ResearchArticle ...downloads.hindawi.com/journals/jcnc/2019/4754615.pdf · tions,”inProceedings...

Research ArticleSpectral Expansion Method for Cloud Reliability Analysis

K Kotteswari 1 and A Bharathi 2

1Department of Computer Science and Engineering Annai Mira College of Engg amp Techn Vellore India2Department of Information Technology Bannari Amman Institute of Technology Sathyamangalam India

Correspondence should be addressed to K Kotteswari kottikarthikeyan17gmailcom

Received 28 May 2019 Accepted 6 August 2019 Published 2 September 2019

Guest Editor Mazdak Zamani

Copyright copy 2019 K Kotteswari and A Bharathi is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

Cloud computing is a computing hypothesis where a huge group of systems is linked together in private public or hybridnetwork to offer dynamically amendable infrastructure for data storage file storage and application With this emergingtechnology application hosting delivery content storage and reduced computation cost are achieved and it acts as an essentialmodule for the backbone of the Internet of ings (IoT) e efficiency of cloud service providers (CSP) could be improved byconsidering significant factors such as availability reliability usability security responsiveness and elasticity Assessment of thesefactors leads to efficiency in designing a scheduler for CSP ese metrics also improved the quality of service (QoS) in the cloudMany existing models and approaches evaluate these metrics But these existing approaches do not offer efficient outcome In thispaper a prominent performance model named the ldquospectral expansion method (SPM)rdquo evaluates cloud reliability e spectralexpansion method (SPM) is a huge technique useful in reliability and performance modelling of the computing system isapproach solves the Markov model of cloud service providers (CSP) to predict the reliability e SPM is better compared tomatrix-geometric methods

1 Introduction

Cloud computing is a computing model for enabling expe-dient on-demand network service to a pool of computingresources such as servers storage networks services andapplications that can be promptly planned and released withminimum executive effort or service provider interface Cloudcomputing has novel characteristics such as service-orientedcomputing huge scale resource sharing and on-demandservices [1 2] Many cloud applications are developed usingmultitier architecture [3] In the traditional model one-tiertwo-tier 3-tier to N-tier models are available in the cloud toprovide n no of services based on the tier type Among thesemodels Multiple-tier or N-tier cloud is a significant modelbecause it can provideN no of service together in a single-tiermodel As it provides multiple services the maintenance ofperformance is more required to this model To maintain thecapacity of themodel the reliability evaluation is necessary forthis multitier cloud system For example Microsoft AzureCloud service in [4] and Amazon cloud service (EC2) in [5]

uses the multitier cloud environment for their web applica-tion Compared to traditional architecture themultitier cloudmodel guarantees the service level agreement (SLA) withcombined service in a single physical machine To manage theSLA the reliability of the system must be predicted Amultitier model can simultaneously manage multiple userswith a high workload To reduce the usage of power andstorage the main concept called virtualization is evolved ineach tier for better performance of the system In [6] theauthor comes out with the outcome thatmultitier architectureis the best suitable with virtualization technology iscombination can save power storage and reliability

Although various studies have proposed approachesrecently on maintaining availability and balancing powerperformance [7ndash10] no one considered reliability anothermajor factor of cloud service Reliability is the assertion thatcloud provisions are free from software faults hardwarefaults and other faults that break down the systemrsquos effi-ciency Reliability modelling is necessary for the cloud en-vironment In [11] the author evaluates the reliability model

HindawiJournal of Computer Networks and CommunicationsVolume 2019 Article ID 4754615 7 pageshttpsdoiorg10115520194754615

for maintaining the performance and power of the cloudvirtualization environment e reliability maintenance ofthe system indirectly affects performance and energy In[12] a quality model called CLOUDQUAL is proposed tomanage QoS among cloud service e quality factorsconsidered in this model are availability reliability usabilitysecurity and elasticity From this reliability is a significantfactor to achieve QoS in a cloud environment In all existingstudies the reliability is calculated in a different way andconsidered as an important parameter for QoS of the cloud

In this work the high-level performance modellingcalled the spectral expansion method is proposed to esti-mate the reliability of the cloud computing environmente spectral expansion method is a mathematical perfor-mance technique for analysis of two-dimensional Markovprocess of finite state space is Markov model occurscommonly in reliability and performance problem ofcomputing systems e Markov model of the computingsystem is first represented in matrix form to compute theeigenvalues λ and eigenvectors Ψ e eigenvalues andvectors form a linear equation ]i and solve it is solutionof the linear equation ]i determines the reliability of thesystem in graphical form e remaining section of thepaper is described as follows Section 2 discusses existingstudies Section 3 explains the background of multitiercloud environment Section 4 describes the spectral ex-pansion model and algorithm Section 5 illustrates nu-merical analysis and comparison between other modelsand finally Section 6 concludes with a conclusion andfuture work

2 Related Work

Reliability and availability are a critical requirement forcloud services and must be represented with appropriateplanning and modelling [13 14] In [15] the reliabilitymodel is focused on a virtual machine (VM) of the cloudenvironment to accomplish high performance Vishwanathand Nagappan [16] considered the reliability parameter tomaintain the consistency of the cloud-based hardwaresystem e quality of service (QoS) is improved using thereliability metric in performance analysis In [17] the authorstates that reliable service and availability services arestrongly associated with the performance analysis of cloud-based service

A reliability optimization algorithm [18] is introduced tomaintain the performance of the top banking sector de-veloped using a cloud system Xia et al [19] determined thereliability analysis of the computing system using a non-Markov stochastic Petri net (NMSPN) is method takesservice invocation and message as model input Reliabilitymodelling is done for predicting the fault tolerance ofcomputers A small change in design or insight may causehigh variation in performance modelling To prevent thevariation reliability modelling is estimated in this work [20]Peng and Huang [21] propose the reliability framework thatcollaborates failure dependencies as well as considers in-dividual services and failure source Reliability of thecomputing system [22] prevents failure and dependency

from occurring Heimann et al [23] compute the de-pendability analysis of the computer system which combinesconcepts like maintainability availability and reliabilitySystem reliability measures the instance of offensive eventsin the computing system From this instance the preventionmeasure can be applied In [24] a survey has been presentedon reliability and energy efficiency in the cloud computingsystem ey predict that key challenge in the cloud is tomanage the reliability of the system Reliability is defined inthe context of resource failure in the context of VM failurein the context of service failure or in the context of securityNachiappan et al [25] have used reliability for cloud storagescheduling in big data From the existing studies very fewreliability modelling is proposed for a cloud-based systemese studies consider only a few parameters and do notproduce efficient outcomes

In this paper the spectral expansion method (SPM) isevolved for estimation of reliability modelling is methodhas been used for performance modelling of the network-based system e main task of SPM is to solve any class ofthe Markov model is method provides a better solutioncompared to the matrix-geometric method [26] Chakka[27] used the spectral expansion technique for finding thesolution for the Markov model in some finite queue ismodel exacts solution for analysis of the Markov processe results include the performance analysis of the com-puting system e spectral expansion method is applied forthe performance and dependability analysis of the com-puting system In this work the SPM is applied to predict thereliability of cloud-based service

3 Background

In this section virtualization technology and multitier ar-chitecture designed are described

31 Virtualization Technology In recent years the virtual-ization technology has been well developed in business andacademics Virtualization technology desires to providebackground where VMs can be operated effectively andshare the resource to another host efficiently is leads toimprovement in QoS with minimized cost [28] Each VMhandles whole software development including operatingsystem middleware and application Virtualization alsoappends the abstraction layer to computer architecture formultiplexing resources among other VMs Several VMs canbe virtualized into a physical system based on its capacitye VMs can be arranged in series or parallel or distributedaccording to userrsquos needs e VMs provide many servicessuch as application service database service security serviceand software service Based on the architectural design eachVM acts as a particular cloud service provider By virtual-ization of VM into a physical system [29] we can provide alot of service within a system VM behaviour [30] ismonitored using a virtual monitor machine e VM canalso facilitate physical resources to the operation and isolatethe environment for execution of virtualization VM can alsoreduce cost consumption power consumption [31] and

2 Journal of Computer Networks and Communications

workloads [32 33]erefore VM hosts as a logical machinethat is similar to the real computer system

32 Multitier Architecture Partitioning the system archi-tecture into layers is a fundamental approach toaddressing the complexity and the order of magnitudeincreases the rate of change e system is constructed as acontinuous sequence of layers each of which is in-dependent of adjacent ones and communicates with theprevious tier via interfaces e multitier application is ascalable architecture [6] e architecture design of themultitier application cloud is good compared [34] to 3-tier application although the implementation complexityis more compared to 3-tier In 3-tier architecture it islimited and only three fundamental components or tierssuch as presentation layer business layer and data layerare used to provide services but in multitier it is notlimited It includes these three fundamental tiers and canadd many components for providing service In 3-tiersecurity component is part of the presentation layer butin multitier security tier is created as an independentlayer to provide secure applications Like this N-com-ponent and their services can be integrated into multitierapplication to provide more application and services tothe client with less cost and high performance [35] In 3-tier application the user interfaces are less interactivecompared to the multitier application It provides morescalability and availability of services compared to the 3-tier application Due to more interaction it provides moreon-demand services is on-demand service is wellsuited in cloud computing design us the multitierapplication is well suited for scheduling and provisioningcloud application in the cloud

e layers deployed in multitier architecture are asfollows e presentation layer provides an interfacebetween user and cloud server and maintains the userinterface between the client and the application server Inthe multitier pattern the presentation layer provides moreinteraction to the end-user e security layer providessecure processing of the application to the user It is aframework that provides authentication and data securityIt offers data integrity and data confidentiality servicese applications are validated and authorized to therequested client e business or domain layer imple-ments client application logic It applies the applicationlogic is layer provides all services related to applica-tion-specific functionality e domain layer is executedin one or more application servers which communicatewith the security presentation and data layers In eachapplication a separate virtual machine is deployed edata layer maintains consistency storage and simplifiesaccess to data stored in persistence storage e details ofeach application are stored in the data layer e appli-cations are developed with the help of information re-quired e data layer is implemented in one or severaldatabase servers e data layer uses many techniques tostore and retrieve data efficiently Several approaches like

caching master-slave replication SQL and NoSQL da-tabase are used

4 Spectral Expansion Method (SPM)

e initial process of evaluating the reliability of the systemis to design the Markov model for multitier cloud envi-ronment Consider the multitier cloud architecture asshown in Figure 1 with M identical virtual machines(VMs) and host machines (HMs) processing different andunbounded queue of job e VM and HM can fail fromtime to time e failure may be single and independent ormultiple and dependent In this system design both singleindependent repair and multiple dependent repair areallowed In execution of tasks in queue the VM and HMprocess a single job at a time and each job requires only oneVM processor at a timee policy applied for the failure ofthe processor is to resume repair and re-sample eservice rate failure rate and repair rate follow an expo-nential distribution

e system is modelled by SPM X(t) is the functioningstate of the system denoting the number of VM processorsrunning at time twhich varies from 0 toM Y(t) is the numberof processes waiting in the queue system and served processesat time t e irreducible Markov model representing themultitier cloud system is defined as I [X(t) Y(t)] tgt 0with state space 0 1 Mtimes 0 1 Tasks are assumed toarrive based on the Poisson process with rate λ when theoperative state X(t) i Two kinds of failures are possible Oneis an individual processor breakdown independently at rate δand is repaired independently at rate θ e second is anldquoOverallrdquo breakdown of all current VM and HM processorsat rate δ0 and the ldquoOverallrdquo repair rate of all current non-processing processors is at θM e processing state of thesystem never changes during the arrival and departure of thetasks unless if there is an independent attack towards thechanges Hence the alteration in VM and HM state of thesystem is done only in matrices P and Py

e single-move upward transition is generated by asingle task arrival HenceQ andQy the single-move upwardtransition matrices rate are defined as

Q Qy diag λ0 λ1 λM1113858 1113859 (1)

is is applicable for all values of y (y 0 1 )e single-move downward transition occurs by de-

campment of the single task that is arrived R and Ry are thesingle-move downward matrices rate Let μ be the service rateof VMandHMprocessore decamping rate of tasks at time tdepends onX(t) x andY(t) y and that is defined asRy (x x)If xgt y then every task is allocated to the processor for serviceprovision and all VM and HM processors are not occupiedthus the decamping rate Ry (x x) yμ Otherwise if xle y thenall the VM and HM processors are occupied with taskstherefore the decamping rate Ry (x x) xμ us we concludethat Ry (x x) does not rely on y if yge x and Ry does not dependupon y if ygeM erefore we have

Journal of Computer Networks and Communications 3

Ry diag [0min(y 1)μmin(y 2)μ min(y M)μ]

0 ltyltM

R diag[0 μ 2μ Mμ] ygeM

(2)

R0 is equal to zeroTo evaluate the reliability of the cloud-based system

three different states are considered based on breakdownand repair rate in the form of matrices P and Py e threestates are as follows

Case 1 In this state VM and HM processors lead to failureindependently at a rate of δ per processor Each non-functional processor has a repair rate of θ ere is nosynchronization between failure or repair of multiple VMand HM processors

e matrix Py and P are defined as

P Py (y 0 1 )

0 Mθ

δ 0 (M minus 1)θ

2δ 0 ⋱

⋱ ⋱ θ

Mδ 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(3)

Case 2 (independent failure and repairs as in state 1 andldquooverallrdquo failure occurring at rate δ0) All currently func-tioning processors fail at this rate except the independentfailure

P Py (y 0 1 )

0 Mθ

δ0 + δ 0 (M minus 1)θ

δ0 2δ 0 ⋱

⋮ ⋱ ⋱ θ

δ0 Mδ 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)

Case 3 It is similar to state 2 but in addition to this thecurrently nonfunctioning processor gets repairs simulta-neously is ldquoOverallrdquo repair occurs at θM

P Py (y 0 1 )

0 Mθ θM

δ0 + δ 0 (M minus 1)θ θM

δ0 2δ 0 ⋱ ⋮

⋮ ⋱ ⋱ θ

δ0 Mδ 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(5)

e threshold limit is given asH and it should beHMe spectral expansion model works until yH minus 1M minus 1e changes occurred in a functioning state is observed inmatrix P it is likely to find a simple form for the total averageservice rate of multiprocessor and the steady-state distri-bution of the number of functioning processors Let u be themarginal distribution of the number of functioning pro-cessors en

u q0 q1 q

M1113872 1113873 1113944

infin

y0uy (6)

is is the probability vector of matrix P minus DP and can beacquired by solving the following equation

Cloudservice

consumer

Cloudservice

developer

Cloud service provider (CSP)

Cloudservice

Securityservice

Virtualizedinfrastructure

Systemresource

Software-as-a

-service(SaaS)

Platform-as-a

-service(PaaS)

Infrastructure-as-a-service(IaaS)

Integrity

Confidentiality

Privacy

Authentication

Consistency

Servervirtualization

Storagevirtualization

Networkvirtualization

Server

Storageserver

Storage

Networkhardware

On-

dem

and

serv

ices

Figure 1 Architecture of the multitier cloud system


u P minus DP

1113872 1113873 0

uε 1(7)

en the total average service rate named as the ca-pacity of multiprocessor service is uRε and average taskarrived is uQε It can be emphasized that the cloud-basedsystem is stable when the average task arrival should be lessthan the capacity of service δ

uQεlt uRε (8)

5 Numerical Analysis

e reliability of the cloud-based system is implementedusing SHARPE tool e SHARPE tool is an analysis toolin which user-designed architecture is developed andanalysis based on spectral Expansion mechanism is doneIn this work the multitier cloud as shown in Figure 2 isdeveloped for the three types of conditions Using theabove mathematical mechanism the reliability of themultitier cloud for three types of conditions is evaluatedTo compare and evaluate the performance of the state thefollowing parameters are considered such as the capacityof service and the processors with the same service ratee overall failure rate δ0 of state 2 is reimbursed byincreasing the value of θ In type 3 δ0 is reimbursed by θMe task arrival rate the capacity of the processing systemand ergodicity condition are the same for all the threestates e three states are compared to show the per-formance evaluation among them and the arrival rate isindependent for VM and HM processors Here the systemwith 10 processors is considered for the implementationprocess

In Figure 3 the effect of the number of tasks executedE(Y) and the arrival rate of the task are described In Cases 2and 3 the repair rate and failure rate of VM and HMprocessors are more compared to Case 1is fact causes thedifferentiation of processing time between them e pro-cessing time required for Case 1 is more than Cases 2 and 3e failure rate of Cases 2 and 3 and the repair rate of Case 3tend to increase the variance of processing time compared toCase 1 As a result the reliability of the cloud system in Case3 is better compared to Case 2 and Case 1 Due to the si-multaneous failure and repair rate maintained in Case 3 theaverage number of jobs execution is increasing compared toother cases

In Figure 4 the number of processors M(Y) and theirservice rate are illustrated For a small range of N(Y) Cases 2and 3 show improving result better than Case 1 whereas forlarge M(Y) Case 1 shows better results e possible ex-planation for this is that (i) the processor availability reduceswhen both failure and repair rates increase (ii) optimal valueofM is larger for Case 1 than for Cases 2 and 3e proposedreliability modelling using SPM is compared with otherstandard reliability models such as reliability graph model[36] and hierarchical correlation model (HCM) [11] esetwo models evaluate reliability in the cloud-based system In

Case1Case2Case3

No

of t

asks

exec

uted

E (Y

)

200

160

120

80

40

03 4 5 6 7

Arrival rate

Figure 3 Reliability analysis

Taskarrival

1

2

M

Taskdeparture

VM and HMprocessor

Failure

Figure 2 Multiprocessor working mechanism

Case1Case2Case3

Service rate0 4 8 12 16 20

No

of t

asks

M (Y

)

80

60

40

20

0

Figure 4 Service rate vs M(Y)


this comparison the three-reliability model is applied tomultitier cloud system and measurements are taken in-dividually ese measurements are drawn as graph com-parison in Figure 5 e figure illustrates that the proposedreliability model is efficient than the other two models

e SPM reliability model maintains accuracy in eval-uating reliability for a long duration compared with othermodels It gives 0999997 accurate result compared toother models Analysing the reliability of multitier cloud is acomplex task e SPM reliability model can analyse thiscomplex task with best accuracy But other models show lessaccuracy compared with the proposed model

6 Conclusion

In this the reliability of the multitier cloud system isevaluated using the spectral expansion method (SPM) eSPM is developed for three cases of the multitier cloudsystem eir reliability modelling is done using SHARPEtool e comparison of the performance concludes that thesystem with simultaneous repair and failure rate works withbetter reliability us using the SPM the multitier cloud-based system can be evaluated and analysed e SPMprovides accurate reliability evaluation compared to otherstandard methods because it considers all parameters forcalculating the model us the graph results show thereliability can be maintained with failure and service rate inprocessing tasks and also the SPM model can produce ac-curate result compared to other models e future work isto implement the SPM reliability model and test on realcloud-based system

Data Availability

No data were used to support this study

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] R Buyya C S Yeo S Venugopal J Broberg and I BrandicldquoCloud computing and emerging IT platforms vision hypeand reality for delivering computing as the 5th utilityrdquo FutureGeneration Computer Systems vol 25 no 6 pp 599ndash6162009

[2] P Barham B Dragovic K Fraser et al ldquoXen and the art ofvirtualizationrdquo in ACM SIGOPS Operating Systems Reviewvol 37 pp 164ndash177 no 5 ACM Newyork NY USA 2003

[3] W Lloyd S Pallickara O David J Lyon M Arabi andK Rojas ldquoPerformance implications of multi-tier applicationdeployments on infrastructure-as-a-service clouds towardsperformance modelingrdquo Future Generation Computer Sys-tems vol 29 no 5 pp 1254ndash1264 2013

[4] S Turkarslan Technical Article for SQL Server and AzureApplication Patterns and Development Strategies for SQL Serverin Azure Virtual Machines 2014 httpmsdnmicrosoftcomen-uslibraryazuredn574746aspxcomparison

[5] M Tavis and P Fitzsimons Web Application Hosting in theAWS Cloud Site Point Melbourne Australia 2012

[6] Y Diao J L Hellerstein S Parekh H Shaikh andM Surendra ldquoControlling quality of service in multi-tier webapplicationsrdquo in Proceedings of the 26th IEEE InternationalConference on Distributed Computing Systems (ICDCSrsquo06)p 25 IEEE Lisboa Portugal July 2006

[7] E Gelenbe and R Lent ldquoEnergyndashQoS trade-offs in mobileservice selectionrdquo Future Internet vol 5 no 2 pp 128ndash1392013

[8] D Kliazovich P Bouvry and S U Khan ldquoDENS data centerenergy-efficient network-aware schedulingrdquo Cluster Com-puting vol 16 no 1 pp 65ndash75 2013

[9] Y Xia M Zhou X Luo S Pang and Q Zhu ldquoA stochasticapproach to analysis of energy-aware DVS-enabled clouddatacentersrdquo IEEE Transactions on Systems Man and Cy-bernetics Systems vol 45 no 1 pp 73ndash83 2015

[10] G Nalinipriya K G Maheswari B Balusamy K Kotteswariand A Kumar Sangaiah ldquoAvailability modeling for multi-tiercloud environmentrdquo Intelligent Automation amp Soft Com-puting vol 23 no 3 pp 485ndash492 2017

[11] X Qiu Y Dai Y Xiang and L Xing ldquoA hierarchical cor-relation model for evaluating reliability performance and

1

095

09

085

08

075

07

065

060 50 100 150 200 250 300 350 400 450

Relia

bilty

Time (hours)

SPMRelibilty graphHCM

Figure 5 Comparison with other reliability models


power consumption of a cloud servicerdquo IEEE Transactions onSystems Man and Cybernetics Systems vol 46 no 3pp 401ndash412 2016

[12] X Zheng P Martin K Brohman and L D XuldquoCLOUDQUAL a quality model for cloud servicesrdquo IEEETransactions on Industrial Informatics vol 10 no 2pp 1527ndash1536 2014

[13] N Kryvinska C Strauss and Z Peter ldquoA model to providehigher services availability for the mission critical applica-tionsrdquo in Proceedings of the International Conference onAmbient Systems Networks and Technologies (ANT-2010) inConjunction with iiWAS2010 vol 8ndash10 pp 221ndash229 ParisFrance November 2010

[14] N Kryvinska and C Strauss ldquoConceptual model of businessservices availability vs interoperability on collaborative IoT-enabled eBusiness platformsrdquo in Internet of Bings and Inter-cooperative Computational Technologies for Collective In-telligence pp 167ndash187 Springer Berlin Germany 2013

[15] Y S Dai B Yang J Dongarra and G Zhang ldquoCloud servicereliability modeling and analysisrdquo in Proceedings of the 15thIEEE Pacific Rim International Symposium on DependableComputing pp 1ndash17 Shanghai China November 2009

[16] K V Vishwanath and N Nagappan ldquoCharacterizing cloudcomputing hardware reliabilityrdquo in Proceedings of the 1stACM Symposium on Cloud Computing pp 193ndash204 ACMIndianapolis IN USA June 2010

[17] E Bauer and R Adams Reliability and Availability of CloudComputing John Wiley amp Sons Hoboken NJ USA 2012

[18] Y Liu W Liu J Song and H He ldquoAn empirical study onimplementing highly reliable stream computing systems withprivate cloudrdquo Ad Hoc Networks vol 35 pp 37ndash50 2015

[19] Y Xia X Luo L Jia and Q Zhu ldquoA petri-net-based approachto reliability determination of ontology-based service com-positionsrdquo IEEE Transactions on Systems Man and Cyber-netics Systems vol 43 no 5 pp 1240ndash1247 2013

[20] W G Bouricius W C Carter D C Jessep P R Schneiderand A B Wadia ldquoReliability modeling for fault-tolerantcomputersrdquo IEEE Transactions on Computers vol C-20no 11 pp 1306ndash1311 1971

[21] K-L Peng and C-Y Huang ldquoReliability analysis of on-de-mand service-based software systems considering failuredependenciesrdquo IEEE Transactions on Services Computingvol 10 no 3 pp 423ndash435 2017

[22] A Zhou S Wang B Cheng et al ldquoCloud service reliabilityenhancement via virtual machine placement optimizationrdquoIEEE Transactions on Services Computing vol 10 no 6pp 902ndash913 2017

[23] D I Heimann N Mittal and K S Trivedi ldquoAvailability andreliability modeling for computer systemsrdquo in Advances inComputers vol 31 pp 175ndash233 Elsevier AmsterdamNetherlands 1990

[24] Y Sharma B Javadi W Si and D Sun ldquoReliability andenergy efficiency in cloud computing systems survey andtaxonomyrdquo Journal of Network and Computer Applicationsvol 74 pp 66ndash85 2016

[25] R Nachiappan B Javadi R N Calheiros and K M MatawieldquoCloud storage reliability for Big Data applications a state ofthe art surveyrdquo Journal of Network and Computer Applica-tions vol 97 pp 35ndash47 2017

[26] I Mitrani and R Chakka ldquoSpectral expansion solution for aclass of Markov models application and comparison with thematrix-geometric methodrdquo Performance Evaluation vol 23no 3 pp 241ndash260 1995

[27] R Chakka ldquoSpectral expansion solution for some finite ca-pacity queuesrdquo Annals of Operations Research vol 79pp 27ndash44 1998

[28] M Armbrust A Fox R Griffith et al ldquoAbove the clouds aberkeley view of cloud computingrdquo Technical Report NoUCBEECS-2009-28 Electrical Engineering and ComputerSciences University of California Berkeley CA USA 2009

[29] J Schad J Dittrich and J-A Quiane-Ruiz ldquoRuntime mea-surements in the cloud observing analyzing and reducingvariancerdquo Proceedings of the VLDB Endowment vol 3 no 1-2 pp 460ndash471 2010

[30] S Fu ldquoFailure-aware resource management for high-avail-ability computing clusters with distributed virtual machinesrdquoJournal of Parallel and Distributed Computing vol 70 no 4pp 384ndash393 2010

[31] Y Ding X Qin L Liu and T Wang ldquoEnergy efficientscheduling of virtual machines in cloud with deadline con-straintrdquo Future Generation Computer Systems vol 50pp 62ndash74 2015

[32] W Zhang J Liu C Liu Q Zheng andW Zhang ldquoWorkloadmodeling for virtual machine-hosted applicationrdquo ExpertSystems with Applications vol 42 no 4 pp 1835ndash1844 2015

[33] X Xu H Jin S Wu and Y Wang ldquoRethink the storage ofvirtual machine images in cloudsrdquo Future Generation Com-puter Systems vol 50 pp 75ndash86 2015

[34] M S Rehman and M F Sakr ldquoInitial findings for pro-visioning variation in cloud computingrdquo in Procedings of the2010 IEEE Second International Conference on Cloud Com-puting Technology and Science (CloudCom) pp 473ndash479IEEE Indianapolis IN USA December 2010

[35] X Bu R Jia and C-Z Xu ldquoA reinforcement learning ap-proach to online web systems auto-configurationrdquo in Pro-ceedings of the 2009 29th IEEE International Conference onDistributed Computing Systems (ICDCSrsquo09) pp 2ndash11 IEEEMontreal Canada June 2009

[36] T A Nguyen DMin E Choi and T D Tran ldquoReliability andavailability evaluation for cloud data center networks usinghierarchical modelsrdquo IEEE Access vol 7 pp 9273ndash9313 2019


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for maintaining the performance and power of the cloudvirtualization environment e reliability maintenance ofthe system indirectly affects performance and energy In[12] a quality model called CLOUDQUAL is proposed tomanage QoS among cloud service e quality factorsconsidered in this model are availability reliability usabilitysecurity and elasticity From this reliability is a significantfactor to achieve QoS in a cloud environment In all existingstudies the reliability is calculated in a different way andconsidered as an important parameter for QoS of the cloud

In this work the high-level performance modellingcalled the spectral expansion method is proposed to esti-mate the reliability of the cloud computing environmente spectral expansion method is a mathematical perfor-mance technique for analysis of two-dimensional Markovprocess of finite state space is Markov model occurscommonly in reliability and performance problem ofcomputing systems e Markov model of the computingsystem is first represented in matrix form to compute theeigenvalues λ and eigenvectors Ψ e eigenvalues andvectors form a linear equation ]i and solve it is solutionof the linear equation ]i determines the reliability of thesystem in graphical form e remaining section of thepaper is described as follows Section 2 discusses existingstudies Section 3 explains the background of multitiercloud environment Section 4 describes the spectral ex-pansion model and algorithm Section 5 illustrates nu-merical analysis and comparison between other modelsand finally Section 6 concludes with a conclusion andfuture work

2 Related Work

Reliability and availability are a critical requirement forcloud services and must be represented with appropriateplanning and modelling [13 14] In [15] the reliabilitymodel is focused on a virtual machine (VM) of the cloudenvironment to accomplish high performance Vishwanathand Nagappan [16] considered the reliability parameter tomaintain the consistency of the cloud-based hardwaresystem e quality of service (QoS) is improved using thereliability metric in performance analysis In [17] the authorstates that reliable service and availability services arestrongly associated with the performance analysis of cloud-based service

A reliability optimization algorithm [18] is introduced tomaintain the performance of the top banking sector de-veloped using a cloud system Xia et al [19] determined thereliability analysis of the computing system using a non-Markov stochastic Petri net (NMSPN) is method takesservice invocation and message as model input Reliabilitymodelling is done for predicting the fault tolerance ofcomputers A small change in design or insight may causehigh variation in performance modelling To prevent thevariation reliability modelling is estimated in this work [20]Peng and Huang [21] propose the reliability framework thatcollaborates failure dependencies as well as considers in-dividual services and failure source Reliability of thecomputing system [22] prevents failure and dependency

from occurring Heimann et al [23] compute the de-pendability analysis of the computer system which combinesconcepts like maintainability availability and reliabilitySystem reliability measures the instance of offensive eventsin the computing system From this instance the preventionmeasure can be applied In [24] a survey has been presentedon reliability and energy efficiency in the cloud computingsystem ey predict that key challenge in the cloud is tomanage the reliability of the system Reliability is defined inthe context of resource failure in the context of VM failurein the context of service failure or in the context of securityNachiappan et al [25] have used reliability for cloud storagescheduling in big data From the existing studies very fewreliability modelling is proposed for a cloud-based systemese studies consider only a few parameters and do notproduce efficient outcomes

In this paper the spectral expansion method (SPM) isevolved for estimation of reliability modelling is methodhas been used for performance modelling of the network-based system e main task of SPM is to solve any class ofthe Markov model is method provides a better solutioncompared to the matrix-geometric method [26] Chakka[27] used the spectral expansion technique for finding thesolution for the Markov model in some finite queue ismodel exacts solution for analysis of the Markov processe results include the performance analysis of the com-puting system e spectral expansion method is applied forthe performance and dependability analysis of the com-puting system In this work the SPM is applied to predict thereliability of cloud-based service

3 Background

In this section virtualization technology and multitier ar-chitecture designed are described

31 Virtualization Technology In recent years the virtual-ization technology has been well developed in business andacademics Virtualization technology desires to providebackground where VMs can be operated effectively andshare the resource to another host efficiently is leads toimprovement in QoS with minimized cost [28] Each VMhandles whole software development including operatingsystem middleware and application Virtualization alsoappends the abstraction layer to computer architecture formultiplexing resources among other VMs Several VMs canbe virtualized into a physical system based on its capacitye VMs can be arranged in series or parallel or distributedaccording to userrsquos needs e VMs provide many servicessuch as application service database service security serviceand software service Based on the architectural design eachVM acts as a particular cloud service provider By virtual-ization of VM into a physical system [29] we can provide alot of service within a system VM behaviour [30] ismonitored using a virtual monitor machine e VM canalso facilitate physical resources to the operation and isolatethe environment for execution of virtualization VM can alsoreduce cost consumption power consumption [31] and










Q Qy diag λ0 λ1 λM1113858 1113859 (1)





0 ltyltM


(2)





P Py (y 0 1 )

0 Mθ

δ 0 (M minus 1)θ

2δ 0 ⋱

⋱ ⋱ θ

Mδ 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(3)


P Py (y 0 1 )

0 Mθ


δ0 2δ 0 ⋱

⋮ ⋱ ⋱ θ

δ0 Mδ 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)


P Py (y 0 1 )

0 Mθ θM


δ0 2δ 0 ⋱ ⋮

⋮ ⋱ ⋱ θ

δ0 Mδ 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(5)


u q0 q1 q

M1113872 1113873 1113944

infin

y0uy (6)


Cloudservice

consumer

Cloudservice

developer


Cloudservice

Securityservice


Systemresource

Software-as-a

-service(SaaS)

Platform-as-a

-service(PaaS)


Integrity

Confidentiality

Privacy

Authentication

Consistency




Server

Storageserver

Storage

Networkhardware

On-

dem

and

serv

ices



u P minus DP

1113872 1113873 0

uε 1(7)


uQεlt uRε (8)





Case1Case2Case3

No

of t

asks

exec

uted

E (Y

)

200

160

120

80

40

03 4 5 6 7

Arrival rate


Taskarrival

1

2

M

Taskdeparture

VM and HMprocessor

Failure


Case1Case2Case3


No

of t

asks

M (Y

)

80

60

40

20

0





6 Conclusion


Data Availability




References












1

095

09

085

08

075

07

065

060 50 100 150 200 250 300 350 400 450

Relia

bilty

Time (hours)

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










Q Qy diag λ0 λ1 λM1113858 1113859 (1)





0 ltyltM


(2)





P Py (y 0 1 )

0 Mθ

δ 0 (M minus 1)θ

2δ 0 ⋱

⋱ ⋱ θ

Mδ 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(3)


P Py (y 0 1 )

0 Mθ


δ0 2δ 0 ⋱

⋮ ⋱ ⋱ θ

δ0 Mδ 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)


P Py (y 0 1 )

0 Mθ θM


δ0 2δ 0 ⋱ ⋮

⋮ ⋱ ⋱ θ

δ0 Mδ 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(5)


u q0 q1 q

M1113872 1113873 1113944

infin

y0uy (6)


Cloudservice

consumer

Cloudservice

developer


Cloudservice

Securityservice


Systemresource

Software-as-a

-service(SaaS)

Platform-as-a

-service(PaaS)


Integrity

Confidentiality

Privacy

Authentication

Consistency




Server

Storageserver

Storage

Networkhardware

On-

dem

and

serv

ices



u P minus DP

1113872 1113873 0

uε 1(7)


uQεlt uRε (8)





Case1Case2Case3

No

of t

asks

exec

uted

E (Y

)

200

160

120

80

40

03 4 5 6 7

Arrival rate


Taskarrival

1

2

M

Taskdeparture

VM and HMprocessor

Failure


Case1Case2Case3


No

of t

asks

M (Y

)

80

60

40

20

0





6 Conclusion


Data Availability




References












1

095

09

085

08

075

07

065

060 50 100 150 200 250 300 350 400 450

Relia

bilty

Time (hours)

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0 ltyltM


(2)





P Py (y 0 1 )

0 Mθ

δ 0 (M minus 1)θ

2δ 0 ⋱

⋱ ⋱ θ

Mδ 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(3)


P Py (y 0 1 )

0 Mθ


δ0 2δ 0 ⋱

⋮ ⋱ ⋱ θ

δ0 Mδ 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(4)


P Py (y 0 1 )

0 Mθ θM


δ0 2δ 0 ⋱ ⋮

⋮ ⋱ ⋱ θ

δ0 Mδ 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(5)


u q0 q1 q

M1113872 1113873 1113944

infin

y0uy (6)


Cloudservice

consumer

Cloudservice

developer


Cloudservice

Securityservice


Systemresource

Software-as-a

-service(SaaS)

Platform-as-a

-service(PaaS)


Integrity

Confidentiality

Privacy

Authentication

Consistency




Server

Storageserver

Storage

Networkhardware

On-

dem

and

serv

ices



u P minus DP

1113872 1113873 0

uε 1(7)


uQεlt uRε (8)





Case1Case2Case3

No

of t

asks

exec

uted

E (Y

)

200

160

120

80

40

03 4 5 6 7

Arrival rate


Taskarrival

1

2

M

Taskdeparture

VM and HMprocessor

Failure


Case1Case2Case3


No

of t

asks

M (Y

)

80

60

40

20

0





6 Conclusion


Data Availability




References












1

095

09

085

08

075

07

065

060 50 100 150 200 250 300 350 400 450

Relia

bilty

Time (hours)

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


u P minus DP

1113872 1113873 0

uε 1(7)


uQεlt uRε (8)





Case1Case2Case3

No

of t

asks

exec

uted

E (Y

)

200

160

120

80

40

03 4 5 6 7

Arrival rate


Taskarrival

1

2

M

Taskdeparture

VM and HMprocessor

Failure


Case1Case2Case3


No

of t

asks

M (Y

)

80

60

40

20

0





6 Conclusion


Data Availability




References












1

095

09

085

08

075

07

065

060 50 100 150 200 250 300 350 400 450

Relia

bilty

Time (hours)

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




6 Conclusion


Data Availability




References












1

095

09

085

08

075

07

065

060 50 100 150 200 250 300 350 400 450

Relia

bilty

Time (hours)

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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