# Development of Mathematical Model for Market-Oriented Cloud Computing

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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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