research article a green strategy for federated and...
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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
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Distributed Sensor Networks
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International Journal of
ReconfigurableComputing
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Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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ArtificialNeural Systems
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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
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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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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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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
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Applied Computational Intelligence and Soft Computing
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ArtificialNeural Systems
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Industrial EngineeringJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Advances in
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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
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ReconfigurableComputing
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Applied Computational Intelligence and Soft Computing
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
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ArtificialNeural Systems
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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
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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