Development of Mathematical Model for Market-Oriented Cloud Computing

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1 Intenational Jounal of Compute Applications ( ) Volume 9 No.11, Novembe 2010 Development of Mathematical Model fo Maket-Oiented Cloud Computing K.Mukhejee Depatment of Compute Science & Engineeing. Bila Institute of Technology Mesa, Ranchi, India G.Sahoo Depatment of Infomation Technology Bila Institute of Technology Mesa, Ranchi, India ABSTRACT Cloud computing is an emeging appoach to a shaed infastuctue of computing esouces in which lage pools of systems o clouds ae linked togethe via the intenet to povide IT sevices, such as secuely managing billions of online tansactions and othe highly data-intensive application. Cloud computing is being diven by seveal factos, including the damatic gowth of connected devices, such as mobile phones, smat cads and othe devices. It can be used to beak many computing tasks into many smalle pieces and managed in paallel on a massive scale. Thus, Cloud computing offes a simplified, centalized platfom fo use when needed, loweing costs and enegy use. But cloud computing is in its nascent stage of pogession. Thee ae no mathematical models egading the pefomance analysis of cloud computing. In this pape, we intend to intoduce Mathematical Model fo cloud computing. Keywods Web Sevice; Ant System; Scalability 1. INTRODUCTION Cloud computing povides a platfom fo the execution of massive tasks on cloud instead of the execution of tasks on uses Pesonal Computes, Seves etc. It is vey beneficial fo small oganizations that cannot affod huge investment on thei IT secto but at the same time expect maximum benefit fom this suppoting industy in ode to suvive in today s complex competitive business wold. Cloud computing can help such oganizations by poviding massive computing powe, unlimited stoage capacity, less maintenance cost, availability of useful web-sevices etc. As pe Buyya et. all [7], A Cloud is a type of paallel as well as distibuted system consisting of a collection of inteconnected and vitualized computes that ae dynamically povisioned and pesented as one o moe unified computing esouces based on sevice-level ageements established though negotiation between the sevice povide and consume. The definition clealy implies that thee is a Sevice Level Ageement (SLA) between the povide and the consume fo getting sevices fom cloud on pay pe use basis. Actually Cloud computing offes the thee layes of abstaction such as Infastuctue as a Sevice (IaaS), Platfom as a Sevice(PaaS), Softwae as a Sevice (SaaS). SaaS povides diffeent types of applications as a Sevice fo the end use. It includes diffeent useful web-sevices. PaaS povides a standad platfom fo bette execution of application with pope exploitation of physical esouces using Middlewae Sevices. PaaS includes Database sevices, Middlewae Sevices etc, In this endeavo we intend to thow light on Softwae as a sevice (SaaS). IaaS povides the infastuctue of cloud consisting of physical esouces like CPU, Stoage, and Netwok etc. Again middlewae of PaaS consists of Coe Middlewae and use level middlewae. Coe Middlewae povides a set of sevices [7] including Admission Contolle, Sevice Request Examine Monitoing, Accounting Billing etc; wheeas the use level middlewae povides access point of sevices as deliveed by the Coe Middlewae. The Sevice Request Examine and Admission Contolle accepts the equest afte ensuing that thee is an availability of esouces fo caying out the equest. Fo this, the Sevice Request Examine and Admission Contolle inteacts continuously with Vitual Machine Monito mechanism egading esouce availability; while the Picing Mechanism decides the chages fo equest sevice. The final cost of the equest sevice is fixed by the Accounting Mechanism, based on the actual usage of esouces fo the equested sevice. The ole of Vitual Machine Monito Mechanism is to keep tack of the availability of Vitual Machines (VM). The Dispatche Mechanism executes the tasks on allocated Vitual Machines, whee as the Sevice Request Monito keeps tack of the execution of the sevice equest. The Vitual Machines execute the job on physical machines, which consist of multiple computing seves, data stoage etc. It is obseved that pefomance monitoing of any application in PaaS is always complex, diffeent and challenging. In the absence of pecise knowledge about the availability of esouces at any point of time and due to the dynamic esouce usage scenaio, pediction-based analysis is not possible. Thus, pefomance analysis in PaaS must be chaacteized by dynamic data collection (as pefomance poblems must be identified duing un-time), data eduction (as the amount of monitoing data is lage), low-cost data captuing (as ovehead due to instumentation and pofiling may contibute to the application pefomance), and adaptability to heteogeneous envionment. Just like the day to day utility sevices such as wate, gas, electicity etc ae essential fo the smooth unning of ou daily lives; the tend of cloud computing [16] is also to povide diffeent IT esouces on demand on a pay pe use basis. The IT esouces include diffeent computational web sevices of diffeent natue like tax calculation web sevice, weathe infomation web sevice, shipping status web sevice etc. The aim of Cloud computing is to be global and to povide such computational web sevices to the masses, anging fom the end use that hosts its pesonal documents on the intenet to entepises outsoucing thei entie IT infastuctue to extenal data centes. In fact, Cloud has given a new appoach to make IT a eal utility which is global and complete fo the end uses. The agenda of computational web sevice of SaaS is to offe simple 19

2 Intenational Jounal of Compute Applications ( ) Volume 9 No.11, Novembe 2010 web methods that computational clients can call to pefom application specific computation on thei own data. Web Sevices ae pogammable and eusable. They ae available anywhee via the intenet. Pogams built on the basis of this model will un acoss multiple websites extacting infomation fom each of them and combining and deliveing it in a customized fom to any device anywhee in the wold. The potential of web sevices is unlimited. Fo example, a softwae company may povide a web sevice to calculate income tax. Any company that wants to calculate income tax can subscibe to this web sevice. The company offeing the sevice can dynamically update it to accommodate new taxation ates. The subscibes need not to do anything to get the new updates. In futue a collection of such web sevices may eplace packaged softwae. As web sevices beak down the distinction between the intenet, standalone applications and computing devices of evey kind, they enable business to collaboate and offe an unpecedented ange of integated and customized solutions that enable thei customes to act on infomation at any time, any place and on any device. Oganization of this pape is as follows: Related wok is discussed in Section II. Poposed Mathematical Model of Cloud Computing is discussed in Section III. Poposed Algoithm is discussed in Section IV. Section V and Section VI give details of the expeimental setup and esults. Section 7 concludes with a diection of the futue wok.. 2. RELATED WORK The potentiality of computing utility was fist pointed by Leonad Kleinock[1], one of the pionee eseache, who seeded the idea of intenet. He had pedicted long back, egading the wide use of compute utilities as ou day to day utilities like Electical Utilities, Telephone Utilities etc. Today, his vision came into existence in the fom of Cloud computing. Cloud computing povides diffeent utilities in the fom of websevices, which ae pay pe use basis. Most of the existing wok in web sevice pefomance focuses on the latest tend of technologies and standads. Andeozzi et al. [2] pesent a model fo igoous epesentation of sevice chaacteistics. Gouscos et al. [3] pesents a simple appoach to model cetain web sevice management attibutes. Thomas et al.[4] epesent distibuted web sevice by modeling the flow of messages and methods in a web sevice tansaction. Tue et al.[5] discuss design stategies to impove the pefomance of web sevice. Levy et al.[6] pesent an achitectue and pototype implementation of pefomance management system fo cluste based web sevice. Cadellini et al. [15] conside diffeent categoies of web applications, and evaluate how static, dynamic and secue web sevice equests affect pefomance and quality of sevice at distibuted web sites. Buyya et. al.[7] have poposed the use of maket oiented esouce management in ode to egulate the supply and demand of cloud esouces at maket equilibium. Again Buiya et. They have poposed the achitectue fo maket oiented allocation of esouces within clouds. Xinhui et. al. [9] have poposed total cost of owneship of cloud computing using a suite of metics and fomulas. But none of above mentioned woks have given any systematic mathematical model egading the analysis of cloud computing. 3. PROPOSED MATHEMATICAL MODEL OF MARKED ORIENTED CLOUD COMPUTING In this pape, we pesent a mathematical model of Maketoiented cloud. The achitectue of maket oiented cloud computing[7] implies that thee ae thee impotant agents viz. Vitual Machine(VM) Monito, Dispatche and Sevice Request Monito, which collectively guide the sevice equest examine and contolle, whethe to accept a job o not and if accepted, how to execute the job effectively and efficiently. Fo these agents to wok effectively and efficiently, we popose Bee and Ant colony system. It is obseved that honey bees [17] wok in a decentalized, self oganized manne. The honey bee colonies pactice division of labo between the foges, who wok in the field collecting the necta and the food-stoes who wok in the hive to stoe necta. The foge bees seach the necta at andom and afte getting specific necta it etuns back to the hive and stats dancing in ode to motivate the followe foges to access that vey necta. The duation of this dance is closely coelated with the seach time expeienced by the dancing bees. The VM Monito is consideed as a hive that consists of bee agents. Fom the bee hive, the agents stat to exploe fo the pupose of collecting the infomation egading esouce availability. Afte etuning to the hive, they stat to pefom dances on the dancing floo in ode to communicate about the food souce i.e. the availability of Vitual Machines. The oientation as well as the duation of dance of bees infom the othe bees egading the exact place as well as its ichness[12][13][14]. Thee ae two types of dance of bees viz. temble dance(t.d) and waggle dance(w.d). The W.D of bees implies that thee is no availability of Vitual Machine fo caying out the new job, whee as the T.D dance of bees implies the availability of V.M fo caying out new jobs. The bees existing in the Sevice Request Monito hive obseve the temble dance of the bees on the dancing floo by VM Monito bees and hence stat to find the necta (i.e. available VMs), in ode to eschedle the pending jobs on the available VMs and hence enhance the pefomance of the Cloud. The waggle dance helps the Sevice Request Contolle and Examine to take the decision of not accepting any new job, wheeas temble dance helps the Sevice Request Contolle and Examine to entetain new jobs and to cay out jobs on V.M by the Dispatche. Now in ode to enhance the pefomance of dispatche, we popose that dispatche should use ant colony system in ode to assign jobs to the available V.Ms. Ant System was poposed by Doigo et al.[18]at the yea In Ant System, ants built tou based on pobabilistic action choice ule, called andom popotional ule. Ant Colony woks to find the shotest paths between food souces and nest[18].due to thei esticted visibility, ants inteact among themselves, by dopping a chemical known as pheomone, which guides them on thei way fom the nest to the food souce and vice vesa. In this pape neithe ant system no bee colony has been discussed in details. In this pape, we have poposed the Mathematical Model of cloud and tavesing cost of job assignment to diffeent VMs by the Dispatche. Thus ole of VM Monito and Sevice Request Monito ae beyond the scope of this pape. Hee we have focused only on the ole of Dispatche in ode to allocate jobs to 20

3 Intenational Jounal of Compute Applications ( ) Volume 9 No.11, Novembe 2010 available VMs based on ant colony system. Fo this, we have poposed a Mathematical Model. In ode to pesent ou new mathematical model, let us conside undiected gaph G(V,A,C), whee V= { 0,1,2,..,n} is a set of nodes epesenting Vitual Machines. Hee we assume that node 0 epesents the dispatche, wheeas node 1 and onwads epesenting available Vitual Machines. Let A = { (i,j): i,j ε V, i j} is a set of acs joining the nodes, having a tavel cost(i.e. distances). Let C = { c ij: i,j ε V, i j } is the cost of tavese between the nodes. Let Ω be the total numbe of ants each with capacity ξ c, assign jobs to M c (Vitual Machine) based on the stochastic demands. Hee Vitual Machine demands ae stochastic vaiables Ψ i, whee i = { 0,1,, n}, which ae independently distibuted with known distibutions. Hee the actual demand of each Vitual Machine is not known unless and until the ant is not aiving at the Vitual Machine. Hee we assume that the demand Ψ i does not exceed the ξ c and follows a discete distibution and pobability mass function p id. p id = Pob(Ψ i = d), Whee d is demand of Vitual Machine and d ε W, set of Whole Numbe. Accoding to the Vitual Machine s actual demand the ant decides whethe to poceed to the next Vitual Machine o to go back to the job execute fo estocking of new job. Sometimes the choice of estocking is bette one, when the ants ae not caying any jobs to assign o do not have sufficient load to seve poceeding Vitual Machine s demand. This action is called peventive estocking. The goal of peventive estocking is backtacking of the ants when they do not have sufficient jobs to assign poceeding Vitual Machine. Thus ants make back and foth tip to the job execute and Vitual Machine fo assigning the jobs to the available Vitual Machine. Let Z i,j,k = Binay flow vaiable Obviously Z i,j,k = 1, if path(i,j) is tavesed by k th agent. = 0, othewise J i,k = Quantity of job is supplied at i th Vitual Machine by k th agent. Ω = Total Numbe of ants initially available at the Job Execute. δ = Remaining jobs associated with the ants. A c = Capacity of ants fo caying out jobs. ф jk p ( δ) = Expected Cost of the move fowad action. ф jk ( δ) = Expected cost of peventive estocking. If ф jk ( δ) is the job assignment to the j th Vitual Machine by the k th ant then ou poposed objective function is: ф jk ( δ) = Minimum ( ф jk p ( δ), ф jk ( δ)) Whee the paametes ae given below: ф jk p (δ)=c j,j+1+ ф j+1,k(δ-d)p i+1,d + 1 d:d<= δ + [2C j+1,0+ф j+1,k(δ+a c-d)p j+1,d] d:d>δ Again ф jk ( δ) be given as: ф jk ( δ) = C j, 0 + C 0, j+1 + ф j+1,k (A c-d)p j+1,d 2 D d=1 Now we discuss two cases as follows: Case I : When δ is geate than next Vitual Machines demand. Fo (j+1) th Vitual Machine, we have only ф j+1,k(δ-d)p i+1,d d: d <= δ Case II : When δ is less than next Vitual Machines demand. Fo (j+1) th Vitual Machine, we have [2C j+1,0+ф j+1,k(δ+a c-d)p j+1,d] Again 2C j+1,0 is the cost of taveling to the job execute and back to oute C j,0 is the distance cost fom j th custome back to Job Execute. C 0,j+1 is the distance cost fom job execute i.e. 0 to j+1 th Vitual Machine. 4. PROPOSED ALGORITHM Based upon the above discussion, the poposed algoithms ae given below: Pocedue Use_Request_Submission (jobs) Boolean flag flag SRBAC(jobs) if (flag = 0) then else wite( Request can not be caied out) wite( Request is accepted ) function Boolean SRBAC (jobs) Boolean flag. flag VMMonito(Request fo checking of If (flag =0) Resouce Avablity) 21

4 Intenational Jounal of Compute Applications ( ) Volume 9 No.11, Novembe 2010 Retun(false) Else do submit Expected_Cost (jobs) Retun(tue) end Function Boolean VMMonito (Request_fo Checking_of Resouce_Avablity) Boolean flag Bee stoes in hive. Foge Bees fom Hive stats to seach fo necta i.e. Availability of VMs. Foge Bees etun back and stat dancing on the dancing floo. If (dance be Waggle Dance) then Retun( false.) else do Call Seve_Request_Monito() Retun(Tue) Pocedue Seve_Request_Monito() Reschedule the Pending jobs Pocedue Expected_cost (job) Cost Submit_jobs_to_Dispatche (jobs) Wite(Expected Cost fo Tavesing is equal to Cost) Function Submit_jobs_to_Dispache(jobs) [Initialization] Set δ A c Set j ξ l // ξ l is last VM accessed by l th Ant Set T1 0 Set T2 0 Set k 1 N Max_No_of_Vitual_Machine Repeat until k N Repeat until δ 0 Repeat until j 1 Compute ф jk ( δ) using 2 T1 T1+ ф jk ( δ) j j - 1 Compute ф jk p (δ) using 1 T2 T2 + ф jk p (δ) δ δ-1 k k+1 T T1 + T2 Retun (T). 5. EXPERIMENTAL SETUP A pivate cloud has been setup based on Ubuntu s Seve edition, that consists of two Seves Seve A and Seve B. Seve A acts as the cloud, cluste, waehouse and stoage contolle and Seve B acts as node contolle. We configued Machine A on a Coe2duoX6800 pocesso based machine with 2GB DDR 2 RAM and 80 GB Had disk. Machine B is unning on an AMD PhenomeII X4 965 pocesso with 4 GB DDR 3 RAM and 250 GB Had disk. The nodes communicate though a fast local aea netwok. This pape demonstates the esults of local accessing of multiple web sevices unning on the web seves. Expeiments have been caied out on above mentioned cloud envionment. In ode to execute the web sevices on Machine A, we have used the following commands: If [! e ~/.euca/mkey.piv]; then fi mkdi p m 700 ~/.euca touch ~/.euca/mykey.piv chmod 0600 ~/.euca/mykey.piv euca-add-keypai mykey > ~/.euca > ~/.euca/mykey Thus ceating keypai, we now log into ou instance as oot. Afte that, we can monito state of instance using the command: watch n5 euca-descibe-instances Thus we stat to access diffeent web sevices. 6. RESULTS We have expeimented with two diffeent web sevices. Howeve, in ode to demonstate the effectiveness of ou system, we submitted multiple images of the same web sevices as sepaate jobs. The jobs have been initiated at diffeent times. The analysis of stochastic demand vesus objective function, based upon ou expeiments, is shown in figue 1. 22

5 Intenational Jounal of Compute Applications ( ) Volume 9 No.11, Novembe 2010 The figue1 clealy implies that as stochastic demand gadually inceases ou poposed objective function slowly inceases and povides moe optimized value when the stochastic demand is within a modeate to maximum ange. At maximum stochastic demand, we do not find the best pefomance exhibited by ou poposed objective function. This fact has been pointed by the colo code. The eddish pat of the colo code implies that the objective function has attained its optimized value and futhe incease of stochastic demand stats its etadation. This fact is tue fo all categoies of jobs including vey small amount of jobs, modeate jobs o fo huge jobs. This fact is shown by diffeent colo cuve in figue1.this suf deteioations of the objective function is due to moe back and foth movements of the ants in ode to assign the jobs to the available VMs, povided that the stochastic demands of VMs ae vey high. Again we obseve that initially when stochastic demand is vey less then also objective function attains its optimized value gadually due to othe paametes like escheduling of the pending jobs by Sevice Request Monito (which takes place befoe Dispatche that dispatches the new jobs to the available VMs.). In this expeiment we have consideed thee values of the stochastic demands, 5-10 value of stochastic demand implies low demand whee as values implies high demand and value 15 implies exteme stochastic demand. 8. CONCLUSIONS AND FUTURE DIRECTION OF WORK In this endeavo we have emphasized on the ole of Dispatche in ode to allocate jobs to available VMs. We have seen that as stochastic demand of VMs is within a specific ange, the pefomance of the Dispatche is the best and the objective function is optimized. But futhe incease in stochastic demand leads the ants to move back and foth moe than eve in ode to assign the jobs to Dispatche and hence a negative impact is obseved in the pefomance of the objective function. Futhe the oles of Vitual Machine Monito and Sevice Request Monito have not discussed in this pape, we intend to do so in ou fothcoming endeavo. 9. REFERENCES [1] L.Keleinock. A vision fo the Intenet. ST Jounal of Reseach, Nov.2005, pages 4-5 [2] S.Adeozzi, P. Ciancaini, D. Montesi, R. Moetti, Towads a model fo quality of web and gid sevice In Poc 13th IEEE intenational Wokshops on Enabling Technologies: Infastuctue fo Colloboative Entepises(WET ICE 04), 2004, page ,. [3] D. Gouscos, M. Kalikakis, and P. Geogiadis. An appoach to modeling Web sevice QoS and povision pice, in Poceding 3 d Intenational Confeence on Web Infomation Systems Engineeing Wokshops, 2003,pages [4] J.P Thomas, M.Thomas and G.Ghinea Modeling of Web sevice flow, in Poceeding IEEE Intenational Confeence on E-Commece (CEC 03), 2003, pages ,. [5] S.Tu, M.Flanagin Y. Wu, M. Abdelguefi, E. Nomand, V. Mahadevan, Design Stategies to impove pefomance of GISWeb sevices, in Poceding Intenational Confeence on Infomation Technology : Coding and Computing(ITCC04), 2004, pages ,. [6] R.Levy, J Nagaajao, G. Pacifici, M. Speitze, A. Tantawi, and A. Youssef, Pefomance management fo cluste based Web sevices, in Poceding IFIP/IEEE 8 th Intenational Symposium on Integated Netwok Management, 2003, pages ,. [7] Rajkuma Buyya, Chee Shin Yeo and Sikuma Venugopal, Maket-Oiented Cloud Computing: Vision, Hype, and Reality fo Deliveing IT Sevices as Computing Utilities, The 10 th IEEE Intenational Confeence on High Pefomance Computing and Communications, IEEE Compute Society, 2008, pages [8] Foste I., C. Kesselman, J. Nick, and S. Tuecke, Gid Sevices fo Distibuted System Integation, IEEE Compute, June 2002, pages [9] Xinhui Li, Ying Li, Tiancheng Liu, Jie Qui, Fengchun Wang Intenational Confeence on Cloud Computing IEEE Compute, 2009, pages , [10] Fulinge K., M. Gendt, A Lightweight Dynamic Application Monito fo SMP Clustes, HLRB and KONWIHR joint Reviewing Wokshop 2004, Mach [11] Fumento N., A. Maye, S. McGough, S. Newhouse, T. field, and J. Dalington, ICENI: Optimization of Component Applications within a Gid envionment, Paallel Computing, 2002, pages ,. [12] H.FWedde and M.Faooq, A compehensive eview of natue inspied outing algoithm fo fixed telecommunication netwoks, Jounal of System Achitectue, 2006, vol. 52, no. 8-9, pages ,. [13] C. Blum and D. Mekle, Eds., Swam Intelligence: Intoduction and Applications, se. Natual Computing Seies. Spinge, 2008, pages

6 Intenational Jounal of Compute Applications ( ) Volume 9 No.11, Novembe 2010 [14] A. Abaham, C. Gosan, and V. Ramos, Stigmegic Optimization Studies in Computational Intelligence. Secaucus, NJ, USA: Spinge-Velag New Yok., 2006, pages [15] V. Cadellini, E. Casalicchio, and M. Colajanni, A pefomance study of distibuted achitectues fo the quality of Web sevices, in Poceding 34 th Annual Hawaii Intenational Confeence on System Sciences,2001 [16] L.Vaqueo, L.Rodeo-Maino,J.Cacees, M.Linde, A beak in the clouds: towads a cloud definition, SIGC- OMM Compute Communication Review,2009, pages [17] T.D. Seely, The Wisdom of the Hive, Havad Univesity Pess, 1995, pages Maco Doigo and Thomas Stutzle Ant Colony Optimization, Pentice-Hall of India, India, 2001 [18] Maco Doigo and Thomas Stutzle Ant Colony Optimization, Pentice-Hall of India, India,

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