputer or data center to be evaluated In the presentwork a common PC server was used To carry out thisanalysis we continuously increased the workload until theserver was saturated We collected measurements about themean response times at eachworkload variation By empiricalanalysis of that experimentation we obtained the Erlang thatbetter fitted the obtained behaviour measurements

The Erlang is used to weight the Relative computingpower Δ

119899V119899

of each VM119899V119899

with its associated workloadfactor determined by an Erlang distribution This optimalworkload model is used to obtain the maximum throughputperformance (number of task executed per unit of time) ofeach VM

119899V119899

In the case presented in this paper the 119909-axis(abscisas) represents the sum of the Processing cost 119875119894

119899V119899

ofeach 119905

119894 assigned to every VM119899V119899

Figure 1 shows an example in which we depict an Erlang

with 120572 = 76 and 120582 = 15 The Erlang reaches its maximumwhen 119883 = 5 Provided that the abscissas represent theworkload of a VM a workload of 5 will give the maximumperformance to such a VM in terms of throughput So we arenot interested in assigning less or more workload to a specificVM119899V119899

because otherwise this would lead us away from theoptimal assignment

Given an Erlang distribution function with fixed param-eters 120572 and 120582 it is possible to calculate the optimal workloadin which the function reaches the maximum by using itsderivative function

119864 (119909 120572 120582)1015840= 119890minus120582minus1lowast119909

lowast 119909 (120582 minus 1 lowast 119909 minus 120572 minus 1) forall119909 120582 ge 0

(4)

4 The Scientific World Journal

0010203040506070809

1

0 5 10 15 20

120572 = 76 120582 = 15

Figure 1 Erlang plots for different 120572 and 120582 values

Accordingly the optimal workload of the Erlang examplein Figure 1 with 120572 = 76 and 120582 = 15 is

119864 (119909 76 15)1015840= 119890minus14lowast119909

lowast 119909 (14119909 minus 75) = 0

119909 =75

14

(5)

Finally in our case provided that the VM workloaddefined as the sum of the processing costs (119875119894

119899V119899

) of the tasksassigned to a particular VM must be an N number theoptimal workload (119909) is

119909 = round(7514

) = 5 (6)

Provided that Boolean variable 119905119894

119899V119899

= 1 is a booleanvariable informing of the assignment of 119905119894 to VM

119899V119899

and119905119894

119899V119899

= 0 if not the Erlang-weighted Δ119899V119899

would be

Δ119899V119899

119864(

119879

sum

119894=1

119875119894

119899V119899

119905119895

V 120572 120582) (7)

35 Task Communication and VM Selection In this sectionthe VM selection is also considered In doing so eachVM can be selected from a range of 119873 nodes forming afederated cloud We want to obtain an OF that considersthe scheduling of heterogeneous and communicating tasksto 119873 heterogeneous nodes made up of different numbers ofheterogeneous VMs

The communication cost (in time) between tasks 119905119894 and119905119895 when in the same VM is denoted by 119862

119894119895 and shouldbe passed to the solver as an argument For reasons ofsimplicity all communication links are considered to havethe same bandwidth and latency Notation119862119894119895

119899V119899

represents thecommunication cost between task 119905

119894 residing in VM119899V119899

withanother task 119905

119895 (located in the same VM or elsewhere) Pro-vided equivalent bandwidth between any two VMs 119862119894119895

119899V119899

=

119862119895119894

119899V1015840119899

forallV V1015840 le 119881 In other words the communication cost doesnot depend on the VM or the links used between the VMs

VM communication links are considered with the samebandwidth capacity Depending on its location we multiplythe communication cost between tasks 119905119894 and 119905

119895 by a givencommunication slowdown If 119905

119894and 119905119895are located in the same

VM the communication slowdown (denoted by Cs119899V119899

) is 1If 119905119895 is assigned to another VM in the same node than 119905

119894

(119905119895119899V119899

= 1 the Communication slowdown (Cs119899V119899

) will bein the range [0 1] Finally if 119905119895 is assigned to anotherVM located in another node (119905119895

119899V119899

= 1) the correspondingcommunication slowdown term (Cs

119899V119899

) will also be in therange [0 1] Cs

119899V119899

and Cs119899V119899

should be obtained withrespect to Cs

119899V119899

In other words Cs119899V119899

and Cs119899V119899

are therespective reduction (in percentage) in task communicationbetween VMs located in the same and different nodescompared with task communication inside the same VM Tosum up Cs

119899V119899

= 1 ge Cs119899V119899

ge Cs119899V119899

ge 0According to task communication the idea is to add a

component in the OF that penalizes (enhances) the com-munications performed between different VMs and differentnodes Grouping tasks inside the same VM will dependon not only their respective processing cost (119875119894

119899V119899

) but alsothe communication costs 119862119894119895

119899V119899

and communication slowdownsCs119899V119899

Cs119899V119899

and Cs119899V119899

We reward the communications donein the same VM but less so the ones done in differentVMs while still in the same node Finally communicationsbetween nodes are left untouched without rewarding orpenalizing

In the same way if we modelled the OF in function of thetak heterogeneity in (2) the communication component willbe as follows (only the communication component of the OFis shown)

max(119873

sum

119899=1

119881119899

sum

V119899=1

119879

sum

119894=1

(119905119894

119899V119899

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

(8)

And the OF function will be

max(119873

sum

119899=1

119881119899

sum

V119899=1

((

119879

sum

119894=1

119905119894

119899V119899

(119875119894

119899V119899

+

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

times Δ119899V119899

119864(

119879

sum

119895=1

119905119895

119899V119899

119875119895

119899V119899

120572 120582)))

(9)

36 Choosing SLA or Energy Saving It is important tohighlight that the optimization goal is two criteria (SLAand energy in our case) Thus the user could prioritize

The Scientific World Journal 5

the criteria Assignments are performed starting from themost powerful VM When this becomes saturated taskassignment continues with the next most powerful VMregardless of the node it resides in When this VM residesin another node (as in our case) the energy-saving criteriawill be harmed It would be interesting to provide a means ofincreasing criteria preferences in the model presented

In order to highlight specific criteria (ie energy saving)one more additional component must be added to the OFThis component must enhance the assignment of tasks to thesame node by assigning tasks to the most powerful nodesand not only to the most powerful VMs as before This is thenatural procedure to follow because the OF is a maximumThus the likelihood of less powerful nodes becoming idleincreases and this gives the opportunity to power them offhence saving energy

The additional component can be defined in a similar wayas for the relative VM computing power (Δ

119899V119899

) of a VM119899V119899

Instead we obtain the relative node computing power of aNode119899(Θ119899) as the normalized summatory of their forming

VMs Θ119899will inform about the computing power of Node

119899

For119873 nodes Θ119899is formally defined as

Θ119899=

sum119881119899

V119899=1Δ119899V119899

sum119873

119899=1sum119881119899

V119899=1Δ119899V119899

(10)

wheresum119873119899=1

Θ119899= 1 To obtainΘ

119899 the parallel Linpack version

(HPL high performance Linpack) can be used It is the oneused to benchmark and rank supercomputers for the TOP500list

Depending on the importance of the energy savingcriteria a weighting factor should be provided to Θ

119899 We

simply call this factor energy Energy Ξ The Ξ will be in therange (0 1] For an Ξ0 our main criteria will be energysaving and forΞ = 1 our goal is only SLAThus the resultingenergy component will beΘ

119899Ξ Thus for a given Node

119899with

Θ119899 we must weigh the energy saving criteria of such a node

by the following factor

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ (11)

The resulting OF function will be

max(119873

sum

119899=1

(

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ)

times

119881119899

sum

V119899=1

((

119879

sum

119894=1

119905119894

119899V119899

(119875119894

119899V119899

+

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

times Δ119899V119899

119864(

119879

sum

119895=1

119905119895

119899V119899

119875119895

119899V119899

120572 120582)))

(12)

37 Enforcing SLA For either prioritized criteria SLA orenergy saving there is a last consideration to be taken intoaccount

Imagine the case where tasks do not communicate Oncethey are assigned to a node one would expect them to beexecuted in the minimum time In this case there is alreadyno need to group tasks in the VM in decreasing order ofpower in the same node because this node is no longereligible to be switched off A better solution in this case wouldbe to balance the tasks between the VMs of such a nodein order to increase SLA performance Note that this notapply in the communicating tasks due to the communicationslowdown between VMs

To implement this we only need to assign every noncom-municating tasks without taking the relative computing power(Δ119899V119899

) of each VM into accountWe only need to replace Δ

119899V119899

in (12) by Δ defined as

Δ = if (

119879

sum

119895lt119894

119862119894119895

119899V119899

ge 0)Δ119899V119899

else 1

(13)

For the case of noncommunicating tasks by assigning aΔ = 1 all the VMs have the same relative computing powerΔ119899V119899

Thus tasks are assigned in a balanced way

38 Model Formulation Finally the OF function and theirconstraints are presented The best task scheduling assign-ment to VMs which takes all the features into account(GS policy) is formally defined by the following nonlinearprogramming model

max(119873

sum

119899=1

(

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ)

times

119881119899

sum

V119899=1

((

119879

sum

119894=1

119905119894

119899V119899

(119875119894

119899V119899

+

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

times Δ119864(

119879

sum

119895=1

119905119895

119899V119899

119875119895

119899V119899

120572 120582)))

(14a)

st119879

sum

119894=1

119872119899V119899

119894le 119872119899V

119899forall119899 le 119873 V

119899le 119881119899

(14b)

119873

sum

119899=1

119881

sum

V119899=1

119905119894

119899V119899

= 1 forall119894 le 119879 (14c)

6 The Scientific World Journal

Equation (14a) is the objective function (OF) to be max-imized Note that OF is an integer and nonlinear problemInequality in (14b) and equality in (14c) are the constraints ofthe objective function variables Given the constants 119879 (thetotal number of requests or tasks) and 119872V for each VM

119899V119899

the solution that maximizes OF will obtain the values of thevariables 119905119894

119899V119899

representing the number of tasks assigned toVM119899V119899

Thus the 119905119899V119899119894obtained will be the assignment found

by this modelOF takes into account the processing costs (119875119894

119899V119899

) and thecommunication times (119862119894119895

119899V119899

) of the tasks assigned to eachVM119899V119899

and the communication slowdownsbetweenVMsCs119899V119899

and nodes Cs119899V119899

Cs119899V119899

= 1 Δ is defined in Section 37 And119864(sum119879

119895=1119905119895

119899V119899

119875119895

119899V119899

120572 120582) represents the power slowdown of eachVM due to its workload (defined in Section 34)

To sum up for the case when the workload is made up ofnoncommunicating tasks if we are interested in prioritizingthe SLA criteria OF 35 should be applied If on the contrarythe goal is to prioritize energy savingOF (14a) should be usedinstead

4 Results

In this section we present the theoretical results obtainedfrom solving the scheduling problems aimed at achievingbest task assignment Two representative experiments wereperformed in order to test the performance of GS

The experiments were performed by using the AMPL(AMPL A Mathematical Programming Language httpamplcom) language and the SCIP (SCIP Solving ConstraintInteger Programs httpscipzibde) solver AMPL is analgebraic modeling language for describing and solving high-complexity problems for large-scale mathematical computa-tion supported by many solvers Integer and nonlinear (ourmodel type) problems can be solved by SCIP one of thesolvers supported by AMPL

Throughout all the experimentation the Erlang argu-ments were obtained empirically by using the strategyexplained in Section 34

As the objective of this section is to prove the correctnessof the policy only a small set of tasks VMs and nodes waschosen The size of the experimental framework was chosento be as much representative of actual cases as possible butat the same time simple enough to be used as an illustrativeexample So the experimental framework chosen was madeup of 2 different nodes one of them comprised 3VMs and theother 1 VM see Figure 2The objective of this simulation wasto achieve the best assignment for 3 tasks Table 1 shows theprocessing cost 119875119894

119899V119899

relating the execution times of the tasks ineach VM To show the good behavior of themodel presentedeach task has the same processing cost independently of theVM The model presented can be efficiently applied to realcloud environments The only weak point is that the modelis static That means that homogenous and static workloadconditions must be stable in our model Job executions indifferent workload sizes can be saved in a database system

Node 2Node 1

VM2VM3 VM1

VM3

Cloud

Figure 2 Cloud architecture

Table 1 Task processing costs

Task 119905119894 Processing costs 119875119894119899V119899

Value1199051

1198751

11 1198751

12 1198751

13 1198751

211

1199052

1198752

1 1198752

12 1198752

13 1198752

215

1199053

1198753

11 1198753

12 1198753

13 1198753

211

Total processing cost (sum119894119875119894

119899V119899

) 7

providing a means for determining the SLA of such a job infuture executions

41 Without Communications In this section a hypotheticalsituation without communication between tasks is evaluatedIn this situation our scheduling policy tends to assign thetasks to the most powerful set of virtual machines (ie withthe higher relative computing power Δ

119899V119899

considering theirindividual saturation in this choice)This saturation becomescritical when more and more tasks are added Here the mostimportant term is the Erlang function since it models thebehaviour of every virtual machine Thus taking this intoaccount our scheduler knows the exact weight of tasks it canassign to the VMs in order to obtain the best return timesThis phenomenon is observed in the following examples

411 Without Communications and High Optimal ErlangTable 2 shows the parameters used in the first example Theamount ofMemory allocated to each task 119905119894 in every VM119872

119899V119899

(as we supposed this amount to be equal in all the VMs wesimply call it119872119894)The relative computing power (Δ

119899VV) of eachVMand finally the120572 and 120582 Erlang arguments Note that all theVMs have the same Erlang parameters The parameters werechosen this way because any VM saturates with the overallworkload assigned In other words the total processing cost 7is lower than the optimal Erlang workload 16

Table 3 shows the solver assignment results The bestscheduling assigns all the tasks to the same VM (VM

21 the

only VM in node 2) because this VM has the biggest relative

The Scientific World Journal 7

Table 2 Without communications High optimal Erlang VM con-figurations

Node VM119899V119899

119872119894

Δ119899VV Erlang

1 VM11 10 075 120572 = 3 120582 = 8

1 VM12 10 035 120572 = 3 120582 = 8

1 VM13 10 01 120572 = 3 120582 = 8

2 VM21 10 085 120572 = 3 120582 = 8

Table 3 Without communications High optimal Erlang Solverassignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

computing power (Δ119899VV) This result is very coherent Due to

the lack of communications the model tends to assign tasksto the most powerful VMwhile its workload does not exceedthe Erlang optimum (a workload of 10 tasks) As in our casethe total workload is 7 and VM

21could host evenmore tasks

412 Without Communications Low Optimal Erlang andPreserving SLA In this example (see Table 4) the VMs haveanother Erlang However the task processing costs do notchange so they remain the same as in Table 1 In this caseeach VM becomes saturated when the assignment workloadweight is higher than 5 (because 5 is the optimal workload)

The best assignment in this case is the one formed bythe minimum set of VMs with the best relative computingpower Δ

119899VV (see Table 5 column Task Assignment SLA) Theassignment of the overall tasks to only one VM (although itwas the most powerful one) as before will decrease the returntime excessively due to its saturation

413 Without Communications Low Optimal Erlang andPreserving Energy Saving Provided that the most importantcriterion is the energy saving the assignment will be some-what different (seeTable 5 columnTaskAssignment Energy)In this case OF (14a) with Ξ = 1was usedThen as expectedall the tasks were again assigned to VM

21of Node

2

42 With Communications Starting from the same VMconfiguration shown on Table 4 in this section we presenta more real situation where the costs of communicationsbetween tasks are also taken into account It is important tohighlight that in some situations the best choice does notinclude the most powerful VMs (ie with the highest relativecomputing powerΔ

119899V119899

)Thus the results shown in this sectionmust show the tradeoff between relative computing powerof VM workload scheduling impact modeled by the Erlangdistribution and communication efficiency between tasks

421 High Communication Slowdown This example showsthe behaviour of the model under large communication costs

Table 4Without communications Low optimal Erlang PreservingSLA VM configurations

Node VM119899V119899

119872119894

Δ119899VV Erlang

1 VM11 10 075 120572 = 5 120582 = 1

1 VM12 10 035 120572 = 5 120582 = 1

1 VM13 10 01 120572 = 5 120582 = 1

2 VM21 10 085 120572 = 5 120582 = 1

Table 5Without communications Low optimal Erlang PreservingSLA Solver assignment

Node VM119899V119899

SLA EnergyTask assignment Task assignment

1 VM11 1199051 1199053 119905

2

1 VM12 0 1199051 1199053

1 VM13 0 02 VM21 119905

2 0

Table 6 High slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

02119862119904119899V119899

01

between VMs (see Table 6) This table shows the commu-nication costs between tasks (119862119894119895) and the communicationslowdown when communications are done between VMsin the same node (Cs

119899V119899

) and the penalty cost when com-munications are performed between different nodes (Cs

119899V119899

)Note that the penalties are very high (02 and 01) when thecommunications are very influential

The solver assignment is shown in Table 7 In orderto avoid communication costs due to slowdowns the bestassignment tends to group tasks first in the same VM andsecond in the same node Although VM

21should become

saturated with this assignment the high communication costcompensates the loss of SLA performance allowing us toswitch off node 1

422 Low Communication Slowdown Now this exampleshows the behaviour of our policy under more normal com-munication conditions Here the communication penaltiesbetween the different VMs or nodes are not as significantas in the previous case because Cs

119899V119899

and Cs119899V119899

are higherTable 8 shows the communication costs between tasks andthe penalty cost if communications are performed betweenVMs in the same node (Cs

119899V119899

) or between different nodes(Cs119899V119899

)In this case the solver got as a result two hosting VMs

(see Table 9) formed by the VM11(with the assigned tasks 1199052

and 1199053) and VM

21with task 119905

1 In this case due to the low

8 The Scientific World Journal

Table 7 High slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

Table 8 Low slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

08

Table 9 Low slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 119905

1 1199053

1 VM12 01 VM13 02 VM21 119905

2

differences between the different communication slowdownstask assignment was distributed between the two nodes

423 Moderate Communication Slowdown We simulated amore normal situation where the communication slowdownbetween nodes is higher than the other ones From the sameexample it was only reduced Cs

119899V119899

to 04 (see Table 10)As expected the resulting solver assignment was differentfrom that in the previous case Theoretically this assignmentshould assign tasks to the powerful unsaturated VMs but asmuch as possible to the VMs residing on the same node Thesolver result was exactly what was expected Although themost powerful VM is in node 2 the tasks were assigned tothe VMs of node 1 because they all fit in the same nodeThatis the reason why a less powerful node like node 1 but onewith more capacity is able to allocate more tasks than node 2due to the communication slowdown between nodes Theseresults are shown in Table 11

5 Conclusions and Future Work

This paper presents a cloud-based system scheduling mech-anism called GS that is able to comply with low powerconsumption and SLA agreements The complexity of themodel developed was increased thus adding more factorsto be taken into account The model was also tested usingthe AMPL modelling language and the SCIP optimizer Theresults obtained proved consistent over a range of scenariosIn all the cases the experiments showed that all the tasks wereassigned to the most powerful subset of virtual machines bykeeping the subset size to the minimum

Table 10 Moderate slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

04

Table 11 Moderate slowdown Solver assignment

Node VM119899V119899

Tasks assignment1 VM11 119905

2 1199053

1 VM12 1199051

1 VM13 02 VM21 0

Although our proposals still have to be tested in real sce-narios these preliminary results corroborate their usefulness

Our efforts are directed towards implementing thosestrategies in a real cloud environment like the OpenStack[22] or OpenNebula [23] frameworks

In the longer term we consider using some statisticalmethod to find an accurate approximation of the workloadusing well-suited Erlang distribution functions

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 MEYC under ContractsTIN2011-28689-C02-02 The authors are members of theresearch groups 2009-SGR145 and 2014-SGR163 funded bythe Generalitat de Catalunya

References

[1] RAversa BDiMartinoMRak S Venticinque andUVillanoPerformance Prediction for HPC on Clouds Cloud ComputingPrinciples and Paradigms John Wiley amp Sons New York NYUSA 2011

[2] A Iosup N Yigitbasi and D Epema ldquoOn the performancevariability of production cloud servicesrdquo in Proceedings of the11th IEEEACM International Symposium on Cluster Cloud andGrid Computing (CCGrid rsquo11) pp 104ndash113 May 2011

[3] J Varia Architection for the Cloud Best Practices Amazon WebServices 2014

[4] Intel cloud computing 2015 vision httpwwwintelcomcon-tentwwwusencloud-computing

[5] M Martinello M Kaaniche and K Kanoun ldquoWeb serviceavailabilitymdashimpact of error recovery and traffic modelrdquo Relia-bility Engineering amp System Safety vol 89 no 1 pp 6ndash16 2005

[6] J Vilaplana F Solsona F Abella R Filgueira and J Rius ldquoThecloud paradigm applied to e-Healthrdquo BMCMedical Informaticsand Decision Making vol 13 no 1 article 35 2013

The Scientific World Journal 9

[7] J Vilaplana F Solsona I Teixido JMateo F Abella and J RiusldquoA queuing theory model for cloud computingrdquo The Journal ofSupercomputing vol 69 no 1 pp 492ndash507 2014

[8] A Beloglazov and R Buyya ldquoOptimal online deterministicalgorithms and adaptive heuristics for energy and performanceefficient dynamic consolidation of virtual machines in Clouddata centersrdquo Concurrency Computation Practice and Experi-ence vol 24 no 13 pp 1397ndash1420 2012

[9] D Kliazovich P Bouvry and S U Khan ldquoGreenCloud apacket-level simulator of energy-aware cloud computing datacentersrdquoThe Journal of Supercomputing vol 62 no 3 pp 1263ndash1283 2012

[10] C Ghribi M Hadji and D Zeghlache ldquoEnergy efficientVM scheduling for cloud data centers exact allocation andmigration algorithmsrdquo in Proceedings of the 13th IEEEACMInternational SymposiumonCluster Cloud andGridComputing(CCGrid rsquo13) pp 671ndash678 May 2013

[11] M F Khan Z Anwar and Q S Ahmad ldquoAssignment of per-sonnels when job completion time follows gamma distributionusing stochastic programming techniquerdquo International Journalof Scientific amp Engineering Research vol 3 no 3 2012

[12] J L Lerida F Solsona P Hernandez F Gine M Hanzichand J Conde ldquoState-based predictions with self-correction onEnterprise Desktop Grid environmentsrdquo Journal of Parallel andDistributed Computing vol 73 no 6 pp 777ndash789 2013

[13] A Goldman and Y Ngoko ldquoA MILP approach to scheduleparallel independent tasksrdquo in Proceedings of the InternationalSymposium on Parallel and Distributed Computing (ISPDC rsquo08)pp 115ndash122 Krakow Poland July 2008

[14] T Vinh T Duy Y Sato and Y Inoguchi ldquoPerformanceevaluation of a green scheduling algorithm for energy savingsin cloud computingrdquo in Proceedings of the IEEE InternationalSymposium on Parallel amp Distributed Processing Workshops andPhd Forum (IPDPSW rsquo10) pp 1ndash8 Atlanta Ga USA April 2010

[15] M Mezmaz N Melab Y Kessaci et al ldquoA parallel bi-objectivehybrid metaheuristic for energy-aware scheduling for cloudcomputing systemsrdquo Journal of Parallel and Distributed Com-puting vol 71 no 11 pp 1497ndash1508 2011

[16] Y C Ouyang Y J Chiang C H Hsu and G Yi ldquoAnoptimal control policy to realize green cloud systems with SLA-awarenessrdquo The Journal of Supercomputing vol 69 no 3 pp1284ndash1310 2014

[17] T C Ferreto M A S Netto R N Calheiros and C AF de Rose ldquoServer consolidation with migration control forvirtualized data centersrdquo Future Generation Computer Systemsvol 27 no 8 pp 1027ndash1034 2011

[18] A Murtazaev and S Oh ldquoSercon server consolidation algo-rithm using live migration of virtual machines for greencomputingrdquo IETE Technical Review (Institution of Electronicsand Telecommunication Engineers India) vol 28 no 3 pp 212ndash231 2011

[19] A F Monteiro M V Azevedo and A Sztajnberg ldquoVirtualizedWeb server cluster self-configuration to optimize resource andpower userdquo Journal of Systems and Software vol 86 no 11 pp2779ndash2796 2013

[20] C-C Lin H-H Chin and D-J Deng ldquoDynamic multiserviceload balancing in cloud-based multimedia systemrdquo IEEE Sys-tems Journal vol 8 no 1 pp 225ndash234 2014

[21] J Vilaplana F Solsona J Mateo and I Teixido ldquoSLA-awareload balancing in a web-based cloud system over OpenStackrdquoin Service-Oriented ComputingmdashICSOC 2013 Workshops vol

8377 of Lecture Notes in Computer Science pp 281ndash293 SpringerInternational Publishing 2014

[22] OpenStack httpwwwopenstackorg[23] OpenNebula httpwwwopennebulaorg

Submit your manuscripts athttpwwwhindawicom

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Volume 2014

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Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Applied Computational Intelligence and Soft Computing

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World Journal 3

GS tries to assign as many tasks as possible to the mostpowerful VMs leaving the remaining ones aside As we willconsider clouds made up of various nodes at the end ofthe scheduling process the nodes all of whose VMs are notassigned any task can then be turned off As SLA based ontheminimization of the return time is also applied themodelalso minimizes the computing and communication time ofthe overall tasks making up a job

31 General Notation Let a jobmade up of119879 communicatingtasks (119905119894 119894 = 1 119879) and a cloud made up of 119873 heteroge-neous nodes (Node

1 Node

119873)

The number of VMs can be different between nodes soweuse notation V

119899(119907119899= 1 119881

119899 where 119899 = 1 119873) to rep-

resent the number of VMs located to Node119899 In other words

each Node119899will be made up by VMs VM

1198991 VM

119899119881119899

Task assignments must show the node and the VM inside

the nodes task 119905119894 is assigned to In doing so Boolean variableswill also be used The notation 119905

119894

119899V119899

is used to represent theassignment of task 119905119894 to Node

119899VM VM

119899V119899

The notation 119872

119894

119899V119899

represents the amount of Memoryallocated to task 119905119894 in VM VM

119899V119899

It is assumed that Memoryrequirements do not change between VMs so 119872

119894

119899V119899

=

119872119894

119899V1015840119899

forall119899 le 119873 and V119899 V1015840119899

le 119881119899 The Boolean variable 119905

119894

119899V119899

represents the assignment of task 119905119894 to VM

119899V119899

Once thesolver is executed the 119905

119894

119899V119899

variables will inform about theassignment of tasks to VMsThis is 119905119894

119899V119899

= 1 if 119905119894 is assigned toVM119899V119899

and 119905119894

119899V119899

= 0 otherwise

32 Virtual Machine Heterogeneity The relative computingpower (Δ

119899V119899

) of a VM119899V119899

is defined as the normalized scoreof such a VM Formally consider

Δ119899V119899

=120575119899V119899

sum119881

119894=1sum119881119894

119896=1120575119894V119896

(1)

wheresum119881119894=1

sum119881119894

119896=1Δ119894V119896

= 1 120575119899V119899

is the score (ie the computingpower) of VM

119899V119899

Although 120575119899V119899

is a theoretical conceptthere are many valid benchmarks it can be obtained with(ie Linpack (Linpack httpwwwnetliborglinpack) orSPEC (SPEC httpwwwspecorg)) Linpack (available in CFortran and Java) for example is used to obtain the numberof floating-point operations per second Note that the closerthe relative computing power is to one (in other words themore powerful it is) the more likely it is that the requests willbe mapped into such a VM

33 Task Heterogeneity In order tomodel task heterogeneityeach task 119905

119894 has its processing cost 119875119894

119899V119899

representing theexecution time of task 119905

119894 in VM119899V119899

with respect to theexecution time of task 119905119894 in the least powerful VM

119899V119899

(in otherwords with the lowest Δ

119899V119899

) It should be a good choice to

maximize 119905119894

119899V119899

119875119894

119899V119899

to obtain the best assignment (in otherwords the OF) as follows

max(119873

sum

119899=1

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

119875119894

119899V119899

) (2)

However there are still a few criteria to consider

34 Virtual MachineWorkload The performance drop expe-rienced by VMs due to workload saturation is also taken intoaccount If a VM is underloaded its throughput (tasks solvedper unit of time) will increase as more tasks are assigned toit When the VM reaches its maximum workload capacityits throughput starts falling asymptotically towards zeroThisbehavior can be modeled with an Erlang distribution densityfunction Erlang is a continuous probability distribution withtwo parameters 120572 and 120582 The 120572 parameter is called the shapeparameter and the 120582 parameter is called the rate parameterThese parameters depend on the VM characteristics When120572 equals 1 the distribution simplifies to the exponentialdistribution The Erlang probability density function is

119864 (119909 120572 120582) = 120582119890minus120582119909 (120582119909)

120572minus1

(120572 minus 1)forall119909 120582 ge 0 (3)

We consider that the Erlang modelling parameters ofeach VM can easily be obtained empirically The Erlangparameters can be obtained by means of a comprehensiveanalysis of all typical workloads being executed in the serversupercomputer or data center to be evaluated In the presentwork a common PC server was used To carry out thisanalysis we continuously increased the workload until theserver was saturated We collected measurements about themean response times at eachworkload variation By empiricalanalysis of that experimentation we obtained the Erlang thatbetter fitted the obtained behaviour measurements

The Erlang is used to weight the Relative computingpower Δ

119899V119899

of each VM119899V119899

with its associated workloadfactor determined by an Erlang distribution This optimalworkload model is used to obtain the maximum throughputperformance (number of task executed per unit of time) ofeach VM

119899V119899

In the case presented in this paper the 119909-axis(abscisas) represents the sum of the Processing cost 119875119894

119899V119899

ofeach 119905

119894 assigned to every VM119899V119899

Figure 1 shows an example in which we depict an Erlang

with 120572 = 76 and 120582 = 15 The Erlang reaches its maximumwhen 119883 = 5 Provided that the abscissas represent theworkload of a VM a workload of 5 will give the maximumperformance to such a VM in terms of throughput So we arenot interested in assigning less or more workload to a specificVM119899V119899

because otherwise this would lead us away from theoptimal assignment

Given an Erlang distribution function with fixed param-eters 120572 and 120582 it is possible to calculate the optimal workloadin which the function reaches the maximum by using itsderivative function

119864 (119909 120572 120582)1015840= 119890minus120582minus1lowast119909

lowast 119909 (120582 minus 1 lowast 119909 minus 120572 minus 1) forall119909 120582 ge 0

(4)

4 The Scientific World Journal

0010203040506070809

1

0 5 10 15 20

120572 = 76 120582 = 15

Figure 1 Erlang plots for different 120572 and 120582 values

Accordingly the optimal workload of the Erlang examplein Figure 1 with 120572 = 76 and 120582 = 15 is

119864 (119909 76 15)1015840= 119890minus14lowast119909

lowast 119909 (14119909 minus 75) = 0

119909 =75

14

(5)

Finally in our case provided that the VM workloaddefined as the sum of the processing costs (119875119894

119899V119899

) of the tasksassigned to a particular VM must be an N number theoptimal workload (119909) is

119909 = round(7514

) = 5 (6)

Provided that Boolean variable 119905119894

119899V119899

= 1 is a booleanvariable informing of the assignment of 119905119894 to VM

119899V119899

and119905119894

119899V119899

= 0 if not the Erlang-weighted Δ119899V119899

would be

Δ119899V119899

119864(

119879

sum

119894=1

119875119894

119899V119899

119905119895

V 120572 120582) (7)

35 Task Communication and VM Selection In this sectionthe VM selection is also considered In doing so eachVM can be selected from a range of 119873 nodes forming afederated cloud We want to obtain an OF that considersthe scheduling of heterogeneous and communicating tasksto 119873 heterogeneous nodes made up of different numbers ofheterogeneous VMs

The communication cost (in time) between tasks 119905119894 and119905119895 when in the same VM is denoted by 119862

119894119895 and shouldbe passed to the solver as an argument For reasons ofsimplicity all communication links are considered to havethe same bandwidth and latency Notation119862119894119895

119899V119899

represents thecommunication cost between task 119905

119894 residing in VM119899V119899

withanother task 119905

119895 (located in the same VM or elsewhere) Pro-vided equivalent bandwidth between any two VMs 119862119894119895

119899V119899

=

119862119895119894

119899V1015840119899

forallV V1015840 le 119881 In other words the communication cost doesnot depend on the VM or the links used between the VMs

VM communication links are considered with the samebandwidth capacity Depending on its location we multiplythe communication cost between tasks 119905119894 and 119905

119895 by a givencommunication slowdown If 119905

119894and 119905119895are located in the same

VM the communication slowdown (denoted by Cs119899V119899

) is 1If 119905119895 is assigned to another VM in the same node than 119905

119894

(119905119895119899V119899

= 1 the Communication slowdown (Cs119899V119899

) will bein the range [0 1] Finally if 119905119895 is assigned to anotherVM located in another node (119905119895

119899V119899

= 1) the correspondingcommunication slowdown term (Cs

119899V119899

) will also be in therange [0 1] Cs

119899V119899

and Cs119899V119899

should be obtained withrespect to Cs

119899V119899

In other words Cs119899V119899

and Cs119899V119899

are therespective reduction (in percentage) in task communicationbetween VMs located in the same and different nodescompared with task communication inside the same VM Tosum up Cs

119899V119899

= 1 ge Cs119899V119899

ge Cs119899V119899

ge 0According to task communication the idea is to add a

component in the OF that penalizes (enhances) the com-munications performed between different VMs and differentnodes Grouping tasks inside the same VM will dependon not only their respective processing cost (119875119894

119899V119899

) but alsothe communication costs 119862119894119895

119899V119899

and communication slowdownsCs119899V119899

Cs119899V119899

and Cs119899V119899

We reward the communications donein the same VM but less so the ones done in differentVMs while still in the same node Finally communicationsbetween nodes are left untouched without rewarding orpenalizing

In the same way if we modelled the OF in function of thetak heterogeneity in (2) the communication component willbe as follows (only the communication component of the OFis shown)

max(119873

sum

119899=1

119881119899

sum

V119899=1

119879

sum

119894=1

(119905119894

119899V119899

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

(8)

And the OF function will be

max(119873

sum

119899=1

119881119899

sum

V119899=1

((

119879

sum

119894=1

119905119894

119899V119899

(119875119894

119899V119899

+

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

times Δ119899V119899

119864(

119879

sum

119895=1

119905119895

119899V119899

119875119895

119899V119899

120572 120582)))

(9)

36 Choosing SLA or Energy Saving It is important tohighlight that the optimization goal is two criteria (SLAand energy in our case) Thus the user could prioritize

The Scientific World Journal 5

the criteria Assignments are performed starting from themost powerful VM When this becomes saturated taskassignment continues with the next most powerful VMregardless of the node it resides in When this VM residesin another node (as in our case) the energy-saving criteriawill be harmed It would be interesting to provide a means ofincreasing criteria preferences in the model presented

In order to highlight specific criteria (ie energy saving)one more additional component must be added to the OFThis component must enhance the assignment of tasks to thesame node by assigning tasks to the most powerful nodesand not only to the most powerful VMs as before This is thenatural procedure to follow because the OF is a maximumThus the likelihood of less powerful nodes becoming idleincreases and this gives the opportunity to power them offhence saving energy

The additional component can be defined in a similar wayas for the relative VM computing power (Δ

119899V119899

) of a VM119899V119899

Instead we obtain the relative node computing power of aNode119899(Θ119899) as the normalized summatory of their forming

VMs Θ119899will inform about the computing power of Node

119899

For119873 nodes Θ119899is formally defined as

Θ119899=

sum119881119899

V119899=1Δ119899V119899

sum119873

119899=1sum119881119899

V119899=1Δ119899V119899

(10)

wheresum119873119899=1

Θ119899= 1 To obtainΘ

119899 the parallel Linpack version

(HPL high performance Linpack) can be used It is the oneused to benchmark and rank supercomputers for the TOP500list

Depending on the importance of the energy savingcriteria a weighting factor should be provided to Θ

119899 We

simply call this factor energy Energy Ξ The Ξ will be in therange (0 1] For an Ξ0 our main criteria will be energysaving and forΞ = 1 our goal is only SLAThus the resultingenergy component will beΘ

119899Ξ Thus for a given Node

119899with

Θ119899 we must weigh the energy saving criteria of such a node

by the following factor

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ (11)

The resulting OF function will be

max(119873

sum

119899=1

(

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ)

times

119881119899

sum

V119899=1

((

119879

sum

119894=1

119905119894

119899V119899

(119875119894

119899V119899

+

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

times Δ119899V119899

119864(

119879

sum

119895=1

119905119895

119899V119899

119875119895

119899V119899

120572 120582)))

(12)

37 Enforcing SLA For either prioritized criteria SLA orenergy saving there is a last consideration to be taken intoaccount

Imagine the case where tasks do not communicate Oncethey are assigned to a node one would expect them to beexecuted in the minimum time In this case there is alreadyno need to group tasks in the VM in decreasing order ofpower in the same node because this node is no longereligible to be switched off A better solution in this case wouldbe to balance the tasks between the VMs of such a nodein order to increase SLA performance Note that this notapply in the communicating tasks due to the communicationslowdown between VMs

To implement this we only need to assign every noncom-municating tasks without taking the relative computing power(Δ119899V119899

) of each VM into accountWe only need to replace Δ

119899V119899

in (12) by Δ defined as

Δ = if (

119879

sum

119895lt119894

119862119894119895

119899V119899

ge 0)Δ119899V119899

else 1

(13)

For the case of noncommunicating tasks by assigning aΔ = 1 all the VMs have the same relative computing powerΔ119899V119899

Thus tasks are assigned in a balanced way

38 Model Formulation Finally the OF function and theirconstraints are presented The best task scheduling assign-ment to VMs which takes all the features into account(GS policy) is formally defined by the following nonlinearprogramming model

max(119873

sum

119899=1

(

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ)

times

119881119899

sum

V119899=1

((

119879

sum

119894=1

119905119894

119899V119899

(119875119894

119899V119899

+

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

times Δ119864(

119879

sum

119895=1

119905119895

119899V119899

119875119895

119899V119899

120572 120582)))

(14a)

st119879

sum

119894=1

119872119899V119899

119894le 119872119899V

119899forall119899 le 119873 V

119899le 119881119899

(14b)

119873

sum

119899=1

119881

sum

V119899=1

119905119894

119899V119899

= 1 forall119894 le 119879 (14c)

6 The Scientific World Journal

Equation (14a) is the objective function (OF) to be max-imized Note that OF is an integer and nonlinear problemInequality in (14b) and equality in (14c) are the constraints ofthe objective function variables Given the constants 119879 (thetotal number of requests or tasks) and 119872V for each VM

119899V119899

the solution that maximizes OF will obtain the values of thevariables 119905119894

119899V119899

representing the number of tasks assigned toVM119899V119899

Thus the 119905119899V119899119894obtained will be the assignment found

by this modelOF takes into account the processing costs (119875119894

119899V119899

) and thecommunication times (119862119894119895

119899V119899

) of the tasks assigned to eachVM119899V119899

and the communication slowdownsbetweenVMsCs119899V119899

and nodes Cs119899V119899

Cs119899V119899

= 1 Δ is defined in Section 37 And119864(sum119879

119895=1119905119895

119899V119899

119875119895

119899V119899

120572 120582) represents the power slowdown of eachVM due to its workload (defined in Section 34)

To sum up for the case when the workload is made up ofnoncommunicating tasks if we are interested in prioritizingthe SLA criteria OF 35 should be applied If on the contrarythe goal is to prioritize energy savingOF (14a) should be usedinstead

4 Results

In this section we present the theoretical results obtainedfrom solving the scheduling problems aimed at achievingbest task assignment Two representative experiments wereperformed in order to test the performance of GS

The experiments were performed by using the AMPL(AMPL A Mathematical Programming Language httpamplcom) language and the SCIP (SCIP Solving ConstraintInteger Programs httpscipzibde) solver AMPL is analgebraic modeling language for describing and solving high-complexity problems for large-scale mathematical computa-tion supported by many solvers Integer and nonlinear (ourmodel type) problems can be solved by SCIP one of thesolvers supported by AMPL

Throughout all the experimentation the Erlang argu-ments were obtained empirically by using the strategyexplained in Section 34

As the objective of this section is to prove the correctnessof the policy only a small set of tasks VMs and nodes waschosen The size of the experimental framework was chosento be as much representative of actual cases as possible butat the same time simple enough to be used as an illustrativeexample So the experimental framework chosen was madeup of 2 different nodes one of them comprised 3VMs and theother 1 VM see Figure 2The objective of this simulation wasto achieve the best assignment for 3 tasks Table 1 shows theprocessing cost 119875119894

119899V119899

relating the execution times of the tasks ineach VM To show the good behavior of themodel presentedeach task has the same processing cost independently of theVM The model presented can be efficiently applied to realcloud environments The only weak point is that the modelis static That means that homogenous and static workloadconditions must be stable in our model Job executions indifferent workload sizes can be saved in a database system

Node 2Node 1

VM2VM3 VM1

VM3

Cloud

Figure 2 Cloud architecture

Table 1 Task processing costs

Task 119905119894 Processing costs 119875119894119899V119899

Value1199051

1198751

11 1198751

12 1198751

13 1198751

211

1199052

1198752

1 1198752

12 1198752

13 1198752

215

1199053

1198753

11 1198753

12 1198753

13 1198753

211

Total processing cost (sum119894119875119894

119899V119899

) 7

providing a means for determining the SLA of such a job infuture executions

41 Without Communications In this section a hypotheticalsituation without communication between tasks is evaluatedIn this situation our scheduling policy tends to assign thetasks to the most powerful set of virtual machines (ie withthe higher relative computing power Δ

119899V119899

considering theirindividual saturation in this choice)This saturation becomescritical when more and more tasks are added Here the mostimportant term is the Erlang function since it models thebehaviour of every virtual machine Thus taking this intoaccount our scheduler knows the exact weight of tasks it canassign to the VMs in order to obtain the best return timesThis phenomenon is observed in the following examples

411 Without Communications and High Optimal ErlangTable 2 shows the parameters used in the first example Theamount ofMemory allocated to each task 119905119894 in every VM119872

119899V119899

(as we supposed this amount to be equal in all the VMs wesimply call it119872119894)The relative computing power (Δ

119899VV) of eachVMand finally the120572 and 120582 Erlang arguments Note that all theVMs have the same Erlang parameters The parameters werechosen this way because any VM saturates with the overallworkload assigned In other words the total processing cost 7is lower than the optimal Erlang workload 16

Table 3 shows the solver assignment results The bestscheduling assigns all the tasks to the same VM (VM

21 the

only VM in node 2) because this VM has the biggest relative

The Scientific World Journal 7

Table 2 Without communications High optimal Erlang VM con-figurations

Node VM119899V119899

119872119894

Δ119899VV Erlang

1 VM11 10 075 120572 = 3 120582 = 8

1 VM12 10 035 120572 = 3 120582 = 8

1 VM13 10 01 120572 = 3 120582 = 8

2 VM21 10 085 120572 = 3 120582 = 8

Table 3 Without communications High optimal Erlang Solverassignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

computing power (Δ119899VV) This result is very coherent Due to

the lack of communications the model tends to assign tasksto the most powerful VMwhile its workload does not exceedthe Erlang optimum (a workload of 10 tasks) As in our casethe total workload is 7 and VM

21could host evenmore tasks

412 Without Communications Low Optimal Erlang andPreserving SLA In this example (see Table 4) the VMs haveanother Erlang However the task processing costs do notchange so they remain the same as in Table 1 In this caseeach VM becomes saturated when the assignment workloadweight is higher than 5 (because 5 is the optimal workload)

The best assignment in this case is the one formed bythe minimum set of VMs with the best relative computingpower Δ

119899VV (see Table 5 column Task Assignment SLA) Theassignment of the overall tasks to only one VM (although itwas the most powerful one) as before will decrease the returntime excessively due to its saturation

413 Without Communications Low Optimal Erlang andPreserving Energy Saving Provided that the most importantcriterion is the energy saving the assignment will be some-what different (seeTable 5 columnTaskAssignment Energy)In this case OF (14a) with Ξ = 1was usedThen as expectedall the tasks were again assigned to VM

21of Node

2

42 With Communications Starting from the same VMconfiguration shown on Table 4 in this section we presenta more real situation where the costs of communicationsbetween tasks are also taken into account It is important tohighlight that in some situations the best choice does notinclude the most powerful VMs (ie with the highest relativecomputing powerΔ

119899V119899

)Thus the results shown in this sectionmust show the tradeoff between relative computing powerof VM workload scheduling impact modeled by the Erlangdistribution and communication efficiency between tasks

421 High Communication Slowdown This example showsthe behaviour of the model under large communication costs

Table 4Without communications Low optimal Erlang PreservingSLA VM configurations

Node VM119899V119899

119872119894

Δ119899VV Erlang

1 VM11 10 075 120572 = 5 120582 = 1

1 VM12 10 035 120572 = 5 120582 = 1

1 VM13 10 01 120572 = 5 120582 = 1

2 VM21 10 085 120572 = 5 120582 = 1

Table 5Without communications Low optimal Erlang PreservingSLA Solver assignment

Node VM119899V119899

SLA EnergyTask assignment Task assignment

1 VM11 1199051 1199053 119905

2

1 VM12 0 1199051 1199053

1 VM13 0 02 VM21 119905

2 0

Table 6 High slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

02119862119904119899V119899

01

between VMs (see Table 6) This table shows the commu-nication costs between tasks (119862119894119895) and the communicationslowdown when communications are done between VMsin the same node (Cs

119899V119899

) and the penalty cost when com-munications are performed between different nodes (Cs

119899V119899

)Note that the penalties are very high (02 and 01) when thecommunications are very influential

The solver assignment is shown in Table 7 In orderto avoid communication costs due to slowdowns the bestassignment tends to group tasks first in the same VM andsecond in the same node Although VM

21should become

saturated with this assignment the high communication costcompensates the loss of SLA performance allowing us toswitch off node 1

422 Low Communication Slowdown Now this exampleshows the behaviour of our policy under more normal com-munication conditions Here the communication penaltiesbetween the different VMs or nodes are not as significantas in the previous case because Cs

119899V119899

and Cs119899V119899

are higherTable 8 shows the communication costs between tasks andthe penalty cost if communications are performed betweenVMs in the same node (Cs

119899V119899

) or between different nodes(Cs119899V119899

)In this case the solver got as a result two hosting VMs

(see Table 9) formed by the VM11(with the assigned tasks 1199052

and 1199053) and VM

21with task 119905

1 In this case due to the low

8 The Scientific World Journal

Table 7 High slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

Table 8 Low slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

08

Table 9 Low slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 119905

1 1199053

1 VM12 01 VM13 02 VM21 119905

2

differences between the different communication slowdownstask assignment was distributed between the two nodes

423 Moderate Communication Slowdown We simulated amore normal situation where the communication slowdownbetween nodes is higher than the other ones From the sameexample it was only reduced Cs

119899V119899

to 04 (see Table 10)As expected the resulting solver assignment was differentfrom that in the previous case Theoretically this assignmentshould assign tasks to the powerful unsaturated VMs but asmuch as possible to the VMs residing on the same node Thesolver result was exactly what was expected Although themost powerful VM is in node 2 the tasks were assigned tothe VMs of node 1 because they all fit in the same nodeThatis the reason why a less powerful node like node 1 but onewith more capacity is able to allocate more tasks than node 2due to the communication slowdown between nodes Theseresults are shown in Table 11

5 Conclusions and Future Work

This paper presents a cloud-based system scheduling mech-anism called GS that is able to comply with low powerconsumption and SLA agreements The complexity of themodel developed was increased thus adding more factorsto be taken into account The model was also tested usingthe AMPL modelling language and the SCIP optimizer Theresults obtained proved consistent over a range of scenariosIn all the cases the experiments showed that all the tasks wereassigned to the most powerful subset of virtual machines bykeeping the subset size to the minimum

Table 10 Moderate slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

04

Table 11 Moderate slowdown Solver assignment

Node VM119899V119899

Tasks assignment1 VM11 119905

2 1199053

1 VM12 1199051

1 VM13 02 VM21 0

Although our proposals still have to be tested in real sce-narios these preliminary results corroborate their usefulness

Our efforts are directed towards implementing thosestrategies in a real cloud environment like the OpenStack[22] or OpenNebula [23] frameworks

In the longer term we consider using some statisticalmethod to find an accurate approximation of the workloadusing well-suited Erlang distribution functions

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 MEYC under ContractsTIN2011-28689-C02-02 The authors are members of theresearch groups 2009-SGR145 and 2014-SGR163 funded bythe Generalitat de Catalunya

References

[1] RAversa BDiMartinoMRak S Venticinque andUVillanoPerformance Prediction for HPC on Clouds Cloud ComputingPrinciples and Paradigms John Wiley amp Sons New York NYUSA 2011

[2] A Iosup N Yigitbasi and D Epema ldquoOn the performancevariability of production cloud servicesrdquo in Proceedings of the11th IEEEACM International Symposium on Cluster Cloud andGrid Computing (CCGrid rsquo11) pp 104ndash113 May 2011

[3] J Varia Architection for the Cloud Best Practices Amazon WebServices 2014

[4] Intel cloud computing 2015 vision httpwwwintelcomcon-tentwwwusencloud-computing

[5] M Martinello M Kaaniche and K Kanoun ldquoWeb serviceavailabilitymdashimpact of error recovery and traffic modelrdquo Relia-bility Engineering amp System Safety vol 89 no 1 pp 6ndash16 2005

[6] J Vilaplana F Solsona F Abella R Filgueira and J Rius ldquoThecloud paradigm applied to e-Healthrdquo BMCMedical Informaticsand Decision Making vol 13 no 1 article 35 2013

The Scientific World Journal 9

[7] J Vilaplana F Solsona I Teixido JMateo F Abella and J RiusldquoA queuing theory model for cloud computingrdquo The Journal ofSupercomputing vol 69 no 1 pp 492ndash507 2014

[8] A Beloglazov and R Buyya ldquoOptimal online deterministicalgorithms and adaptive heuristics for energy and performanceefficient dynamic consolidation of virtual machines in Clouddata centersrdquo Concurrency Computation Practice and Experi-ence vol 24 no 13 pp 1397ndash1420 2012

[9] D Kliazovich P Bouvry and S U Khan ldquoGreenCloud apacket-level simulator of energy-aware cloud computing datacentersrdquoThe Journal of Supercomputing vol 62 no 3 pp 1263ndash1283 2012

[10] C Ghribi M Hadji and D Zeghlache ldquoEnergy efficientVM scheduling for cloud data centers exact allocation andmigration algorithmsrdquo in Proceedings of the 13th IEEEACMInternational SymposiumonCluster Cloud andGridComputing(CCGrid rsquo13) pp 671ndash678 May 2013

[11] M F Khan Z Anwar and Q S Ahmad ldquoAssignment of per-sonnels when job completion time follows gamma distributionusing stochastic programming techniquerdquo International Journalof Scientific amp Engineering Research vol 3 no 3 2012

[12] J L Lerida F Solsona P Hernandez F Gine M Hanzichand J Conde ldquoState-based predictions with self-correction onEnterprise Desktop Grid environmentsrdquo Journal of Parallel andDistributed Computing vol 73 no 6 pp 777ndash789 2013

[13] A Goldman and Y Ngoko ldquoA MILP approach to scheduleparallel independent tasksrdquo in Proceedings of the InternationalSymposium on Parallel and Distributed Computing (ISPDC rsquo08)pp 115ndash122 Krakow Poland July 2008

[14] T Vinh T Duy Y Sato and Y Inoguchi ldquoPerformanceevaluation of a green scheduling algorithm for energy savingsin cloud computingrdquo in Proceedings of the IEEE InternationalSymposium on Parallel amp Distributed Processing Workshops andPhd Forum (IPDPSW rsquo10) pp 1ndash8 Atlanta Ga USA April 2010

[15] M Mezmaz N Melab Y Kessaci et al ldquoA parallel bi-objectivehybrid metaheuristic for energy-aware scheduling for cloudcomputing systemsrdquo Journal of Parallel and Distributed Com-puting vol 71 no 11 pp 1497ndash1508 2011

[16] Y C Ouyang Y J Chiang C H Hsu and G Yi ldquoAnoptimal control policy to realize green cloud systems with SLA-awarenessrdquo The Journal of Supercomputing vol 69 no 3 pp1284ndash1310 2014

[17] T C Ferreto M A S Netto R N Calheiros and C AF de Rose ldquoServer consolidation with migration control forvirtualized data centersrdquo Future Generation Computer Systemsvol 27 no 8 pp 1027ndash1034 2011

[18] A Murtazaev and S Oh ldquoSercon server consolidation algo-rithm using live migration of virtual machines for greencomputingrdquo IETE Technical Review (Institution of Electronicsand Telecommunication Engineers India) vol 28 no 3 pp 212ndash231 2011

[19] A F Monteiro M V Azevedo and A Sztajnberg ldquoVirtualizedWeb server cluster self-configuration to optimize resource andpower userdquo Journal of Systems and Software vol 86 no 11 pp2779ndash2796 2013

[20] C-C Lin H-H Chin and D-J Deng ldquoDynamic multiserviceload balancing in cloud-based multimedia systemrdquo IEEE Sys-tems Journal vol 8 no 1 pp 225ndash234 2014

[21] J Vilaplana F Solsona J Mateo and I Teixido ldquoSLA-awareload balancing in a web-based cloud system over OpenStackrdquoin Service-Oriented ComputingmdashICSOC 2013 Workshops vol

8377 of Lecture Notes in Computer Science pp 281ndash293 SpringerInternational Publishing 2014

[22] OpenStack httpwwwopenstackorg[23] OpenNebula httpwwwopennebulaorg

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

4 The Scientific World Journal

0010203040506070809

1

0 5 10 15 20

120572 = 76 120582 = 15

Figure 1 Erlang plots for different 120572 and 120582 values

Accordingly the optimal workload of the Erlang examplein Figure 1 with 120572 = 76 and 120582 = 15 is

119864 (119909 76 15)1015840= 119890minus14lowast119909

lowast 119909 (14119909 minus 75) = 0

119909 =75

14

(5)

Finally in our case provided that the VM workloaddefined as the sum of the processing costs (119875119894

119899V119899

) of the tasksassigned to a particular VM must be an N number theoptimal workload (119909) is

119909 = round(7514

) = 5 (6)

Provided that Boolean variable 119905119894

119899V119899

= 1 is a booleanvariable informing of the assignment of 119905119894 to VM

119899V119899

and119905119894

119899V119899

= 0 if not the Erlang-weighted Δ119899V119899

would be

Δ119899V119899

119864(

119879

sum

119894=1

119875119894

119899V119899

119905119895

V 120572 120582) (7)

35 Task Communication and VM Selection In this sectionthe VM selection is also considered In doing so eachVM can be selected from a range of 119873 nodes forming afederated cloud We want to obtain an OF that considersthe scheduling of heterogeneous and communicating tasksto 119873 heterogeneous nodes made up of different numbers ofheterogeneous VMs

The communication cost (in time) between tasks 119905119894 and119905119895 when in the same VM is denoted by 119862

119894119895 and shouldbe passed to the solver as an argument For reasons ofsimplicity all communication links are considered to havethe same bandwidth and latency Notation119862119894119895

119899V119899

represents thecommunication cost between task 119905

119894 residing in VM119899V119899

withanother task 119905

119895 (located in the same VM or elsewhere) Pro-vided equivalent bandwidth between any two VMs 119862119894119895

119899V119899

=

119862119895119894

119899V1015840119899

forallV V1015840 le 119881 In other words the communication cost doesnot depend on the VM or the links used between the VMs

VM communication links are considered with the samebandwidth capacity Depending on its location we multiplythe communication cost between tasks 119905119894 and 119905

119895 by a givencommunication slowdown If 119905

119894and 119905119895are located in the same

VM the communication slowdown (denoted by Cs119899V119899

) is 1If 119905119895 is assigned to another VM in the same node than 119905

119894

(119905119895119899V119899

= 1 the Communication slowdown (Cs119899V119899

) will bein the range [0 1] Finally if 119905119895 is assigned to anotherVM located in another node (119905119895

119899V119899

= 1) the correspondingcommunication slowdown term (Cs

119899V119899

) will also be in therange [0 1] Cs

119899V119899

and Cs119899V119899

should be obtained withrespect to Cs

119899V119899

In other words Cs119899V119899

and Cs119899V119899

are therespective reduction (in percentage) in task communicationbetween VMs located in the same and different nodescompared with task communication inside the same VM Tosum up Cs

119899V119899

= 1 ge Cs119899V119899

ge Cs119899V119899

ge 0According to task communication the idea is to add a

component in the OF that penalizes (enhances) the com-munications performed between different VMs and differentnodes Grouping tasks inside the same VM will dependon not only their respective processing cost (119875119894

119899V119899

) but alsothe communication costs 119862119894119895

119899V119899

and communication slowdownsCs119899V119899

Cs119899V119899

and Cs119899V119899

We reward the communications donein the same VM but less so the ones done in differentVMs while still in the same node Finally communicationsbetween nodes are left untouched without rewarding orpenalizing

In the same way if we modelled the OF in function of thetak heterogeneity in (2) the communication component willbe as follows (only the communication component of the OFis shown)

max(119873

sum

119899=1

119881119899

sum

V119899=1

119879

sum

119894=1

(119905119894

119899V119899

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

(8)

And the OF function will be

max(119873

sum

119899=1

119881119899

sum

V119899=1

((

119879

sum

119894=1

119905119894

119899V119899

(119875119894

119899V119899

+

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

times Δ119899V119899

119864(

119879

sum

119895=1

119905119895

119899V119899

119875119895

119899V119899

120572 120582)))

(9)

36 Choosing SLA or Energy Saving It is important tohighlight that the optimization goal is two criteria (SLAand energy in our case) Thus the user could prioritize

The Scientific World Journal 5

the criteria Assignments are performed starting from themost powerful VM When this becomes saturated taskassignment continues with the next most powerful VMregardless of the node it resides in When this VM residesin another node (as in our case) the energy-saving criteriawill be harmed It would be interesting to provide a means ofincreasing criteria preferences in the model presented

In order to highlight specific criteria (ie energy saving)one more additional component must be added to the OFThis component must enhance the assignment of tasks to thesame node by assigning tasks to the most powerful nodesand not only to the most powerful VMs as before This is thenatural procedure to follow because the OF is a maximumThus the likelihood of less powerful nodes becoming idleincreases and this gives the opportunity to power them offhence saving energy

The additional component can be defined in a similar wayas for the relative VM computing power (Δ

119899V119899

) of a VM119899V119899

Instead we obtain the relative node computing power of aNode119899(Θ119899) as the normalized summatory of their forming

VMs Θ119899will inform about the computing power of Node

119899

For119873 nodes Θ119899is formally defined as

Θ119899=

sum119881119899

V119899=1Δ119899V119899

sum119873

119899=1sum119881119899

V119899=1Δ119899V119899

(10)

wheresum119873119899=1

Θ119899= 1 To obtainΘ

119899 the parallel Linpack version

(HPL high performance Linpack) can be used It is the oneused to benchmark and rank supercomputers for the TOP500list

Depending on the importance of the energy savingcriteria a weighting factor should be provided to Θ

119899 We

simply call this factor energy Energy Ξ The Ξ will be in therange (0 1] For an Ξ0 our main criteria will be energysaving and forΞ = 1 our goal is only SLAThus the resultingenergy component will beΘ

119899Ξ Thus for a given Node

119899with

Θ119899 we must weigh the energy saving criteria of such a node

by the following factor

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ (11)

The resulting OF function will be

max(119873

sum

119899=1

(

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ)

times

119881119899

sum

V119899=1

((

119879

sum

119894=1

119905119894

119899V119899

(119875119894

119899V119899

+

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

times Δ119899V119899

119864(

119879

sum

119895=1

119905119895

119899V119899

119875119895

119899V119899

120572 120582)))

(12)

37 Enforcing SLA For either prioritized criteria SLA orenergy saving there is a last consideration to be taken intoaccount

Imagine the case where tasks do not communicate Oncethey are assigned to a node one would expect them to beexecuted in the minimum time In this case there is alreadyno need to group tasks in the VM in decreasing order ofpower in the same node because this node is no longereligible to be switched off A better solution in this case wouldbe to balance the tasks between the VMs of such a nodein order to increase SLA performance Note that this notapply in the communicating tasks due to the communicationslowdown between VMs

To implement this we only need to assign every noncom-municating tasks without taking the relative computing power(Δ119899V119899

) of each VM into accountWe only need to replace Δ

119899V119899

in (12) by Δ defined as

Δ = if (

119879

sum

119895lt119894

119862119894119895

119899V119899

ge 0)Δ119899V119899

else 1

(13)

For the case of noncommunicating tasks by assigning aΔ = 1 all the VMs have the same relative computing powerΔ119899V119899

Thus tasks are assigned in a balanced way

38 Model Formulation Finally the OF function and theirconstraints are presented The best task scheduling assign-ment to VMs which takes all the features into account(GS policy) is formally defined by the following nonlinearprogramming model

max(119873

sum

119899=1

(

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ)

times

119881119899

sum

V119899=1

((

119879

sum

119894=1

119905119894

119899V119899

(119875119894

119899V119899

+

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

times Δ119864(

119879

sum

119895=1

119905119895

119899V119899

119875119895

119899V119899

120572 120582)))

(14a)

st119879

sum

119894=1

119872119899V119899

119894le 119872119899V

119899forall119899 le 119873 V

119899le 119881119899

(14b)

119873

sum

119899=1

119881

sum

V119899=1

119905119894

119899V119899

= 1 forall119894 le 119879 (14c)

6 The Scientific World Journal

Equation (14a) is the objective function (OF) to be max-imized Note that OF is an integer and nonlinear problemInequality in (14b) and equality in (14c) are the constraints ofthe objective function variables Given the constants 119879 (thetotal number of requests or tasks) and 119872V for each VM

119899V119899

the solution that maximizes OF will obtain the values of thevariables 119905119894

119899V119899

representing the number of tasks assigned toVM119899V119899

Thus the 119905119899V119899119894obtained will be the assignment found

by this modelOF takes into account the processing costs (119875119894

119899V119899

) and thecommunication times (119862119894119895

119899V119899

) of the tasks assigned to eachVM119899V119899

and the communication slowdownsbetweenVMsCs119899V119899

and nodes Cs119899V119899

Cs119899V119899

= 1 Δ is defined in Section 37 And119864(sum119879

119895=1119905119895

119899V119899

119875119895

119899V119899

120572 120582) represents the power slowdown of eachVM due to its workload (defined in Section 34)

To sum up for the case when the workload is made up ofnoncommunicating tasks if we are interested in prioritizingthe SLA criteria OF 35 should be applied If on the contrarythe goal is to prioritize energy savingOF (14a) should be usedinstead

4 Results

In this section we present the theoretical results obtainedfrom solving the scheduling problems aimed at achievingbest task assignment Two representative experiments wereperformed in order to test the performance of GS

The experiments were performed by using the AMPL(AMPL A Mathematical Programming Language httpamplcom) language and the SCIP (SCIP Solving ConstraintInteger Programs httpscipzibde) solver AMPL is analgebraic modeling language for describing and solving high-complexity problems for large-scale mathematical computa-tion supported by many solvers Integer and nonlinear (ourmodel type) problems can be solved by SCIP one of thesolvers supported by AMPL

Throughout all the experimentation the Erlang argu-ments were obtained empirically by using the strategyexplained in Section 34

As the objective of this section is to prove the correctnessof the policy only a small set of tasks VMs and nodes waschosen The size of the experimental framework was chosento be as much representative of actual cases as possible butat the same time simple enough to be used as an illustrativeexample So the experimental framework chosen was madeup of 2 different nodes one of them comprised 3VMs and theother 1 VM see Figure 2The objective of this simulation wasto achieve the best assignment for 3 tasks Table 1 shows theprocessing cost 119875119894

119899V119899

relating the execution times of the tasks ineach VM To show the good behavior of themodel presentedeach task has the same processing cost independently of theVM The model presented can be efficiently applied to realcloud environments The only weak point is that the modelis static That means that homogenous and static workloadconditions must be stable in our model Job executions indifferent workload sizes can be saved in a database system

Node 2Node 1

VM2VM3 VM1

VM3

Cloud

Figure 2 Cloud architecture

Table 1 Task processing costs

Task 119905119894 Processing costs 119875119894119899V119899

Value1199051

1198751

11 1198751

12 1198751

13 1198751

211

1199052

1198752

1 1198752

12 1198752

13 1198752

215

1199053

1198753

11 1198753

12 1198753

13 1198753

211

Total processing cost (sum119894119875119894

119899V119899

) 7

providing a means for determining the SLA of such a job infuture executions

41 Without Communications In this section a hypotheticalsituation without communication between tasks is evaluatedIn this situation our scheduling policy tends to assign thetasks to the most powerful set of virtual machines (ie withthe higher relative computing power Δ

119899V119899

considering theirindividual saturation in this choice)This saturation becomescritical when more and more tasks are added Here the mostimportant term is the Erlang function since it models thebehaviour of every virtual machine Thus taking this intoaccount our scheduler knows the exact weight of tasks it canassign to the VMs in order to obtain the best return timesThis phenomenon is observed in the following examples

411 Without Communications and High Optimal ErlangTable 2 shows the parameters used in the first example Theamount ofMemory allocated to each task 119905119894 in every VM119872

119899V119899

(as we supposed this amount to be equal in all the VMs wesimply call it119872119894)The relative computing power (Δ

119899VV) of eachVMand finally the120572 and 120582 Erlang arguments Note that all theVMs have the same Erlang parameters The parameters werechosen this way because any VM saturates with the overallworkload assigned In other words the total processing cost 7is lower than the optimal Erlang workload 16

Table 3 shows the solver assignment results The bestscheduling assigns all the tasks to the same VM (VM

21 the

only VM in node 2) because this VM has the biggest relative

The Scientific World Journal 7

Table 2 Without communications High optimal Erlang VM con-figurations

Node VM119899V119899

119872119894

Δ119899VV Erlang

1 VM11 10 075 120572 = 3 120582 = 8

1 VM12 10 035 120572 = 3 120582 = 8

1 VM13 10 01 120572 = 3 120582 = 8

2 VM21 10 085 120572 = 3 120582 = 8

Table 3 Without communications High optimal Erlang Solverassignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

computing power (Δ119899VV) This result is very coherent Due to

the lack of communications the model tends to assign tasksto the most powerful VMwhile its workload does not exceedthe Erlang optimum (a workload of 10 tasks) As in our casethe total workload is 7 and VM

21could host evenmore tasks

412 Without Communications Low Optimal Erlang andPreserving SLA In this example (see Table 4) the VMs haveanother Erlang However the task processing costs do notchange so they remain the same as in Table 1 In this caseeach VM becomes saturated when the assignment workloadweight is higher than 5 (because 5 is the optimal workload)

The best assignment in this case is the one formed bythe minimum set of VMs with the best relative computingpower Δ

119899VV (see Table 5 column Task Assignment SLA) Theassignment of the overall tasks to only one VM (although itwas the most powerful one) as before will decrease the returntime excessively due to its saturation

413 Without Communications Low Optimal Erlang andPreserving Energy Saving Provided that the most importantcriterion is the energy saving the assignment will be some-what different (seeTable 5 columnTaskAssignment Energy)In this case OF (14a) with Ξ = 1was usedThen as expectedall the tasks were again assigned to VM

21of Node

2

42 With Communications Starting from the same VMconfiguration shown on Table 4 in this section we presenta more real situation where the costs of communicationsbetween tasks are also taken into account It is important tohighlight that in some situations the best choice does notinclude the most powerful VMs (ie with the highest relativecomputing powerΔ

119899V119899

)Thus the results shown in this sectionmust show the tradeoff between relative computing powerof VM workload scheduling impact modeled by the Erlangdistribution and communication efficiency between tasks

421 High Communication Slowdown This example showsthe behaviour of the model under large communication costs

Table 4Without communications Low optimal Erlang PreservingSLA VM configurations

Node VM119899V119899

119872119894

Δ119899VV Erlang

1 VM11 10 075 120572 = 5 120582 = 1

1 VM12 10 035 120572 = 5 120582 = 1

1 VM13 10 01 120572 = 5 120582 = 1

2 VM21 10 085 120572 = 5 120582 = 1

Table 5Without communications Low optimal Erlang PreservingSLA Solver assignment

Node VM119899V119899

SLA EnergyTask assignment Task assignment

1 VM11 1199051 1199053 119905

2

1 VM12 0 1199051 1199053

1 VM13 0 02 VM21 119905

2 0

Table 6 High slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

02119862119904119899V119899

01

between VMs (see Table 6) This table shows the commu-nication costs between tasks (119862119894119895) and the communicationslowdown when communications are done between VMsin the same node (Cs

119899V119899

) and the penalty cost when com-munications are performed between different nodes (Cs

119899V119899

)Note that the penalties are very high (02 and 01) when thecommunications are very influential

The solver assignment is shown in Table 7 In orderto avoid communication costs due to slowdowns the bestassignment tends to group tasks first in the same VM andsecond in the same node Although VM

21should become

saturated with this assignment the high communication costcompensates the loss of SLA performance allowing us toswitch off node 1

422 Low Communication Slowdown Now this exampleshows the behaviour of our policy under more normal com-munication conditions Here the communication penaltiesbetween the different VMs or nodes are not as significantas in the previous case because Cs

119899V119899

and Cs119899V119899

are higherTable 8 shows the communication costs between tasks andthe penalty cost if communications are performed betweenVMs in the same node (Cs

119899V119899

) or between different nodes(Cs119899V119899

)In this case the solver got as a result two hosting VMs

(see Table 9) formed by the VM11(with the assigned tasks 1199052

and 1199053) and VM

21with task 119905

1 In this case due to the low

8 The Scientific World Journal

Table 7 High slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

Table 8 Low slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

08

Table 9 Low slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 119905

1 1199053

1 VM12 01 VM13 02 VM21 119905

2

differences between the different communication slowdownstask assignment was distributed between the two nodes

423 Moderate Communication Slowdown We simulated amore normal situation where the communication slowdownbetween nodes is higher than the other ones From the sameexample it was only reduced Cs

119899V119899

to 04 (see Table 10)As expected the resulting solver assignment was differentfrom that in the previous case Theoretically this assignmentshould assign tasks to the powerful unsaturated VMs but asmuch as possible to the VMs residing on the same node Thesolver result was exactly what was expected Although themost powerful VM is in node 2 the tasks were assigned tothe VMs of node 1 because they all fit in the same nodeThatis the reason why a less powerful node like node 1 but onewith more capacity is able to allocate more tasks than node 2due to the communication slowdown between nodes Theseresults are shown in Table 11

5 Conclusions and Future Work

This paper presents a cloud-based system scheduling mech-anism called GS that is able to comply with low powerconsumption and SLA agreements The complexity of themodel developed was increased thus adding more factorsto be taken into account The model was also tested usingthe AMPL modelling language and the SCIP optimizer Theresults obtained proved consistent over a range of scenariosIn all the cases the experiments showed that all the tasks wereassigned to the most powerful subset of virtual machines bykeeping the subset size to the minimum

Table 10 Moderate slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

04

Table 11 Moderate slowdown Solver assignment

Node VM119899V119899

Tasks assignment1 VM11 119905

2 1199053

1 VM12 1199051

1 VM13 02 VM21 0

Although our proposals still have to be tested in real sce-narios these preliminary results corroborate their usefulness

Our efforts are directed towards implementing thosestrategies in a real cloud environment like the OpenStack[22] or OpenNebula [23] frameworks

In the longer term we consider using some statisticalmethod to find an accurate approximation of the workloadusing well-suited Erlang distribution functions

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 MEYC under ContractsTIN2011-28689-C02-02 The authors are members of theresearch groups 2009-SGR145 and 2014-SGR163 funded bythe Generalitat de Catalunya

References

[1] RAversa BDiMartinoMRak S Venticinque andUVillanoPerformance Prediction for HPC on Clouds Cloud ComputingPrinciples and Paradigms John Wiley amp Sons New York NYUSA 2011

[2] A Iosup N Yigitbasi and D Epema ldquoOn the performancevariability of production cloud servicesrdquo in Proceedings of the11th IEEEACM International Symposium on Cluster Cloud andGrid Computing (CCGrid rsquo11) pp 104ndash113 May 2011

[3] J Varia Architection for the Cloud Best Practices Amazon WebServices 2014

[4] Intel cloud computing 2015 vision httpwwwintelcomcon-tentwwwusencloud-computing

[5] M Martinello M Kaaniche and K Kanoun ldquoWeb serviceavailabilitymdashimpact of error recovery and traffic modelrdquo Relia-bility Engineering amp System Safety vol 89 no 1 pp 6ndash16 2005

[6] J Vilaplana F Solsona F Abella R Filgueira and J Rius ldquoThecloud paradigm applied to e-Healthrdquo BMCMedical Informaticsand Decision Making vol 13 no 1 article 35 2013

The Scientific World Journal 9

[7] J Vilaplana F Solsona I Teixido JMateo F Abella and J RiusldquoA queuing theory model for cloud computingrdquo The Journal ofSupercomputing vol 69 no 1 pp 492ndash507 2014

[8] A Beloglazov and R Buyya ldquoOptimal online deterministicalgorithms and adaptive heuristics for energy and performanceefficient dynamic consolidation of virtual machines in Clouddata centersrdquo Concurrency Computation Practice and Experi-ence vol 24 no 13 pp 1397ndash1420 2012

[9] D Kliazovich P Bouvry and S U Khan ldquoGreenCloud apacket-level simulator of energy-aware cloud computing datacentersrdquoThe Journal of Supercomputing vol 62 no 3 pp 1263ndash1283 2012

[10] C Ghribi M Hadji and D Zeghlache ldquoEnergy efficientVM scheduling for cloud data centers exact allocation andmigration algorithmsrdquo in Proceedings of the 13th IEEEACMInternational SymposiumonCluster Cloud andGridComputing(CCGrid rsquo13) pp 671ndash678 May 2013

[11] M F Khan Z Anwar and Q S Ahmad ldquoAssignment of per-sonnels when job completion time follows gamma distributionusing stochastic programming techniquerdquo International Journalof Scientific amp Engineering Research vol 3 no 3 2012

[12] J L Lerida F Solsona P Hernandez F Gine M Hanzichand J Conde ldquoState-based predictions with self-correction onEnterprise Desktop Grid environmentsrdquo Journal of Parallel andDistributed Computing vol 73 no 6 pp 777ndash789 2013

[13] A Goldman and Y Ngoko ldquoA MILP approach to scheduleparallel independent tasksrdquo in Proceedings of the InternationalSymposium on Parallel and Distributed Computing (ISPDC rsquo08)pp 115ndash122 Krakow Poland July 2008

[14] T Vinh T Duy Y Sato and Y Inoguchi ldquoPerformanceevaluation of a green scheduling algorithm for energy savingsin cloud computingrdquo in Proceedings of the IEEE InternationalSymposium on Parallel amp Distributed Processing Workshops andPhd Forum (IPDPSW rsquo10) pp 1ndash8 Atlanta Ga USA April 2010

[15] M Mezmaz N Melab Y Kessaci et al ldquoA parallel bi-objectivehybrid metaheuristic for energy-aware scheduling for cloudcomputing systemsrdquo Journal of Parallel and Distributed Com-puting vol 71 no 11 pp 1497ndash1508 2011

[16] Y C Ouyang Y J Chiang C H Hsu and G Yi ldquoAnoptimal control policy to realize green cloud systems with SLA-awarenessrdquo The Journal of Supercomputing vol 69 no 3 pp1284ndash1310 2014

[17] T C Ferreto M A S Netto R N Calheiros and C AF de Rose ldquoServer consolidation with migration control forvirtualized data centersrdquo Future Generation Computer Systemsvol 27 no 8 pp 1027ndash1034 2011

[18] A Murtazaev and S Oh ldquoSercon server consolidation algo-rithm using live migration of virtual machines for greencomputingrdquo IETE Technical Review (Institution of Electronicsand Telecommunication Engineers India) vol 28 no 3 pp 212ndash231 2011

[19] A F Monteiro M V Azevedo and A Sztajnberg ldquoVirtualizedWeb server cluster self-configuration to optimize resource andpower userdquo Journal of Systems and Software vol 86 no 11 pp2779ndash2796 2013

[20] C-C Lin H-H Chin and D-J Deng ldquoDynamic multiserviceload balancing in cloud-based multimedia systemrdquo IEEE Sys-tems Journal vol 8 no 1 pp 225ndash234 2014

[21] J Vilaplana F Solsona J Mateo and I Teixido ldquoSLA-awareload balancing in a web-based cloud system over OpenStackrdquoin Service-Oriented ComputingmdashICSOC 2013 Workshops vol

8377 of Lecture Notes in Computer Science pp 281ndash293 SpringerInternational Publishing 2014

[22] OpenStack httpwwwopenstackorg[23] OpenNebula httpwwwopennebulaorg

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

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RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World Journal 5

the criteria Assignments are performed starting from themost powerful VM When this becomes saturated taskassignment continues with the next most powerful VMregardless of the node it resides in When this VM residesin another node (as in our case) the energy-saving criteriawill be harmed It would be interesting to provide a means ofincreasing criteria preferences in the model presented

In order to highlight specific criteria (ie energy saving)one more additional component must be added to the OFThis component must enhance the assignment of tasks to thesame node by assigning tasks to the most powerful nodesand not only to the most powerful VMs as before This is thenatural procedure to follow because the OF is a maximumThus the likelihood of less powerful nodes becoming idleincreases and this gives the opportunity to power them offhence saving energy

The additional component can be defined in a similar wayas for the relative VM computing power (Δ

119899V119899

) of a VM119899V119899

Instead we obtain the relative node computing power of aNode119899(Θ119899) as the normalized summatory of their forming

VMs Θ119899will inform about the computing power of Node

119899

For119873 nodes Θ119899is formally defined as

Θ119899=

sum119881119899

V119899=1Δ119899V119899

sum119873

119899=1sum119881119899

V119899=1Δ119899V119899

(10)

wheresum119873119899=1

Θ119899= 1 To obtainΘ

119899 the parallel Linpack version

(HPL high performance Linpack) can be used It is the oneused to benchmark and rank supercomputers for the TOP500list

Depending on the importance of the energy savingcriteria a weighting factor should be provided to Θ

119899 We

simply call this factor energy Energy Ξ The Ξ will be in therange (0 1] For an Ξ0 our main criteria will be energysaving and forΞ = 1 our goal is only SLAThus the resultingenergy component will beΘ

119899Ξ Thus for a given Node

119899with

Θ119899 we must weigh the energy saving criteria of such a node

by the following factor

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ (11)

The resulting OF function will be

max(119873

sum

119899=1

(

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ)

times

119881119899

sum

V119899=1

((

119879

sum

119894=1

119905119894

119899V119899

(119875119894

119899V119899

+

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

times Δ119899V119899

119864(

119879

sum

119895=1

119905119895

119899V119899

119875119895

119899V119899

120572 120582)))

(12)

37 Enforcing SLA For either prioritized criteria SLA orenergy saving there is a last consideration to be taken intoaccount

Imagine the case where tasks do not communicate Oncethey are assigned to a node one would expect them to beexecuted in the minimum time In this case there is alreadyno need to group tasks in the VM in decreasing order ofpower in the same node because this node is no longereligible to be switched off A better solution in this case wouldbe to balance the tasks between the VMs of such a nodein order to increase SLA performance Note that this notapply in the communicating tasks due to the communicationslowdown between VMs

To implement this we only need to assign every noncom-municating tasks without taking the relative computing power(Δ119899V119899

) of each VM into accountWe only need to replace Δ

119899V119899

in (12) by Δ defined as

Δ = if (

119879

sum

119895lt119894

119862119894119895

119899V119899

ge 0)Δ119899V119899

else 1

(13)

For the case of noncommunicating tasks by assigning aΔ = 1 all the VMs have the same relative computing powerΔ119899V119899

Thus tasks are assigned in a balanced way

38 Model Formulation Finally the OF function and theirconstraints are presented The best task scheduling assign-ment to VMs which takes all the features into account(GS policy) is formally defined by the following nonlinearprogramming model

max(119873

sum

119899=1

(

119881119899

sum

V119899=1

119879

sum

119894=1

119905119894

119899V119899

Θ119899Ξ)

times

119881119899

sum

V119899=1

((

119879

sum

119894=1

119905119894

119899V119899

(119875119894

119899V119899

+

119879

sum

119895lt119894

119862119894119895

119899V119899

(119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

+ 119905119895

119899V119899

Cs119899V119899

)))

times Δ119864(

119879

sum

119895=1

119905119895

119899V119899

119875119895

119899V119899

120572 120582)))

(14a)

st119879

sum

119894=1

119872119899V119899

119894le 119872119899V

119899forall119899 le 119873 V

119899le 119881119899

(14b)

119873

sum

119899=1

119881

sum

V119899=1

119905119894

119899V119899

= 1 forall119894 le 119879 (14c)

6 The Scientific World Journal

Equation (14a) is the objective function (OF) to be max-imized Note that OF is an integer and nonlinear problemInequality in (14b) and equality in (14c) are the constraints ofthe objective function variables Given the constants 119879 (thetotal number of requests or tasks) and 119872V for each VM

119899V119899

the solution that maximizes OF will obtain the values of thevariables 119905119894

119899V119899

representing the number of tasks assigned toVM119899V119899

Thus the 119905119899V119899119894obtained will be the assignment found

by this modelOF takes into account the processing costs (119875119894

119899V119899

) and thecommunication times (119862119894119895

119899V119899

) of the tasks assigned to eachVM119899V119899

and the communication slowdownsbetweenVMsCs119899V119899

and nodes Cs119899V119899

Cs119899V119899

= 1 Δ is defined in Section 37 And119864(sum119879

119895=1119905119895

119899V119899

119875119895

119899V119899

120572 120582) represents the power slowdown of eachVM due to its workload (defined in Section 34)

To sum up for the case when the workload is made up ofnoncommunicating tasks if we are interested in prioritizingthe SLA criteria OF 35 should be applied If on the contrarythe goal is to prioritize energy savingOF (14a) should be usedinstead

4 Results

In this section we present the theoretical results obtainedfrom solving the scheduling problems aimed at achievingbest task assignment Two representative experiments wereperformed in order to test the performance of GS

The experiments were performed by using the AMPL(AMPL A Mathematical Programming Language httpamplcom) language and the SCIP (SCIP Solving ConstraintInteger Programs httpscipzibde) solver AMPL is analgebraic modeling language for describing and solving high-complexity problems for large-scale mathematical computa-tion supported by many solvers Integer and nonlinear (ourmodel type) problems can be solved by SCIP one of thesolvers supported by AMPL

Throughout all the experimentation the Erlang argu-ments were obtained empirically by using the strategyexplained in Section 34

As the objective of this section is to prove the correctnessof the policy only a small set of tasks VMs and nodes waschosen The size of the experimental framework was chosento be as much representative of actual cases as possible butat the same time simple enough to be used as an illustrativeexample So the experimental framework chosen was madeup of 2 different nodes one of them comprised 3VMs and theother 1 VM see Figure 2The objective of this simulation wasto achieve the best assignment for 3 tasks Table 1 shows theprocessing cost 119875119894

119899V119899

relating the execution times of the tasks ineach VM To show the good behavior of themodel presentedeach task has the same processing cost independently of theVM The model presented can be efficiently applied to realcloud environments The only weak point is that the modelis static That means that homogenous and static workloadconditions must be stable in our model Job executions indifferent workload sizes can be saved in a database system

Node 2Node 1

VM2VM3 VM1

VM3

Cloud

Figure 2 Cloud architecture

Table 1 Task processing costs

Task 119905119894 Processing costs 119875119894119899V119899

Value1199051

1198751

11 1198751

12 1198751

13 1198751

211

1199052

1198752

1 1198752

12 1198752

13 1198752

215

1199053

1198753

11 1198753

12 1198753

13 1198753

211

Total processing cost (sum119894119875119894

119899V119899

) 7

providing a means for determining the SLA of such a job infuture executions

41 Without Communications In this section a hypotheticalsituation without communication between tasks is evaluatedIn this situation our scheduling policy tends to assign thetasks to the most powerful set of virtual machines (ie withthe higher relative computing power Δ

119899V119899

considering theirindividual saturation in this choice)This saturation becomescritical when more and more tasks are added Here the mostimportant term is the Erlang function since it models thebehaviour of every virtual machine Thus taking this intoaccount our scheduler knows the exact weight of tasks it canassign to the VMs in order to obtain the best return timesThis phenomenon is observed in the following examples

411 Without Communications and High Optimal ErlangTable 2 shows the parameters used in the first example Theamount ofMemory allocated to each task 119905119894 in every VM119872

119899V119899

(as we supposed this amount to be equal in all the VMs wesimply call it119872119894)The relative computing power (Δ

119899VV) of eachVMand finally the120572 and 120582 Erlang arguments Note that all theVMs have the same Erlang parameters The parameters werechosen this way because any VM saturates with the overallworkload assigned In other words the total processing cost 7is lower than the optimal Erlang workload 16

Table 3 shows the solver assignment results The bestscheduling assigns all the tasks to the same VM (VM

21 the

only VM in node 2) because this VM has the biggest relative

The Scientific World Journal 7

Table 2 Without communications High optimal Erlang VM con-figurations

Node VM119899V119899

119872119894

Δ119899VV Erlang

1 VM11 10 075 120572 = 3 120582 = 8

1 VM12 10 035 120572 = 3 120582 = 8

1 VM13 10 01 120572 = 3 120582 = 8

2 VM21 10 085 120572 = 3 120582 = 8

Table 3 Without communications High optimal Erlang Solverassignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

computing power (Δ119899VV) This result is very coherent Due to

the lack of communications the model tends to assign tasksto the most powerful VMwhile its workload does not exceedthe Erlang optimum (a workload of 10 tasks) As in our casethe total workload is 7 and VM

21could host evenmore tasks

412 Without Communications Low Optimal Erlang andPreserving SLA In this example (see Table 4) the VMs haveanother Erlang However the task processing costs do notchange so they remain the same as in Table 1 In this caseeach VM becomes saturated when the assignment workloadweight is higher than 5 (because 5 is the optimal workload)

The best assignment in this case is the one formed bythe minimum set of VMs with the best relative computingpower Δ

119899VV (see Table 5 column Task Assignment SLA) Theassignment of the overall tasks to only one VM (although itwas the most powerful one) as before will decrease the returntime excessively due to its saturation

413 Without Communications Low Optimal Erlang andPreserving Energy Saving Provided that the most importantcriterion is the energy saving the assignment will be some-what different (seeTable 5 columnTaskAssignment Energy)In this case OF (14a) with Ξ = 1was usedThen as expectedall the tasks were again assigned to VM

21of Node

2

42 With Communications Starting from the same VMconfiguration shown on Table 4 in this section we presenta more real situation where the costs of communicationsbetween tasks are also taken into account It is important tohighlight that in some situations the best choice does notinclude the most powerful VMs (ie with the highest relativecomputing powerΔ

119899V119899

)Thus the results shown in this sectionmust show the tradeoff between relative computing powerof VM workload scheduling impact modeled by the Erlangdistribution and communication efficiency between tasks

421 High Communication Slowdown This example showsthe behaviour of the model under large communication costs

Table 4Without communications Low optimal Erlang PreservingSLA VM configurations

Node VM119899V119899

119872119894

Δ119899VV Erlang

1 VM11 10 075 120572 = 5 120582 = 1

1 VM12 10 035 120572 = 5 120582 = 1

1 VM13 10 01 120572 = 5 120582 = 1

2 VM21 10 085 120572 = 5 120582 = 1

Table 5Without communications Low optimal Erlang PreservingSLA Solver assignment

Node VM119899V119899

SLA EnergyTask assignment Task assignment

1 VM11 1199051 1199053 119905

2

1 VM12 0 1199051 1199053

1 VM13 0 02 VM21 119905

2 0

Table 6 High slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

02119862119904119899V119899

01

between VMs (see Table 6) This table shows the commu-nication costs between tasks (119862119894119895) and the communicationslowdown when communications are done between VMsin the same node (Cs

119899V119899

) and the penalty cost when com-munications are performed between different nodes (Cs

119899V119899

)Note that the penalties are very high (02 and 01) when thecommunications are very influential

The solver assignment is shown in Table 7 In orderto avoid communication costs due to slowdowns the bestassignment tends to group tasks first in the same VM andsecond in the same node Although VM

21should become

saturated with this assignment the high communication costcompensates the loss of SLA performance allowing us toswitch off node 1

422 Low Communication Slowdown Now this exampleshows the behaviour of our policy under more normal com-munication conditions Here the communication penaltiesbetween the different VMs or nodes are not as significantas in the previous case because Cs

119899V119899

and Cs119899V119899

are higherTable 8 shows the communication costs between tasks andthe penalty cost if communications are performed betweenVMs in the same node (Cs

119899V119899

) or between different nodes(Cs119899V119899

)In this case the solver got as a result two hosting VMs

(see Table 9) formed by the VM11(with the assigned tasks 1199052

and 1199053) and VM

21with task 119905

1 In this case due to the low

8 The Scientific World Journal

Table 7 High slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

Table 8 Low slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

08

Table 9 Low slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 119905

1 1199053

1 VM12 01 VM13 02 VM21 119905

2

differences between the different communication slowdownstask assignment was distributed between the two nodes

423 Moderate Communication Slowdown We simulated amore normal situation where the communication slowdownbetween nodes is higher than the other ones From the sameexample it was only reduced Cs

119899V119899

to 04 (see Table 10)As expected the resulting solver assignment was differentfrom that in the previous case Theoretically this assignmentshould assign tasks to the powerful unsaturated VMs but asmuch as possible to the VMs residing on the same node Thesolver result was exactly what was expected Although themost powerful VM is in node 2 the tasks were assigned tothe VMs of node 1 because they all fit in the same nodeThatis the reason why a less powerful node like node 1 but onewith more capacity is able to allocate more tasks than node 2due to the communication slowdown between nodes Theseresults are shown in Table 11

5 Conclusions and Future Work

This paper presents a cloud-based system scheduling mech-anism called GS that is able to comply with low powerconsumption and SLA agreements The complexity of themodel developed was increased thus adding more factorsto be taken into account The model was also tested usingthe AMPL modelling language and the SCIP optimizer Theresults obtained proved consistent over a range of scenariosIn all the cases the experiments showed that all the tasks wereassigned to the most powerful subset of virtual machines bykeeping the subset size to the minimum

Table 10 Moderate slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

04

Table 11 Moderate slowdown Solver assignment

Node VM119899V119899

Tasks assignment1 VM11 119905

2 1199053

1 VM12 1199051

1 VM13 02 VM21 0

Although our proposals still have to be tested in real sce-narios these preliminary results corroborate their usefulness

Our efforts are directed towards implementing thosestrategies in a real cloud environment like the OpenStack[22] or OpenNebula [23] frameworks

In the longer term we consider using some statisticalmethod to find an accurate approximation of the workloadusing well-suited Erlang distribution functions

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 MEYC under ContractsTIN2011-28689-C02-02 The authors are members of theresearch groups 2009-SGR145 and 2014-SGR163 funded bythe Generalitat de Catalunya

References

[1] RAversa BDiMartinoMRak S Venticinque andUVillanoPerformance Prediction for HPC on Clouds Cloud ComputingPrinciples and Paradigms John Wiley amp Sons New York NYUSA 2011

[2] A Iosup N Yigitbasi and D Epema ldquoOn the performancevariability of production cloud servicesrdquo in Proceedings of the11th IEEEACM International Symposium on Cluster Cloud andGrid Computing (CCGrid rsquo11) pp 104ndash113 May 2011

[3] J Varia Architection for the Cloud Best Practices Amazon WebServices 2014

[4] Intel cloud computing 2015 vision httpwwwintelcomcon-tentwwwusencloud-computing

[5] M Martinello M Kaaniche and K Kanoun ldquoWeb serviceavailabilitymdashimpact of error recovery and traffic modelrdquo Relia-bility Engineering amp System Safety vol 89 no 1 pp 6ndash16 2005

[6] J Vilaplana F Solsona F Abella R Filgueira and J Rius ldquoThecloud paradigm applied to e-Healthrdquo BMCMedical Informaticsand Decision Making vol 13 no 1 article 35 2013

The Scientific World Journal 9

[7] J Vilaplana F Solsona I Teixido JMateo F Abella and J RiusldquoA queuing theory model for cloud computingrdquo The Journal ofSupercomputing vol 69 no 1 pp 492ndash507 2014

[8] A Beloglazov and R Buyya ldquoOptimal online deterministicalgorithms and adaptive heuristics for energy and performanceefficient dynamic consolidation of virtual machines in Clouddata centersrdquo Concurrency Computation Practice and Experi-ence vol 24 no 13 pp 1397ndash1420 2012

[9] D Kliazovich P Bouvry and S U Khan ldquoGreenCloud apacket-level simulator of energy-aware cloud computing datacentersrdquoThe Journal of Supercomputing vol 62 no 3 pp 1263ndash1283 2012

[10] C Ghribi M Hadji and D Zeghlache ldquoEnergy efficientVM scheduling for cloud data centers exact allocation andmigration algorithmsrdquo in Proceedings of the 13th IEEEACMInternational SymposiumonCluster Cloud andGridComputing(CCGrid rsquo13) pp 671ndash678 May 2013

[11] M F Khan Z Anwar and Q S Ahmad ldquoAssignment of per-sonnels when job completion time follows gamma distributionusing stochastic programming techniquerdquo International Journalof Scientific amp Engineering Research vol 3 no 3 2012

[12] J L Lerida F Solsona P Hernandez F Gine M Hanzichand J Conde ldquoState-based predictions with self-correction onEnterprise Desktop Grid environmentsrdquo Journal of Parallel andDistributed Computing vol 73 no 6 pp 777ndash789 2013

[13] A Goldman and Y Ngoko ldquoA MILP approach to scheduleparallel independent tasksrdquo in Proceedings of the InternationalSymposium on Parallel and Distributed Computing (ISPDC rsquo08)pp 115ndash122 Krakow Poland July 2008

[14] T Vinh T Duy Y Sato and Y Inoguchi ldquoPerformanceevaluation of a green scheduling algorithm for energy savingsin cloud computingrdquo in Proceedings of the IEEE InternationalSymposium on Parallel amp Distributed Processing Workshops andPhd Forum (IPDPSW rsquo10) pp 1ndash8 Atlanta Ga USA April 2010

[15] M Mezmaz N Melab Y Kessaci et al ldquoA parallel bi-objectivehybrid metaheuristic for energy-aware scheduling for cloudcomputing systemsrdquo Journal of Parallel and Distributed Com-puting vol 71 no 11 pp 1497ndash1508 2011

[16] Y C Ouyang Y J Chiang C H Hsu and G Yi ldquoAnoptimal control policy to realize green cloud systems with SLA-awarenessrdquo The Journal of Supercomputing vol 69 no 3 pp1284ndash1310 2014

[17] T C Ferreto M A S Netto R N Calheiros and C AF de Rose ldquoServer consolidation with migration control forvirtualized data centersrdquo Future Generation Computer Systemsvol 27 no 8 pp 1027ndash1034 2011

[18] A Murtazaev and S Oh ldquoSercon server consolidation algo-rithm using live migration of virtual machines for greencomputingrdquo IETE Technical Review (Institution of Electronicsand Telecommunication Engineers India) vol 28 no 3 pp 212ndash231 2011

[19] A F Monteiro M V Azevedo and A Sztajnberg ldquoVirtualizedWeb server cluster self-configuration to optimize resource andpower userdquo Journal of Systems and Software vol 86 no 11 pp2779ndash2796 2013

[20] C-C Lin H-H Chin and D-J Deng ldquoDynamic multiserviceload balancing in cloud-based multimedia systemrdquo IEEE Sys-tems Journal vol 8 no 1 pp 225ndash234 2014

[21] J Vilaplana F Solsona J Mateo and I Teixido ldquoSLA-awareload balancing in a web-based cloud system over OpenStackrdquoin Service-Oriented ComputingmdashICSOC 2013 Workshops vol

8377 of Lecture Notes in Computer Science pp 281ndash293 SpringerInternational Publishing 2014

[22] OpenStack httpwwwopenstackorg[23] OpenNebula httpwwwopennebulaorg

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

6 The Scientific World Journal

Equation (14a) is the objective function (OF) to be max-imized Note that OF is an integer and nonlinear problemInequality in (14b) and equality in (14c) are the constraints ofthe objective function variables Given the constants 119879 (thetotal number of requests or tasks) and 119872V for each VM

119899V119899

the solution that maximizes OF will obtain the values of thevariables 119905119894

119899V119899

representing the number of tasks assigned toVM119899V119899

Thus the 119905119899V119899119894obtained will be the assignment found

by this modelOF takes into account the processing costs (119875119894

119899V119899

) and thecommunication times (119862119894119895

119899V119899

) of the tasks assigned to eachVM119899V119899

and the communication slowdownsbetweenVMsCs119899V119899

and nodes Cs119899V119899

Cs119899V119899

= 1 Δ is defined in Section 37 And119864(sum119879

119895=1119905119895

119899V119899

119875119895

119899V119899

120572 120582) represents the power slowdown of eachVM due to its workload (defined in Section 34)

To sum up for the case when the workload is made up ofnoncommunicating tasks if we are interested in prioritizingthe SLA criteria OF 35 should be applied If on the contrarythe goal is to prioritize energy savingOF (14a) should be usedinstead

4 Results

In this section we present the theoretical results obtainedfrom solving the scheduling problems aimed at achievingbest task assignment Two representative experiments wereperformed in order to test the performance of GS

The experiments were performed by using the AMPL(AMPL A Mathematical Programming Language httpamplcom) language and the SCIP (SCIP Solving ConstraintInteger Programs httpscipzibde) solver AMPL is analgebraic modeling language for describing and solving high-complexity problems for large-scale mathematical computa-tion supported by many solvers Integer and nonlinear (ourmodel type) problems can be solved by SCIP one of thesolvers supported by AMPL

Throughout all the experimentation the Erlang argu-ments were obtained empirically by using the strategyexplained in Section 34

As the objective of this section is to prove the correctnessof the policy only a small set of tasks VMs and nodes waschosen The size of the experimental framework was chosento be as much representative of actual cases as possible butat the same time simple enough to be used as an illustrativeexample So the experimental framework chosen was madeup of 2 different nodes one of them comprised 3VMs and theother 1 VM see Figure 2The objective of this simulation wasto achieve the best assignment for 3 tasks Table 1 shows theprocessing cost 119875119894

119899V119899

relating the execution times of the tasks ineach VM To show the good behavior of themodel presentedeach task has the same processing cost independently of theVM The model presented can be efficiently applied to realcloud environments The only weak point is that the modelis static That means that homogenous and static workloadconditions must be stable in our model Job executions indifferent workload sizes can be saved in a database system

Node 2Node 1

VM2VM3 VM1

VM3

Cloud

Figure 2 Cloud architecture

Table 1 Task processing costs

Task 119905119894 Processing costs 119875119894119899V119899

Value1199051

1198751

11 1198751

12 1198751

13 1198751

211

1199052

1198752

1 1198752

12 1198752

13 1198752

215

1199053

1198753

11 1198753

12 1198753

13 1198753

211

Total processing cost (sum119894119875119894

119899V119899

) 7

providing a means for determining the SLA of such a job infuture executions

41 Without Communications In this section a hypotheticalsituation without communication between tasks is evaluatedIn this situation our scheduling policy tends to assign thetasks to the most powerful set of virtual machines (ie withthe higher relative computing power Δ

119899V119899

considering theirindividual saturation in this choice)This saturation becomescritical when more and more tasks are added Here the mostimportant term is the Erlang function since it models thebehaviour of every virtual machine Thus taking this intoaccount our scheduler knows the exact weight of tasks it canassign to the VMs in order to obtain the best return timesThis phenomenon is observed in the following examples

411 Without Communications and High Optimal ErlangTable 2 shows the parameters used in the first example Theamount ofMemory allocated to each task 119905119894 in every VM119872

119899V119899

(as we supposed this amount to be equal in all the VMs wesimply call it119872119894)The relative computing power (Δ

119899VV) of eachVMand finally the120572 and 120582 Erlang arguments Note that all theVMs have the same Erlang parameters The parameters werechosen this way because any VM saturates with the overallworkload assigned In other words the total processing cost 7is lower than the optimal Erlang workload 16

Table 3 shows the solver assignment results The bestscheduling assigns all the tasks to the same VM (VM

21 the

only VM in node 2) because this VM has the biggest relative

The Scientific World Journal 7

Table 2 Without communications High optimal Erlang VM con-figurations

Node VM119899V119899

119872119894

Δ119899VV Erlang

1 VM11 10 075 120572 = 3 120582 = 8

1 VM12 10 035 120572 = 3 120582 = 8

1 VM13 10 01 120572 = 3 120582 = 8

2 VM21 10 085 120572 = 3 120582 = 8

Table 3 Without communications High optimal Erlang Solverassignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

computing power (Δ119899VV) This result is very coherent Due to

the lack of communications the model tends to assign tasksto the most powerful VMwhile its workload does not exceedthe Erlang optimum (a workload of 10 tasks) As in our casethe total workload is 7 and VM

21could host evenmore tasks

412 Without Communications Low Optimal Erlang andPreserving SLA In this example (see Table 4) the VMs haveanother Erlang However the task processing costs do notchange so they remain the same as in Table 1 In this caseeach VM becomes saturated when the assignment workloadweight is higher than 5 (because 5 is the optimal workload)

The best assignment in this case is the one formed bythe minimum set of VMs with the best relative computingpower Δ

119899VV (see Table 5 column Task Assignment SLA) Theassignment of the overall tasks to only one VM (although itwas the most powerful one) as before will decrease the returntime excessively due to its saturation

413 Without Communications Low Optimal Erlang andPreserving Energy Saving Provided that the most importantcriterion is the energy saving the assignment will be some-what different (seeTable 5 columnTaskAssignment Energy)In this case OF (14a) with Ξ = 1was usedThen as expectedall the tasks were again assigned to VM

21of Node

2

42 With Communications Starting from the same VMconfiguration shown on Table 4 in this section we presenta more real situation where the costs of communicationsbetween tasks are also taken into account It is important tohighlight that in some situations the best choice does notinclude the most powerful VMs (ie with the highest relativecomputing powerΔ

119899V119899

)Thus the results shown in this sectionmust show the tradeoff between relative computing powerof VM workload scheduling impact modeled by the Erlangdistribution and communication efficiency between tasks

421 High Communication Slowdown This example showsthe behaviour of the model under large communication costs

Table 4Without communications Low optimal Erlang PreservingSLA VM configurations

Node VM119899V119899

119872119894

Δ119899VV Erlang

1 VM11 10 075 120572 = 5 120582 = 1

1 VM12 10 035 120572 = 5 120582 = 1

1 VM13 10 01 120572 = 5 120582 = 1

2 VM21 10 085 120572 = 5 120582 = 1

Table 5Without communications Low optimal Erlang PreservingSLA Solver assignment

Node VM119899V119899

SLA EnergyTask assignment Task assignment

1 VM11 1199051 1199053 119905

2

1 VM12 0 1199051 1199053

1 VM13 0 02 VM21 119905

2 0

Table 6 High slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

02119862119904119899V119899

01

between VMs (see Table 6) This table shows the commu-nication costs between tasks (119862119894119895) and the communicationslowdown when communications are done between VMsin the same node (Cs

119899V119899

) and the penalty cost when com-munications are performed between different nodes (Cs

119899V119899

)Note that the penalties are very high (02 and 01) when thecommunications are very influential

The solver assignment is shown in Table 7 In orderto avoid communication costs due to slowdowns the bestassignment tends to group tasks first in the same VM andsecond in the same node Although VM

21should become

saturated with this assignment the high communication costcompensates the loss of SLA performance allowing us toswitch off node 1

422 Low Communication Slowdown Now this exampleshows the behaviour of our policy under more normal com-munication conditions Here the communication penaltiesbetween the different VMs or nodes are not as significantas in the previous case because Cs

119899V119899

and Cs119899V119899

are higherTable 8 shows the communication costs between tasks andthe penalty cost if communications are performed betweenVMs in the same node (Cs

119899V119899

) or between different nodes(Cs119899V119899

)In this case the solver got as a result two hosting VMs

(see Table 9) formed by the VM11(with the assigned tasks 1199052

and 1199053) and VM

21with task 119905

1 In this case due to the low

8 The Scientific World Journal

Table 7 High slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

Table 8 Low slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

08

Table 9 Low slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 119905

1 1199053

1 VM12 01 VM13 02 VM21 119905

2

differences between the different communication slowdownstask assignment was distributed between the two nodes

423 Moderate Communication Slowdown We simulated amore normal situation where the communication slowdownbetween nodes is higher than the other ones From the sameexample it was only reduced Cs

119899V119899

to 04 (see Table 10)As expected the resulting solver assignment was differentfrom that in the previous case Theoretically this assignmentshould assign tasks to the powerful unsaturated VMs but asmuch as possible to the VMs residing on the same node Thesolver result was exactly what was expected Although themost powerful VM is in node 2 the tasks were assigned tothe VMs of node 1 because they all fit in the same nodeThatis the reason why a less powerful node like node 1 but onewith more capacity is able to allocate more tasks than node 2due to the communication slowdown between nodes Theseresults are shown in Table 11

5 Conclusions and Future Work

This paper presents a cloud-based system scheduling mech-anism called GS that is able to comply with low powerconsumption and SLA agreements The complexity of themodel developed was increased thus adding more factorsto be taken into account The model was also tested usingthe AMPL modelling language and the SCIP optimizer Theresults obtained proved consistent over a range of scenariosIn all the cases the experiments showed that all the tasks wereassigned to the most powerful subset of virtual machines bykeeping the subset size to the minimum

Table 10 Moderate slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

04

Table 11 Moderate slowdown Solver assignment

Node VM119899V119899

Tasks assignment1 VM11 119905

2 1199053

1 VM12 1199051

1 VM13 02 VM21 0

Although our proposals still have to be tested in real sce-narios these preliminary results corroborate their usefulness

Our efforts are directed towards implementing thosestrategies in a real cloud environment like the OpenStack[22] or OpenNebula [23] frameworks

In the longer term we consider using some statisticalmethod to find an accurate approximation of the workloadusing well-suited Erlang distribution functions

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 MEYC under ContractsTIN2011-28689-C02-02 The authors are members of theresearch groups 2009-SGR145 and 2014-SGR163 funded bythe Generalitat de Catalunya

References

[1] RAversa BDiMartinoMRak S Venticinque andUVillanoPerformance Prediction for HPC on Clouds Cloud ComputingPrinciples and Paradigms John Wiley amp Sons New York NYUSA 2011

[2] A Iosup N Yigitbasi and D Epema ldquoOn the performancevariability of production cloud servicesrdquo in Proceedings of the11th IEEEACM International Symposium on Cluster Cloud andGrid Computing (CCGrid rsquo11) pp 104ndash113 May 2011

[3] J Varia Architection for the Cloud Best Practices Amazon WebServices 2014

[4] Intel cloud computing 2015 vision httpwwwintelcomcon-tentwwwusencloud-computing

[5] M Martinello M Kaaniche and K Kanoun ldquoWeb serviceavailabilitymdashimpact of error recovery and traffic modelrdquo Relia-bility Engineering amp System Safety vol 89 no 1 pp 6ndash16 2005

[6] J Vilaplana F Solsona F Abella R Filgueira and J Rius ldquoThecloud paradigm applied to e-Healthrdquo BMCMedical Informaticsand Decision Making vol 13 no 1 article 35 2013

The Scientific World Journal 9

[7] J Vilaplana F Solsona I Teixido JMateo F Abella and J RiusldquoA queuing theory model for cloud computingrdquo The Journal ofSupercomputing vol 69 no 1 pp 492ndash507 2014

[8] A Beloglazov and R Buyya ldquoOptimal online deterministicalgorithms and adaptive heuristics for energy and performanceefficient dynamic consolidation of virtual machines in Clouddata centersrdquo Concurrency Computation Practice and Experi-ence vol 24 no 13 pp 1397ndash1420 2012

[9] D Kliazovich P Bouvry and S U Khan ldquoGreenCloud apacket-level simulator of energy-aware cloud computing datacentersrdquoThe Journal of Supercomputing vol 62 no 3 pp 1263ndash1283 2012

[10] C Ghribi M Hadji and D Zeghlache ldquoEnergy efficientVM scheduling for cloud data centers exact allocation andmigration algorithmsrdquo in Proceedings of the 13th IEEEACMInternational SymposiumonCluster Cloud andGridComputing(CCGrid rsquo13) pp 671ndash678 May 2013

[11] M F Khan Z Anwar and Q S Ahmad ldquoAssignment of per-sonnels when job completion time follows gamma distributionusing stochastic programming techniquerdquo International Journalof Scientific amp Engineering Research vol 3 no 3 2012

[12] J L Lerida F Solsona P Hernandez F Gine M Hanzichand J Conde ldquoState-based predictions with self-correction onEnterprise Desktop Grid environmentsrdquo Journal of Parallel andDistributed Computing vol 73 no 6 pp 777ndash789 2013

[13] A Goldman and Y Ngoko ldquoA MILP approach to scheduleparallel independent tasksrdquo in Proceedings of the InternationalSymposium on Parallel and Distributed Computing (ISPDC rsquo08)pp 115ndash122 Krakow Poland July 2008

[14] T Vinh T Duy Y Sato and Y Inoguchi ldquoPerformanceevaluation of a green scheduling algorithm for energy savingsin cloud computingrdquo in Proceedings of the IEEE InternationalSymposium on Parallel amp Distributed Processing Workshops andPhd Forum (IPDPSW rsquo10) pp 1ndash8 Atlanta Ga USA April 2010

[15] M Mezmaz N Melab Y Kessaci et al ldquoA parallel bi-objectivehybrid metaheuristic for energy-aware scheduling for cloudcomputing systemsrdquo Journal of Parallel and Distributed Com-puting vol 71 no 11 pp 1497ndash1508 2011

[16] Y C Ouyang Y J Chiang C H Hsu and G Yi ldquoAnoptimal control policy to realize green cloud systems with SLA-awarenessrdquo The Journal of Supercomputing vol 69 no 3 pp1284ndash1310 2014

[17] T C Ferreto M A S Netto R N Calheiros and C AF de Rose ldquoServer consolidation with migration control forvirtualized data centersrdquo Future Generation Computer Systemsvol 27 no 8 pp 1027ndash1034 2011

[18] A Murtazaev and S Oh ldquoSercon server consolidation algo-rithm using live migration of virtual machines for greencomputingrdquo IETE Technical Review (Institution of Electronicsand Telecommunication Engineers India) vol 28 no 3 pp 212ndash231 2011

[19] A F Monteiro M V Azevedo and A Sztajnberg ldquoVirtualizedWeb server cluster self-configuration to optimize resource andpower userdquo Journal of Systems and Software vol 86 no 11 pp2779ndash2796 2013

[20] C-C Lin H-H Chin and D-J Deng ldquoDynamic multiserviceload balancing in cloud-based multimedia systemrdquo IEEE Sys-tems Journal vol 8 no 1 pp 225ndash234 2014

[21] J Vilaplana F Solsona J Mateo and I Teixido ldquoSLA-awareload balancing in a web-based cloud system over OpenStackrdquoin Service-Oriented ComputingmdashICSOC 2013 Workshops vol

8377 of Lecture Notes in Computer Science pp 281ndash293 SpringerInternational Publishing 2014

[22] OpenStack httpwwwopenstackorg[23] OpenNebula httpwwwopennebulaorg

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World Journal 7

Table 2 Without communications High optimal Erlang VM con-figurations

Node VM119899V119899

119872119894

Δ119899VV Erlang

1 VM11 10 075 120572 = 3 120582 = 8

1 VM12 10 035 120572 = 3 120582 = 8

1 VM13 10 01 120572 = 3 120582 = 8

2 VM21 10 085 120572 = 3 120582 = 8

Table 3 Without communications High optimal Erlang Solverassignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

computing power (Δ119899VV) This result is very coherent Due to

the lack of communications the model tends to assign tasksto the most powerful VMwhile its workload does not exceedthe Erlang optimum (a workload of 10 tasks) As in our casethe total workload is 7 and VM

21could host evenmore tasks

412 Without Communications Low Optimal Erlang andPreserving SLA In this example (see Table 4) the VMs haveanother Erlang However the task processing costs do notchange so they remain the same as in Table 1 In this caseeach VM becomes saturated when the assignment workloadweight is higher than 5 (because 5 is the optimal workload)

The best assignment in this case is the one formed bythe minimum set of VMs with the best relative computingpower Δ

119899VV (see Table 5 column Task Assignment SLA) Theassignment of the overall tasks to only one VM (although itwas the most powerful one) as before will decrease the returntime excessively due to its saturation

413 Without Communications Low Optimal Erlang andPreserving Energy Saving Provided that the most importantcriterion is the energy saving the assignment will be some-what different (seeTable 5 columnTaskAssignment Energy)In this case OF (14a) with Ξ = 1was usedThen as expectedall the tasks were again assigned to VM

21of Node

2

42 With Communications Starting from the same VMconfiguration shown on Table 4 in this section we presenta more real situation where the costs of communicationsbetween tasks are also taken into account It is important tohighlight that in some situations the best choice does notinclude the most powerful VMs (ie with the highest relativecomputing powerΔ

119899V119899

)Thus the results shown in this sectionmust show the tradeoff between relative computing powerof VM workload scheduling impact modeled by the Erlangdistribution and communication efficiency between tasks

421 High Communication Slowdown This example showsthe behaviour of the model under large communication costs

Table 4Without communications Low optimal Erlang PreservingSLA VM configurations

Node VM119899V119899

119872119894

Δ119899VV Erlang

1 VM11 10 075 120572 = 5 120582 = 1

1 VM12 10 035 120572 = 5 120582 = 1

1 VM13 10 01 120572 = 5 120582 = 1

2 VM21 10 085 120572 = 5 120582 = 1

Table 5Without communications Low optimal Erlang PreservingSLA Solver assignment

Node VM119899V119899

SLA EnergyTask assignment Task assignment

1 VM11 1199051 1199053 119905

2

1 VM12 0 1199051 1199053

1 VM13 0 02 VM21 119905

2 0

Table 6 High slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

02119862119904119899V119899

01

between VMs (see Table 6) This table shows the commu-nication costs between tasks (119862119894119895) and the communicationslowdown when communications are done between VMsin the same node (Cs

119899V119899

) and the penalty cost when com-munications are performed between different nodes (Cs

119899V119899

)Note that the penalties are very high (02 and 01) when thecommunications are very influential

The solver assignment is shown in Table 7 In orderto avoid communication costs due to slowdowns the bestassignment tends to group tasks first in the same VM andsecond in the same node Although VM

21should become

saturated with this assignment the high communication costcompensates the loss of SLA performance allowing us toswitch off node 1

422 Low Communication Slowdown Now this exampleshows the behaviour of our policy under more normal com-munication conditions Here the communication penaltiesbetween the different VMs or nodes are not as significantas in the previous case because Cs

119899V119899

and Cs119899V119899

are higherTable 8 shows the communication costs between tasks andthe penalty cost if communications are performed betweenVMs in the same node (Cs

119899V119899

) or between different nodes(Cs119899V119899

)In this case the solver got as a result two hosting VMs

(see Table 9) formed by the VM11(with the assigned tasks 1199052

and 1199053) and VM

21with task 119905

1 In this case due to the low

8 The Scientific World Journal

Table 7 High slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

Table 8 Low slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

08

Table 9 Low slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 119905

1 1199053

1 VM12 01 VM13 02 VM21 119905

2

differences between the different communication slowdownstask assignment was distributed between the two nodes

423 Moderate Communication Slowdown We simulated amore normal situation where the communication slowdownbetween nodes is higher than the other ones From the sameexample it was only reduced Cs

119899V119899

to 04 (see Table 10)As expected the resulting solver assignment was differentfrom that in the previous case Theoretically this assignmentshould assign tasks to the powerful unsaturated VMs but asmuch as possible to the VMs residing on the same node Thesolver result was exactly what was expected Although themost powerful VM is in node 2 the tasks were assigned tothe VMs of node 1 because they all fit in the same nodeThatis the reason why a less powerful node like node 1 but onewith more capacity is able to allocate more tasks than node 2due to the communication slowdown between nodes Theseresults are shown in Table 11

5 Conclusions and Future Work

This paper presents a cloud-based system scheduling mech-anism called GS that is able to comply with low powerconsumption and SLA agreements The complexity of themodel developed was increased thus adding more factorsto be taken into account The model was also tested usingthe AMPL modelling language and the SCIP optimizer Theresults obtained proved consistent over a range of scenariosIn all the cases the experiments showed that all the tasks wereassigned to the most powerful subset of virtual machines bykeeping the subset size to the minimum

Table 10 Moderate slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

04

Table 11 Moderate slowdown Solver assignment

Node VM119899V119899

Tasks assignment1 VM11 119905

2 1199053

1 VM12 1199051

1 VM13 02 VM21 0

Although our proposals still have to be tested in real sce-narios these preliminary results corroborate their usefulness

Our efforts are directed towards implementing thosestrategies in a real cloud environment like the OpenStack[22] or OpenNebula [23] frameworks

In the longer term we consider using some statisticalmethod to find an accurate approximation of the workloadusing well-suited Erlang distribution functions

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 MEYC under ContractsTIN2011-28689-C02-02 The authors are members of theresearch groups 2009-SGR145 and 2014-SGR163 funded bythe Generalitat de Catalunya

References

[1] RAversa BDiMartinoMRak S Venticinque andUVillanoPerformance Prediction for HPC on Clouds Cloud ComputingPrinciples and Paradigms John Wiley amp Sons New York NYUSA 2011

[2] A Iosup N Yigitbasi and D Epema ldquoOn the performancevariability of production cloud servicesrdquo in Proceedings of the11th IEEEACM International Symposium on Cluster Cloud andGrid Computing (CCGrid rsquo11) pp 104ndash113 May 2011

[3] J Varia Architection for the Cloud Best Practices Amazon WebServices 2014

[4] Intel cloud computing 2015 vision httpwwwintelcomcon-tentwwwusencloud-computing

[5] M Martinello M Kaaniche and K Kanoun ldquoWeb serviceavailabilitymdashimpact of error recovery and traffic modelrdquo Relia-bility Engineering amp System Safety vol 89 no 1 pp 6ndash16 2005

[6] J Vilaplana F Solsona F Abella R Filgueira and J Rius ldquoThecloud paradigm applied to e-Healthrdquo BMCMedical Informaticsand Decision Making vol 13 no 1 article 35 2013

The Scientific World Journal 9

[7] J Vilaplana F Solsona I Teixido JMateo F Abella and J RiusldquoA queuing theory model for cloud computingrdquo The Journal ofSupercomputing vol 69 no 1 pp 492ndash507 2014

[8] A Beloglazov and R Buyya ldquoOptimal online deterministicalgorithms and adaptive heuristics for energy and performanceefficient dynamic consolidation of virtual machines in Clouddata centersrdquo Concurrency Computation Practice and Experi-ence vol 24 no 13 pp 1397ndash1420 2012

[9] D Kliazovich P Bouvry and S U Khan ldquoGreenCloud apacket-level simulator of energy-aware cloud computing datacentersrdquoThe Journal of Supercomputing vol 62 no 3 pp 1263ndash1283 2012

[10] C Ghribi M Hadji and D Zeghlache ldquoEnergy efficientVM scheduling for cloud data centers exact allocation andmigration algorithmsrdquo in Proceedings of the 13th IEEEACMInternational SymposiumonCluster Cloud andGridComputing(CCGrid rsquo13) pp 671ndash678 May 2013

[11] M F Khan Z Anwar and Q S Ahmad ldquoAssignment of per-sonnels when job completion time follows gamma distributionusing stochastic programming techniquerdquo International Journalof Scientific amp Engineering Research vol 3 no 3 2012

[12] J L Lerida F Solsona P Hernandez F Gine M Hanzichand J Conde ldquoState-based predictions with self-correction onEnterprise Desktop Grid environmentsrdquo Journal of Parallel andDistributed Computing vol 73 no 6 pp 777ndash789 2013

[13] A Goldman and Y Ngoko ldquoA MILP approach to scheduleparallel independent tasksrdquo in Proceedings of the InternationalSymposium on Parallel and Distributed Computing (ISPDC rsquo08)pp 115ndash122 Krakow Poland July 2008

[14] T Vinh T Duy Y Sato and Y Inoguchi ldquoPerformanceevaluation of a green scheduling algorithm for energy savingsin cloud computingrdquo in Proceedings of the IEEE InternationalSymposium on Parallel amp Distributed Processing Workshops andPhd Forum (IPDPSW rsquo10) pp 1ndash8 Atlanta Ga USA April 2010

[15] M Mezmaz N Melab Y Kessaci et al ldquoA parallel bi-objectivehybrid metaheuristic for energy-aware scheduling for cloudcomputing systemsrdquo Journal of Parallel and Distributed Com-puting vol 71 no 11 pp 1497ndash1508 2011

[16] Y C Ouyang Y J Chiang C H Hsu and G Yi ldquoAnoptimal control policy to realize green cloud systems with SLA-awarenessrdquo The Journal of Supercomputing vol 69 no 3 pp1284ndash1310 2014

[17] T C Ferreto M A S Netto R N Calheiros and C AF de Rose ldquoServer consolidation with migration control forvirtualized data centersrdquo Future Generation Computer Systemsvol 27 no 8 pp 1027ndash1034 2011

[18] A Murtazaev and S Oh ldquoSercon server consolidation algo-rithm using live migration of virtual machines for greencomputingrdquo IETE Technical Review (Institution of Electronicsand Telecommunication Engineers India) vol 28 no 3 pp 212ndash231 2011

[19] A F Monteiro M V Azevedo and A Sztajnberg ldquoVirtualizedWeb server cluster self-configuration to optimize resource andpower userdquo Journal of Systems and Software vol 86 no 11 pp2779ndash2796 2013

[20] C-C Lin H-H Chin and D-J Deng ldquoDynamic multiserviceload balancing in cloud-based multimedia systemrdquo IEEE Sys-tems Journal vol 8 no 1 pp 225ndash234 2014

[21] J Vilaplana F Solsona J Mateo and I Teixido ldquoSLA-awareload balancing in a web-based cloud system over OpenStackrdquoin Service-Oriented ComputingmdashICSOC 2013 Workshops vol

8377 of Lecture Notes in Computer Science pp 281ndash293 SpringerInternational Publishing 2014

[22] OpenStack httpwwwopenstackorg[23] OpenNebula httpwwwopennebulaorg

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

8 The Scientific World Journal

Table 7 High slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 01 VM12 01 VM13 02 VM21 119905

1 1199052 1199053

Table 8 Low slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

08

Table 9 Low slowdown Solver assignment

Node VM119899V119899

Task assignment1 VM11 119905

1 1199053

1 VM12 01 VM13 02 VM21 119905

2

differences between the different communication slowdownstask assignment was distributed between the two nodes

423 Moderate Communication Slowdown We simulated amore normal situation where the communication slowdownbetween nodes is higher than the other ones From the sameexample it was only reduced Cs

119899V119899

to 04 (see Table 10)As expected the resulting solver assignment was differentfrom that in the previous case Theoretically this assignmentshould assign tasks to the powerful unsaturated VMs but asmuch as possible to the VMs residing on the same node Thesolver result was exactly what was expected Although themost powerful VM is in node 2 the tasks were assigned tothe VMs of node 1 because they all fit in the same nodeThatis the reason why a less powerful node like node 1 but onewith more capacity is able to allocate more tasks than node 2due to the communication slowdown between nodes Theseresults are shown in Table 11

5 Conclusions and Future Work

This paper presents a cloud-based system scheduling mech-anism called GS that is able to comply with low powerconsumption and SLA agreements The complexity of themodel developed was increased thus adding more factorsto be taken into account The model was also tested usingthe AMPL modelling language and the SCIP optimizer Theresults obtained proved consistent over a range of scenariosIn all the cases the experiments showed that all the tasks wereassigned to the most powerful subset of virtual machines bykeeping the subset size to the minimum

Table 10 Moderate slowdown Communication configurations

Task 119905119894 Task 119905119895 Communication costs 119862119894119895

1199051

1199052 02

1199051

1199053 06

1199052

1199053 03

119862119904119899V119899

09119862119904119899V119899

04

Table 11 Moderate slowdown Solver assignment

Node VM119899V119899

Tasks assignment1 VM11 119905

2 1199053

1 VM12 1199051

1 VM13 02 VM21 0

Although our proposals still have to be tested in real sce-narios these preliminary results corroborate their usefulness

Our efforts are directed towards implementing thosestrategies in a real cloud environment like the OpenStack[22] or OpenNebula [23] frameworks

In the longer term we consider using some statisticalmethod to find an accurate approximation of the workloadusing well-suited Erlang distribution functions

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 MEYC under ContractsTIN2011-28689-C02-02 The authors are members of theresearch groups 2009-SGR145 and 2014-SGR163 funded bythe Generalitat de Catalunya

References

[1] RAversa BDiMartinoMRak S Venticinque andUVillanoPerformance Prediction for HPC on Clouds Cloud ComputingPrinciples and Paradigms John Wiley amp Sons New York NYUSA 2011

[2] A Iosup N Yigitbasi and D Epema ldquoOn the performancevariability of production cloud servicesrdquo in Proceedings of the11th IEEEACM International Symposium on Cluster Cloud andGrid Computing (CCGrid rsquo11) pp 104ndash113 May 2011

[3] J Varia Architection for the Cloud Best Practices Amazon WebServices 2014

[4] Intel cloud computing 2015 vision httpwwwintelcomcon-tentwwwusencloud-computing

[5] M Martinello M Kaaniche and K Kanoun ldquoWeb serviceavailabilitymdashimpact of error recovery and traffic modelrdquo Relia-bility Engineering amp System Safety vol 89 no 1 pp 6ndash16 2005

[6] J Vilaplana F Solsona F Abella R Filgueira and J Rius ldquoThecloud paradigm applied to e-Healthrdquo BMCMedical Informaticsand Decision Making vol 13 no 1 article 35 2013

The Scientific World Journal 9

[7] J Vilaplana F Solsona I Teixido JMateo F Abella and J RiusldquoA queuing theory model for cloud computingrdquo The Journal ofSupercomputing vol 69 no 1 pp 492ndash507 2014

[8] A Beloglazov and R Buyya ldquoOptimal online deterministicalgorithms and adaptive heuristics for energy and performanceefficient dynamic consolidation of virtual machines in Clouddata centersrdquo Concurrency Computation Practice and Experi-ence vol 24 no 13 pp 1397ndash1420 2012

[9] D Kliazovich P Bouvry and S U Khan ldquoGreenCloud apacket-level simulator of energy-aware cloud computing datacentersrdquoThe Journal of Supercomputing vol 62 no 3 pp 1263ndash1283 2012

[10] C Ghribi M Hadji and D Zeghlache ldquoEnergy efficientVM scheduling for cloud data centers exact allocation andmigration algorithmsrdquo in Proceedings of the 13th IEEEACMInternational SymposiumonCluster Cloud andGridComputing(CCGrid rsquo13) pp 671ndash678 May 2013

[11] M F Khan Z Anwar and Q S Ahmad ldquoAssignment of per-sonnels when job completion time follows gamma distributionusing stochastic programming techniquerdquo International Journalof Scientific amp Engineering Research vol 3 no 3 2012

[12] J L Lerida F Solsona P Hernandez F Gine M Hanzichand J Conde ldquoState-based predictions with self-correction onEnterprise Desktop Grid environmentsrdquo Journal of Parallel andDistributed Computing vol 73 no 6 pp 777ndash789 2013

[13] A Goldman and Y Ngoko ldquoA MILP approach to scheduleparallel independent tasksrdquo in Proceedings of the InternationalSymposium on Parallel and Distributed Computing (ISPDC rsquo08)pp 115ndash122 Krakow Poland July 2008

[14] T Vinh T Duy Y Sato and Y Inoguchi ldquoPerformanceevaluation of a green scheduling algorithm for energy savingsin cloud computingrdquo in Proceedings of the IEEE InternationalSymposium on Parallel amp Distributed Processing Workshops andPhd Forum (IPDPSW rsquo10) pp 1ndash8 Atlanta Ga USA April 2010

[15] M Mezmaz N Melab Y Kessaci et al ldquoA parallel bi-objectivehybrid metaheuristic for energy-aware scheduling for cloudcomputing systemsrdquo Journal of Parallel and Distributed Com-puting vol 71 no 11 pp 1497ndash1508 2011

[16] Y C Ouyang Y J Chiang C H Hsu and G Yi ldquoAnoptimal control policy to realize green cloud systems with SLA-awarenessrdquo The Journal of Supercomputing vol 69 no 3 pp1284ndash1310 2014

[17] T C Ferreto M A S Netto R N Calheiros and C AF de Rose ldquoServer consolidation with migration control forvirtualized data centersrdquo Future Generation Computer Systemsvol 27 no 8 pp 1027ndash1034 2011

[18] A Murtazaev and S Oh ldquoSercon server consolidation algo-rithm using live migration of virtual machines for greencomputingrdquo IETE Technical Review (Institution of Electronicsand Telecommunication Engineers India) vol 28 no 3 pp 212ndash231 2011

[19] A F Monteiro M V Azevedo and A Sztajnberg ldquoVirtualizedWeb server cluster self-configuration to optimize resource andpower userdquo Journal of Systems and Software vol 86 no 11 pp2779ndash2796 2013

[20] C-C Lin H-H Chin and D-J Deng ldquoDynamic multiserviceload balancing in cloud-based multimedia systemrdquo IEEE Sys-tems Journal vol 8 no 1 pp 225ndash234 2014

[21] J Vilaplana F Solsona J Mateo and I Teixido ldquoSLA-awareload balancing in a web-based cloud system over OpenStackrdquoin Service-Oriented ComputingmdashICSOC 2013 Workshops vol

8377 of Lecture Notes in Computer Science pp 281ndash293 SpringerInternational Publishing 2014

[22] OpenStack httpwwwopenstackorg[23] OpenNebula httpwwwopennebulaorg

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World Journal 9

[7] J Vilaplana F Solsona I Teixido JMateo F Abella and J RiusldquoA queuing theory model for cloud computingrdquo The Journal ofSupercomputing vol 69 no 1 pp 492ndash507 2014

[8] A Beloglazov and R Buyya ldquoOptimal online deterministicalgorithms and adaptive heuristics for energy and performanceefficient dynamic consolidation of virtual machines in Clouddata centersrdquo Concurrency Computation Practice and Experi-ence vol 24 no 13 pp 1397ndash1420 2012

[9] D Kliazovich P Bouvry and S U Khan ldquoGreenCloud apacket-level simulator of energy-aware cloud computing datacentersrdquoThe Journal of Supercomputing vol 62 no 3 pp 1263ndash1283 2012

[10] C Ghribi M Hadji and D Zeghlache ldquoEnergy efficientVM scheduling for cloud data centers exact allocation andmigration algorithmsrdquo in Proceedings of the 13th IEEEACMInternational SymposiumonCluster Cloud andGridComputing(CCGrid rsquo13) pp 671ndash678 May 2013

[11] M F Khan Z Anwar and Q S Ahmad ldquoAssignment of per-sonnels when job completion time follows gamma distributionusing stochastic programming techniquerdquo International Journalof Scientific amp Engineering Research vol 3 no 3 2012

[12] J L Lerida F Solsona P Hernandez F Gine M Hanzichand J Conde ldquoState-based predictions with self-correction onEnterprise Desktop Grid environmentsrdquo Journal of Parallel andDistributed Computing vol 73 no 6 pp 777ndash789 2013

[13] A Goldman and Y Ngoko ldquoA MILP approach to scheduleparallel independent tasksrdquo in Proceedings of the InternationalSymposium on Parallel and Distributed Computing (ISPDC rsquo08)pp 115ndash122 Krakow Poland July 2008

[14] T Vinh T Duy Y Sato and Y Inoguchi ldquoPerformanceevaluation of a green scheduling algorithm for energy savingsin cloud computingrdquo in Proceedings of the IEEE InternationalSymposium on Parallel amp Distributed Processing Workshops andPhd Forum (IPDPSW rsquo10) pp 1ndash8 Atlanta Ga USA April 2010

[15] M Mezmaz N Melab Y Kessaci et al ldquoA parallel bi-objectivehybrid metaheuristic for energy-aware scheduling for cloudcomputing systemsrdquo Journal of Parallel and Distributed Com-puting vol 71 no 11 pp 1497ndash1508 2011

[16] Y C Ouyang Y J Chiang C H Hsu and G Yi ldquoAnoptimal control policy to realize green cloud systems with SLA-awarenessrdquo The Journal of Supercomputing vol 69 no 3 pp1284ndash1310 2014

[17] T C Ferreto M A S Netto R N Calheiros and C AF de Rose ldquoServer consolidation with migration control forvirtualized data centersrdquo Future Generation Computer Systemsvol 27 no 8 pp 1027ndash1034 2011

[18] A Murtazaev and S Oh ldquoSercon server consolidation algo-rithm using live migration of virtual machines for greencomputingrdquo IETE Technical Review (Institution of Electronicsand Telecommunication Engineers India) vol 28 no 3 pp 212ndash231 2011

[19] A F Monteiro M V Azevedo and A Sztajnberg ldquoVirtualizedWeb server cluster self-configuration to optimize resource andpower userdquo Journal of Systems and Software vol 86 no 11 pp2779ndash2796 2013

[20] C-C Lin H-H Chin and D-J Deng ldquoDynamic multiserviceload balancing in cloud-based multimedia systemrdquo IEEE Sys-tems Journal vol 8 no 1 pp 225ndash234 2014

[21] J Vilaplana F Solsona J Mateo and I Teixido ldquoSLA-awareload balancing in a web-based cloud system over OpenStackrdquoin Service-Oriented ComputingmdashICSOC 2013 Workshops vol

8377 of Lecture Notes in Computer Science pp 281ndash293 SpringerInternational Publishing 2014

[22] OpenStack httpwwwopenstackorg[23] OpenNebula httpwwwopennebulaorg

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014