Keywords: Cloud Computing, Resource Allocation, Queueing Theory, Performance Measures.

Transcription

1 Volume, Issue 9, Setember ISSN: 77 8X Internatonal Journal of Advanced Research n Comuter Scence and Software Engneerng Research Paer Avalable onlne at: wwwjarcssecom Resource Allocaton n Cloud Comutng wth M/G/s- Queueng System R Murugesan C Elango S Kannan Det of Comuter Scence, Det of Mathematcal Scences, Det of Comuter Alcatons CPA College, C PA College, Madura Kamaraj Unversty Bodnayakanur, TN, Inda Bodnayakanur, TN, Inda Madura, TN, Inda Abstract-Cloud comutng s a new trend for comutng resource allocaton Successful develoment of cloud comutng aradgm necesstates accurate erformance evaluaton of cloud data centers The comutng resource allocaton and erformance managng have been one of the most mortant asects of cloud comutng In ths model, the resource allocaton are modeled as queues and the vrtual machnes are modeled as servce centers We consdered, M/G/s queue as a tool regulate task s arrvals, and general servce tme for requests wth sngle server and nfnte watng sace We used ths model n order to evaluate the erformance analyss of cloud server farms and we solved t to obtan accurate estmaton of the comlete robablty dstrbuton of the request resonse tme and other mortant erformance ndcators Keywords: Cloud Comutng, Resource Allocaton, Queueng Theory, Performance Measures I INTRODUCTION Cloud comutng s a novel aradgm for the rovson of comutng nfrastructure, whch ams to shft the locaton of the comutng nfrastructure to the network n order to reduce the costs of management and mantenance of hardware and software resources Ths cloud concet emhaszes the transfers of management, mantenance and nvestment from the customer to the rovder Cloud comutng s a model for enablng ubqutous, convenent, ondemand network access to a shared ool of confgurable comutng resources (eg, Networks, servers, storage, alcatons, and servces) that can be radly rovsoned and released wth mnmal management effort or servce rovder nteracton Users get the comutng resources and servces by means of customzed servce level agreement (SLA); they only ay the fee accordng to the usng tme, usng manner or the amount of data transferrng [6] The man focuses on the SLA t emhass the QoS of servces, t ncludes avalablty, throughut, relablty, securty, and many other arameters, but erformance ndcators are such as resonse tme, task blockng robablty, robablty of mmedate servce, and mean number of tasks n the system, all of whch may be determned by usng the tool of queung theory Cloud Comutng has become one of the most talked about technologes n recent tmes and has got lots of attenton from meda as well as analysts because of the oortuntes t s offerng Cloud Comutng encomasses dfferent tyes of servces The cloud has a servce-orented archtecture, and there are three classes of technology caabltes that are beng offered as a servce: Infrastructure-as-a-Servce (IaaS), where equment such as hardware, storage, servers and network comonents are accessble va the Internet, the latform-as-a-servce (PaaS), whch s a central comonent of the Cloud: the PaaS s resonsble for develong alcatons for the cloud It ncludes hardware wth oeratng systems, vrtualzed servers, etc; and fnally the Software-as-a-Servce (SaaS) (resources software), whch ncludes alcatons and other hosted servces [] Queung theory s a collecton of mathematcal models of varous queung systems Queues or watng lnes arse when demand for a servce faclty exceeds the caacty of that faclty e the customers do not get servce mmedately uon request but must wat or the servce facltes stand dle and watng for customers The basc queung rocess conssts of customers arrvng at a queung system to receve some servce If the servers are busy, they jon the queue n a watng room (e, wat n lne) They are then served accordng to a rescrbed However, cloud centers dffer from tradtonal queung systems n a number of mortant asects A cloud center can have a large number of faclty (server) nodes, tycally of the order of hundreds or thousands; tradtonal queung analyss rarely consders systems of ths sze Task servce tmes must be modeled by a general, rather than the more convenent exonental, robablty dstrbuton Moreover, the coeffcent of varaton of task servce tme may be hgh (well over the value of ) Due to the dynamc nature of cloud envronments, dversty of user s requests and tme deendency of load, cloud centers must rovde exected qualty of servce at wdely varyng loads [] The authors already develoed a CCN model, whch has M/M/s tye servce statons [8] In ths aer, we study the resource allocaton technques to mnmze the resource cost and mnmze the servce resonse tme for cloud servce, IJARCSSE All Rghts Reserved Page

2 Murugesan et al, Internatonal Journal of Advanced Research n Comuter Scence and Software Engneerng (9), Setember -, -7 rovders We model the cloud center as M/G/s queung system wth sngle task arrvals and a task buffer of nfnte caacty We evaluate ts erformance usng a combnaton of a transform-based analytcal model and an aroxmate Markov chan model, whch allows us to obtan a comlete robablty dstrbuton of resonse tme and number of tasks n the system II RELATED WORK Although cloud comutng has attracted research attenton, only a small orton of the work has addressed erformance otmzaton queston so far In [] an analytcal technque based on an aroxmate Markov Chan model for erformance evaluaton of a cloud comutng center Due to the nature of the cloud envronment, general servce tme for requests as well as large number of servers, whch makes the model flexble n terms of scalablty and dversty of servce tme Numercal results showed that the roosed aroxmate method rovdes results wth hgh degree of accuracy for the mean number of tasks n the system, blockng robablty, robablty of mmedate servce In [] Cloud center as an [(M/G/) : ( /GD )] queung system wth sngle task arrvals and a task request buffer of nfnte caacty Evaluate the erformance of queung system usng an analytcal model and solve t to obtan mortant erformance factors lke mean number of tasks n the system In [] the cloud center as an M/G/m/m+r queueng system wth sngle task arrvals and a task request buffer of fnte caacty The erformance usng analytcal model and solve t to obtan mortant erformance factors lke mean number of tasks n the system In [5] cloud envronment as an M/G/m queung system whch ndcates that nter-arrval tme of requests s exonentally dstrbuted, the servce tme s generally dstrbuted and the number of faclty nodes s m, wthout any restrctons on the number of faclty nodes There are lot works are carred out n ths felds In [] Fatma Oumellal, Mohamed Hann and Abdelkrm Haqq, MMPP/G/m/m+r, the Markov modulated Posson Process and the erformance measures such as average number of tasks n the system blockng robablty, robablty of mmedate serve the average resonse tme We focused on the how the comuter resource can effcently allocate dfferent tasks n the cloud centers III PROPOSED MODEL Consder a cloud comutng networks (CCN) whch rovdes resources ranges from comutng nfrastructure and alcatons The nter-arrval tme of requests to the classfer node s exonentally dstrbuted wth arameter λ > and the task servce tmes are d random varable wth mean τ > Generally there are three knds of requests Deendng on the tye of clents request, three tyes of servces are rovded, namely Software (SaaS), Platform as a Servce (PaaS) and Infrastructure as a Servce (IaaS) The bag of task are arrvng the frst statons namely Classfer, accordng to a Posson rocess wth rate λ > The bag of tasks (BoTs) are taken for classfcaton n FCFS dsclne After classfcaton of BoTs accordng to SLA t moves to any one of the statons whch rovdes SaaS, PaaS and IaaS Each statons has s ndeendent servers, and the queueng model at staton s M/G/s tye The cloud comutng network dagram s descrbed n fgure Fg A Analyss We model the Cloud Comutng network, as a Oen Jackson Queueng Network Consder a general CCN wth the followng assumtons The network has N sngle statons wth s servers at each staton There s an unlmted watng sace at each staton (the classfcaton and servce statons) The customers (BoTs request) arrve at staton from outsde the network accordng to a Posson rocess wth arameters λ ( =,,, N) and λ > All arrval rocess s ndeendent of each other Servce tmes for customers (servce requests) of staton are ndeendent and dentcally dstrbuted (d) random varables wth mean τ Customers (servce requests) fnshng servce at staton roceeds to jon the queue at staton j wth robablty j or leave the network altogether wth robablty r ndeendently of each other[8] The robabltes j,,j Є S ={,,, N} s called the routng robabltes and the matrx P = ( j ),j Є S s called the routng robablty matrx By our assumton, the stochastc model of cloud comutng network, we descrbed becomes an Oen Jackson Queung Network wth N statons and s server at each staton [] The routng matrx P can be exressed as a transton robablty matrx of the form, IJARCSSE All Rghts Reserved Page

3 Murugesan et al, Internatonal Journal of Advanced Research n Comuter Scence and Software Engneerng (9), Setember -, -7 P N N N We assumed n the CCN that each staton has nfnte caacty for watng requests (jobs) Next we have to show that the CCN s stable n the long run Our revous work [8] s based on M/M/s reresents a sngle staton that has unlmted queue caacty and nfnte callng oulaton, arrval rocess s Posson and servce tme s exonentally dstrbuted meanng the statstcal dstrbuton of both the nter-arrval tmes and the servce tmes follow the exonental dstrbuton Because of the mathematcal nature of the exonental dstrbuton, a number of qute smle relatonshs can be derved for several erformance measures based on the arrval rate and servce rate are obtaned M/G/s system has a s servers that has unlmted queue caacty and nfnte callng oulaton, whle the arrval s stll Posson rocess, meanng the statstcal dstrbuton of the nter-arrval tmes stll follow the exonental dstrbuton, the dstrbuton of the servce tme does not The dstrbuton of the servce tme may follow any general statstcal dstrbuton, not just exonental Relatonshs can stll be derved for a (lmted) number of erformance measures f one knows the arrval rate and the mean and varance of the servce tmes [6] Consder a sngle-staton queueng system where customers arrve accordng to a PP (λ) and requre d servce tmes wth mean τ, varance σ and second moment s = σ + τ The servce tmes may not be exonentally dstrbuted The queue s servced by a s servers at each statons and has nfnte watng room Such a system s called a network of M/G/s queues Let X(t) be the number of customers n the system at tme t {X(t)t } s a contnuous-tme stochastc rocess wth state sace {,,, } Knowng the current state X(t) does not rovde enough nformaton about the remanng servce tme of the customer n servce (unless the servce tmes are exonentally dstrbuted), and hence we cannot redct the future based solely on X(t) Hence {X(t)t } s not a CTMC Hence we wll not be able to study an M/G/s queue n as much detal as the M/M/ queue Instead we shall satsfy ourselves wth results about the exected number and exected watng tme of customers n the M/G/s queue n steady state Snce the arrval rocess to our Oen Jackson networks Posson, the whole networks (CCN) can be vewed as ndeendent M/G/s queue [6] B Stablty For the CCN, we consdered, Let ρ = λ τ, be the traffc ntensty Theorem (Condton of Stablty) Consder a sngle-staton queue wth s servers and nfnte caacty Suose the customers enter at rate λ and the mean servce tme s τ The queue s stable f λ τ s Proof: We have, B = exected number of busy servers = λ τ, Where, λ s the arrval rate of enterng customers However, the number of busy servers cannot exceeds, the total number of servers Hence, for the argument to be vald, we must have λ τ s It follows that the M/G/s queue s stable f ρ <, for each, where, where s s the number of servers at staton s Indeed, t s ossble to show that the M/G/s queue s unstable f ρ : Thus ρ < for every s a necessary and suffcent condton of stablty We shall assume that the queue s stable IV STEADY STATE ANALYSIS Consder the CCN wth statons namely classfcaton, SaaS, PaaS and IaaS The lmtng behavor of the system n steady state can be studed as follows Let X (t) be the number of requests (BoTs) n the th staton =,,, at tme t The state of the system at tme t be denoted as X(t) = (X (t), X (t), X (t), X (t)) Hence the CCN becomes an Oen Jackson Queueng N N N NN, IJARCSSE All Rghts Reserved Page 5

4 Murugesan et al, Internatonal Journal of Advanced Research n Comuter Scence and Software Engneerng (9), Setember -, -7 network wth M/G/s, at each statons, where λ = λ, λ =, =,, Mean servce tme at staton s τ The routng robablty matrx s, IJARCSSE All Rghts Reserved Page 6 and r =, r = r = r = As each staton (=,,, ) has a M/G/s queue, the exected number of customer n staton s gven by S L =, - where, S = σ + τ, and the exected watng tme n the queue s gven by S W = Where S - = s the samle varance for servce tme at staton V SYSTEM PERFORMANCE ANALYSIS As we obtaned the steady state robabltes for the number of customers n the each of the statons We are able to fnd the mean number of BoTs watng The followng system erformance measures are crucal for our model [7] The traffc ntensty s gven by s Exected watng tme n the system S W = Where, S - = σ + τ, The exected number of tasks watng for transmsson s gven by S L = - VI NUMERICAL EXAMPLES In ths secton, we evaluate the erformance of a of cloud comutng center as a network of M/G/s queue The followng numercal examle llustrates the model Consder the CCN wth statons, τ = (,,, ), λ =, and σ = (,,, ) Table for Average no of server, watng tme and length of queue Number of servers Server Average Watng tme (W) Length of queue ( L) s s s s

5 Watng tme Length of queue Murugesan et al, Internatonal Journal of Advanced Research n Comuter Scence and Software Engneerng (9), Setember -, Number of servers (Average) Nuber of servers (Average) From table, we observe that the length of queue n the system decreases wth the average number of servers and the watng tme of a customer n the system also decreases wth the average number of servers In general effcency of a server s measured by the mean servce tme τ of a customer and ts varance σ VII CONCLUSION AND FUTURE DEVELOPMENT In ths aer, we roosed an aroxmate model to evaluate the erformance of a center of cloud comutng usng the M/G/s queue model method Due to the nature of the envronment of cloud comutng and the dverse needs and demands of users, we consdered a M/G/s queueng system that reflects the nature of BoTs arrvals n the cloud Ths system has general servce tme, number of servers and a nfnte buffer caacty We descrbed a new analytcal aroxmaton for erformance evaluaton of a center of cloud comutng and resolved t to get a very decent estmate Ths result may be extended to a general case when arrval rocess to the CCN s of arbtrary nature, but servce tme s exonental, that s G/M/s system REFERENCE [] An Brown MaryN and KSaravanan, Performance factors of Cloud comutng data centers usng, [(M/G/) : ( /GDMODEL)] Queueng system, Internatonal Journal of Grd Comutng & Alcatons (IJGCA) Vol, No, March [] Bharath, M, Sandee Kumar, P, Poornma, G V Performance factors of cloud comutng data centers usng M/G/m/m+r queung systems, IOSR Journal of Engneerng (IOSRJEN) e-issn: 5-, -ISSN: , wwwosrjenorg Volume, Issue 9 (Setember ), PP 6- DOI: 5 [] Fatma Oumellal, Mohamed Hann and Abdelkrm Haqq, MMPP/G/m/m+r Queung System Model to Analytcally Evaluate Cloud Comutng Center Performances, Brtsh Journal of Mathematcs & Comuter Scence, (): -7, [] Hamzeh Khazae, Jelena Msc,and Vojslav B Msc, Performance Analyss of Cloud Comutng Centers Usng M/G/m/m+r Queung Systems, IEEE transactons on arallel and dstrbuted systems, VOL, NO 5, MAY [5] Hamzeh Khazae,Jelena M s c,vojslav B M s c, Modellng of Cloud Comutng Centers Usng M/G/m Queues, st Internatonal Conference on Dstrbuted Comutng Systems Workshos [6] Kulkarn, VG, Introducton to modelng and analyss of stochastc system nd edton, Srnger text n statstc, [7] Lzheng Guo,Tao Yan, Shuguang Zhao, Changyuan Jang, Dynamc Performance Otmzaton for Cloud Comutng Usng M/M/m Queueng System, [8] Murugesan R, CElango, SKannan, Cloud Comutng Networks wth Posson Arrval Process-Dynamc Resource Allocaton (In rnt), IJARCSSE All Rghts Reserved Page 7