Performance and Cost-effectiveness Analyses for Cloud Services Based on Rejected and Impatient Users

Transcription

1 IEEE TRANSACTIONS ON SERVICES COMPUTING, TSC R1 Performace ad Cost-effectiveess Aalyses for Cloud Services Based o Rejected ad Impatiet Users Yi-Ju Chiag 1, Studet Member, IEEE, Ye-Chieh Ouyag 1 *, Member, IEEE, ad Chig- Hsie Hsu 2, Seior Member, IEEE 1 Abstract Cloud computig is a iovative service platform to offer diverse resources such as ifrastructure, platform ad software as services. However, oe challegig aspect of such a service is the impatiet user threat, which directly leads to umerous egative impacts such as poor throughput, upredictable workload variatio ad resources wasted. I this paper, the problems of coductig system cotrols i a cost-effective way ad simultaeously satisfyig performace guaratees are first studied. System losses are aalyzed accordig to the related performace factors ad waitig buffer sizes. A cost model is developed to address a performaces/cost tradeoff issue i which the user balkig, reegig, system blockig ad resources provisioig are all take ito accout. The relatioship betwee system cotrols ad throughput variatios i a multi-servers system with a fiite buffer is demostrated. A proposed policy combied with a heuristic algorithm allows cloud providers to cotrol the service rate ad buffer size withi a system loss guaratee by solvig costraied optimizatio problems. Simulatio results show that more cost-savig ad system throughput ehacemet ca be verified as compared to a system without applyig our policy. Idex Terms Cost optimality, loss probability, system blockig, throughput rate 1 INTRODUCTION C LOUD computig is a emergig service paradigm to elimiate the burde of complex ifrastructure maagemet for compaies/users. This service paradigm is developed as a utility computig to offer the pool of computig resources i a pay-as-you-go maer rather tha traditioal ow-ad-use patters [1], [2]. Cloud providers supply service resources based o several fudametal models, icludig ifrastructure as a service (IaaS), platform as a service (PaaS), ad software as a service (SaaS). For example, Amazo Elastic Compute Cloud (EC2), Amazo S3, Google s App Egie, Salesforce, etc. are all existig busiess models to provide computig ifrastructure, data-storage, programmig platforms, ad software applicatios as services, respectively. Cloud resources for providig o-demad or reserved istaces ca be leased through a etwork for temporary or log-term project eeds. However, it is difficult to avoid either over-provisioig or uder-provisioig whe workloads have upredictable/seasoal chages. Geerally, resource over-provisioig helps to maitai quality of service (QoS), provide scalable resources, ad Y. J. Chiag ad Y.C. Ouyag are with Dept. of Electrical Egieerig, Natioal Chug Hsig Uiversity, Taichug, Taiwa. {yjchiag0320@gmail.com}, {ycouyag@chu.edu.tw} C. H. Hsu is with Dept. of Computer Sciece ad Iformatio Egieerig Chug Hua Uiversity Hsichu, Taiwa. chh@chu.edu.tw avoid poor performaces. Nevertheless, this approach will lead to may shortcomigs as follows. First, it is difficult for a cloud provider to determie the best peak load provisioig. Secod, huge eergy cosumptio ad resources provisioig cost are required; Third, most resources suffer from uder-utilizatio for some days or moths durig off-seasos. Coversely, resource uderprovisioig ca coserve operatioal costs. However, performace degradatios such as log waitig time, queuig legth, high system loss, etc. are difficult to avoid. Some impatiet users may abado this services system immediately after experiecig itolerable latecy. Furthermore, Impatiet users [3], [4] that are commoly foud i etwork services will ievitably occur i a cloud eviromet for makig use of applicatio software [5], [6]. A cloud service system with impatiet users/jobs has attracted some research attetios from balacig electricity bill [7], impatiet task mappig [8] to pricig model [9]. Here, we focus o the balkig ad reegig i a queuig system, as show i Fig. 1 (a) ad Fig. 1 (b), respectively. The balkig meas that users refuse to joi the queue due to log queuig legth. Ulike the balkig, users who choose ot to wait i a queue after facig latecy would be accused of reegig. To avoid poor throughput, performace levels should be egotiated accordig to user s expectatios ad system s abilities i advace. To reach a cosesus o service cotets, sigig a service level agreemet (SLA) is a essetial process by all iterested parties [10]. The xxxx-xxxx/0x/$xx x IEEE Published by the IEEE Computer Society

2 2 IEEE TRANSACTIONS ON SERVICES COMPUTING, TSC R1 SLA outlies all aspects of cloud service usages ad obligatios, such as Quality of Service (QoS) guaratees, billig, etc. Therefore, a pealty or compesatio is required to pay whe ay party violates a SLA cotract. I short, coductig a accurate performace aalysis is required to satisfy performaces guaratees i service-orieted systems. Sectio 2 gives a brief overview related to fiite-buffer queues, impatiet users, cost-effectiveess aalyses ad latecy iformatio. Sectio 3 describes a multi-servers queuig system with a fiite buffer ad impatiet users. Probabilities of related system loss are calculated. I Sectio 4, a cost model is developed ad the Cost-Effective policy i a Abadoed system (CEA policy) is preseted to solve costraied optimizatio problems. Simulatios ad compariso of results are show i Sectio 5. The whole work ad future research are cocluded i Sectio 6. User requests User requests Balkig Balkig (a) (a) User requests User requests Reegig Reegig (b) (b) eb service Request trasmissio Fig. 1 Systems with (a) Balkig (b) Reegig. I this paper, we discuss the problems: (i) what is the system cotrol effect o operatioal costs ad performaces whe facig upredictable request arrival rates? (ii) How to evaluate the relatioship betwee user balkig/reegig ad system blockig o fial throughput rates? (iii) How to address the optimal resource provisioig to achieve the cost optimality withi a performace guaratee? The optimal resource provisioig problem that we previously dealt with i [11] for profit optimizatio is further exteded by takig ito accout the service rate cotrol ad user reegig impact. The mai cotributios of this paper ca be summarized as follows: The challege issues of arrival rate variatios ad resources wasted for a fiite buffer queue with impatiet users are studied by takig ito accout some related performace factors ad the possible losses i a service system. A cost-effective policy combied with a heuristic algorithm is first proposed to address costraied optimizatio problems. The relatioship betwee importat performace idicators ad operatioal costs ca be determied i our desiged service model. Simulatios are coducted by cosiderig differet threats of potetial balkig ad reegig factors. Experimet results show that more costsavig ad system throughput ehacemet ca be verified as compared to a system without applyig our policy. The remaider of this paper is structured as follows: 2 RELATED OR 2.1 Queuig Systems with Impatiet Users Researches i diverse systems with impatiet users have bee a log history; a review of related works is provided as follows. I [12], the performace of a telephoe system with patiet ad impatiet users were both studied. Expressios of performace measures, icludig the average umber of patiet customers or impatiet customers i the system, etc. could be expressed i terms of the joit probabilities. The waitig time probabilities, the average waitig time of a customer i a buffer, ad the probability that a customer would be served as a patiet customer were also obtaied. I [13], Madelbaum ad Zelty were motivated by a pheomeo that had bee observed i a telephoe call data ceter: a clear liear relatio betwee a abadoed probability ad a average waitig time. The issues that arose i the itroductio would be explored withi the framework of the M/M/+G queuig system. System performaces for a variety of patiece distributios were explored over differet arrival rates. Uder the assumptio that the arrival rate coverged to zero, they computed the asymptotic ratio betwee the probabilities of abadoig. A aalytic cost model for M/G/1/N queuig systems was preseted i [14]. Dora, Lipsky ad Thompso explored the iterplay of queue size, customer loss, ad mea service time for various service time distributios. It cosidered the cost of customer loss versus customer delays by varyig buffer size ad processor speed. I [15], Ghosh ad eerasighe addressed a rate cotrol problem associated with a sigle server. A ifiite horizo cost miimizatio problem was cosidered. They obtaied a explicit optimal strategy for the limitig diffusio cotrol problem (the Browia cotrol problem or BCP) which cosisted of a threshold-type optimal rejectio process ad a feedback-type optimal drift cotrol. This solutio was the used to costruct a asymptotically optimal cotrol policy. A service system with impatiet customer was a importat research issue i cloud resources provisioig, but little metioed i previous works. I [5], Mehdi et al.

3 AUTHOR ET AL.: TITLE 3 evaluated the proposed model impact o impatiet jobs. The proposed algorithm mapped the jobs with ispiratio by usig Miimum Completio Time schedulig algorithm (MCT). However, this work oly preseted a algorithm to evaluate the impact of the proposed model o impatiet jobs. Rigorous aalyses i performaces factors were igored. 2.2 Cloud Systems with Fiite Buffers ad Delay Iformatio Cloud computig has attracted cosiderable research attetio, but oly a few works doe so far have addressed fiite capacity models. I [16], a cloud ceter was model as a M/M/m/m queuig system to coduct a prelimiary study of the fault recovery impact o a cloud service performace. he a user submitted a service request to the cloud, the request would first arrive at the cloud maagemet system (CMS) which maitaied a request queue. If the queue was ot full, the request would eter the queue; otherwise it would be dropped ad the requested service failed. Cloud service performace was quatified by a service respose time, whose probability desity fuctio was derived. I [17], hazaei, Misic ad Misic described a ovel approximate aalytical model for performace evaluatio of cloud server farms ad solved it to obtai estimatio of the complete probability distributio of request respose time ad other importat performace idicators. They also poited out that accommodated heterogeeous services i a cloud ceter might impose loger waitig time for its cliets tha a homogeeous equivalet. However, o buffer size cotrol or o impatiet behavior was discussed or metioed i their work. O the other had, for the purpose of ehacig service quality, iformatio about delays was provided to users i cloud systems. I [18], Cappos et al. showed the Seattle program measures etwork latecy to a list of IP addresses ad displayed a webpage for showig the latecy to each ode. For modelig global cloud resources, a Vorooi Diagrams device was combied with ear-realtime etwork latecy iformatio i [19]. Shouraboura ad Bleher preseted a ovel Virtual Cloud Model (VCM) supplemeted with ear-real-time etwork latecy iformatio. Istaces would commuicate state iformatio with each other i order to keep the world cosistet i appearace to all participats. VCM could also be used to share applicatio placemet iformatio across differet Clouds. I [20], Lim et al. proposed a Cloud Resource Estimatio Module based o service latecy iformatio. A highly accurate service latecy predictio mechaism was derived. Their desiged system could provide a framework which facilitated service latecy iformatio collectio for better cloud service maagemet. It aimed to use service latecy iformatio to provide fast respose for various delay-sesitive cloud services. 2.3 Cost Effective Aalyses for Cloud Computig I additioal, some existig researches focus o the issue of cost-beefit aalysis i cloud computig. I [21], Selvarai ad Sadhasivam discussed a job groupig algorithm which was used to allocate the task-groups to differet available resources. This schedulig algorithm measured both resource cost ad computatio performace, it also improved the computatio/commuicatio ratio by groupig the user tasks accordig to a particular cloud resource s processig capability ad set the grouped jobs to the resource. A cost-based resource schedulig paradigm was preseted i [22] by leveragig market theory to schedule compute resources ad meet user s requiremet. The set of computig resources with the lowest price were assiged to the user accordig to curret suppliers resource availability ad price. A algorithm ad protocol were desiged for cost-based cloud resource schedulig. The schedulig algorithm ad protocol were described i the pure Java based platform, which had three-tiered hierarchical ad extesible architecture. I [23], a miimum cost maximum flow algorithm was proposed for resources (e.g. virtual machies) placemet i clouds. Hadji ad Zeghlache focused o the optimal dyamic placemet of virtual resources i data ceters ad cloud ifrastructures to serve multiple users ad teats with time varyig demads ad workloads. Providers could use the miimum cost maximum flow algorithm to opportuistically select the most appropriate physical resources. I [24], Hwag et al. preseted a two-phase algorithm for service operators to miimize their service provisio cost. I the first phase, a mathematical formula was proposed to compute the optimal amout of log-term reserved resources. I the secod phase, the alma filter was used to predict resource demad ad adaptively chage the subscribed o-demad resources such that provisio cost could be miimized. They exploited a predictive-based resource maagemet to adaptively cofigure VMs. To the best of our kowledge, the problems of achievig a cost-effective cloud system with fiite buffer aalyses ad impatiet job cocers have ot bee studied. 3 MODEL DESCRIPTION 3.1 A Multi-Servers System with Blockig Cotrol e cosider a cloud server farm with a fiite buffer ad model it as a M/M/R/ queuig system. The mathematical expressios are stated i detail as follows.

4 4 IEEE TRANSACTIONS ON SERVICES COMPUTING, TSC R1 There have R idetical servers ad at most user requests are allowed i the system. User requests arrive from a ifiite source with a mea arrival rate ad follow a Poisso distributio [25], while service times have a expoetial distributio with parameter μ. The first-come-first-served (FCFS) queuig disciplie is adopted ad let the states (= 0, 1, 2,..., ) represet the umber of user requests i the system. The value of the request arrival rate ad the service rate are take to be, 0 1,, 1 R 1, 0,, R, R, The probability of user requests that are beig served i the system is deoted by P. I a steady state, the probability fuctios P ca be obtaied from the birth-addeath formula. Accordig to the value may happe, two segmets are defied by the vector: [Segmet 1, Segmet 2] = [1 R 1, R ]. ith expressios i Eq. (1), the iitial state probability fuctios P ca be derived as follows: Po 1 R 1! P Po. R R R! R To obtai P o, Eq. (2) ad Eq. (3) are brought ito the ormalizig equatio: 0 (1) (2) P 1 (3), ad the steady-state probability of zero service Po ca be obtaied as follows: R 1 P 0 Po P 1 P R 1 (4) R1 Po [ ]. (5) 0 R R! R! R System utilizatio is equal to ρ=λ/rμ, the steady-state solutio always exists for all positive value of λ ad µ, but whe λ > Rµ, the umber of user requests will be restricted withi i the system sice there has o buffer (waitig space). 3.2 A Fiite Buffer Queue with Impatiet Users There are various balkig ad reegig rules discussed i previous works. The queuig legth ad waitig time are usually the mai factors to affect user balkig ad reegig behaviors, respectively. As illustrated i Fig. 2 (a), the system blockig loss (deoted by ) ca be reduced by expadig the buffer size. However, a larger waitig buffer will lead to a log queue ad waitig time durig peak load, which directly result i a higher balkig rate (deoted by B) ad reegig rate (deoted by R), respectively. O the cotrary, balkig ad reegig rates ca be lesseed by reducig the buffer size; however, it will lead to more system blockig loss, as depicted i Fig. 2 (b). B Larger loss Smaller loss Expadig the buffer B (a) (b) R Reducig the buffer Fig. 2 (a) The effect of expadig the buffer size (b) The effect of reducig the buffer size o system losses. Sice a user whose job request is blocked will simply be dropped, a cloud provider should keep system losses as low as possible to satisfy performace guaratees. Fig. 3 shows the proposed cloud service model which is comprised of R servers with a fiite buffer size, deoted by β. Dyamic system cotrols are used to alleviate system losses ad deal with a widely varyig load. Due to the fact that a system loss at a frot stage directly affects subsequet performaces, the request arrival rate at the middle ode (MN) queue ad the fial system throughput are evaluated by takig ito accout resources provisioig, related performace factors ad potetial user behaviors i the followig. 3.3 Balkig Probability For the purpose of deliverig quality service [26], [27], the delay iformatio about the predicted queuig legth is set to iform each arrival user [28]. By usig Eq. (5), the expected queuig legth Lq ca be obtaied as: L ( R) P q R1 P ( / ) R! R o R1 = ( R). (6) R1 R S1 SR S1 SR

5 AUTHOR ET AL.: TITLE 5 cotrol cotrol Arrival rate λ eb server λm β Delay iformatio S1 S2 Throughput User balkig probability Pb P System blockig probability Pr User reegig probability SR R servers Arrival rate at the middle ode Fig. 3 A cloud service model with a fiite buffer ad impatiet users Few arrival users may decide ot to joi the queue ad leave the system whe the queuig legth is too log to be accepted. The severity of balkig ad reegig rates at the ed of per plaig period will be recorded i this system. The correspodig otatios used i this paper are listed i Table 1. Notatio Ub Ur Pb, Pr P λb λr λ λm λf PL TABLE 1 List of ey Notatios Descriptio Potetial balkig factor accordig to historical data. Potetial reegig factor accordig to historical data. Potetial balkig probability of which would be expressed as a fuctio of Ub ad Lq. Potetial reegig probability of which would be expressed as a fuctio of Ur ad q. Blockig probability whe the system capacity is. Mea balkig rate. Mea reegig rate. System blockig rate whe the system capacity is. Arrival rate at the middle ode (MN) depeded o λb ad λr. Fial throughput rate. System loss probability. By takig divided by the mea queuig legth ad b iitial arrival rate, the potetial balkig factor, deoted by Ub ca be obtaied as follow: U b b. (7) L The balkig probability ca be calculated by multiplyig the mea queuig legth ad its potetial balkig factor together as below: q Pb L. (8) q Ub Based o the same service type at a subsequet period [29] with a arrival rate λ, the mea balkig rate ca be obtaied as follow. P b b 3.4 System Blockig Probability The blockig probability meas that user requests caot be retaied i the queue due to lack of waitig-space whe all servers are busy. That is, user requests are allowed to eter ad obtai service if the buffer has t bee completely occupied. The subsequet request arrival rate is (λ λb) after excludig the balkig loss. Sice the cotrolled system capacity i the proposed system is, the blockig probability ca be calculated by usig Eq. (5) as below: (9) ( b ) P Po. (10) R R! R The the system blockig rate, deoted by λ ca be obtaied as follow. ( ) P. (11) Accordig to the user balkig rate ad the system blockig rate, the request arrival rate at the MN queue, deoted by λm ca be give as follow. b M b. (12)

6 6 IEEE TRANSACTIONS ON SERVICES COMPUTING, TSC R1 3.5 Reegig probability Based o the rate of λm, the system performaces at the MN queue, deoted by P0 *, P * ad the mea queuig legth Lq * ca be calculated by usig Eq.(1) Eq. (5). L * M where. R P ( / ) d 1 ( ). (13) R! d 1 * R * * R1 * 0 M q * * To fid the predicted waitig time q * at the MN queue, the well-kow Little s law is applied [25]. It states that the average umber of items waitig to receive service is equal to the average arrival rate multiplied by the mea time. Historically, it has bee writte as L=λ (14) The, the waitig time at the MN queue ca be obtaied as * q * Lq. (15) Dividig the mea recorded reegig rate M r by the mea waitig time ad the arrival rate at the MN queue, the potetial reegig factor ca be obtaied as follow. U r r. (16) * q Similarly, the reegig probability ca be calculated by multiplyig the mea waitig time ad the potetial reegig factor together as below: M P U * r q r (17) The, the expected reegig rate i the queue ca be obtaied as follow: P M r r (18) For the system with fiite waitig buffer ad impatiet users, the fial throughput rate, deoted by λf, is calculated as below: F. (19) b r After excludig all system losses, the fial system utilizatio ca be obtaied as follow: M r F. (20) R Hece, the system loss probability ca be estimated as: F P L. (21) 4. Cost aalyses ad the CEA policy 4.1 A Cost Model I a cloud system, the major operatioal costs of resources provisioig (icurred by server quatity, power cosumptio ad buffer capacity), system losses (icurred by impatiet users, system blockig ad activatig VMs) ad performaces (icurred by system rejectio pealty ad system cogestio) are all take ito accout, as show i Fig. 4. Operatioal costs System losses Resources provisioig Performaces Impatiet users ad system Impatiet blockig users ad system blockig Startig-up VMs without Startig-up releasig VMs them without releasig them Buffer capacity Buffer capacity Power cosumptio Power cosumptio Server quatity Server quatity System rejectio pealty System cogestio Fig. 4 The major operatioal costs i a cloud system. I geeral, virtual machies (VMs) will be activated whe a job request has bee accepted ad forwarded ito the buffer. However, some impatiet users will reege after eterig the queue ad abado the VMs immediately. Therefore, the specific problem of cost overhead for activatig VMs but without releasig them is required to be evaluated for a system with impatiet users. The descriptios of cost otatios are summarized as follows. C1 Expected server provisioig cost per server per uit time; C2 Expected power cosumptio cost per service rate per uit time; C3 Expected cost icurred by preparig per buffer space per uit time; C4 Impatiet users ad system blockig losses icurred by per request; C5 Startig-up cost icurred by activatig per VM; C6 System rejectio pealty; C7 Cost icurred by holdig jobs i the system per uit time; C8 Cost icurred by jobs waitig i the system per uit time; Sice system performaces, loss probability ad operatioal costs strogly deped o the buffer space ad the service rate, a expected cost fuctio per uit time is developed i which both the service rate ad the buffer size are the mai decisio variables. Apparetly, o users wat to be blocked or abado service due to iadequate buffer space or itolerable system delay, respectively. Hece, there should has a loss probability guaratee i a service system, which is also perceived as oe of the most importat performace cocers to measure service levels [30]. Here, the SLA costrait is specified by guarateeig: loss probability x%, where x is the maximum threshold value, deoted by SLA (x%). The cost miimizatio (CM) with a loss probability guaratee ca be rep-

7 AUTHOR ET AL.: TITLE 7 reseted mathematically as Miimize CM Subject to 0 PL < x here CM = F (μ, β) = (RC1+μC2) /ρf +βc3+ (λr+λb+λ)c4+λrc5 +P C6 + LqC7+q* C8 (22) 4.2 The Proposed CEA Policy Here, the desiged Cost-Effective policy i a Abadoed system (CEA policy) is preseted to address the optimal solutio of (μ, β), say (μ*, β*), so as to miimize the operatioal cost without violatig a SLA costrait. It focuses o solvig the cotradictory problem amog reducig system losses ad coservig operatioal cost. However, it is extremely difficult to obtai the aalytical result of the optimal solutio due to the fact that the cost fuctio is highly oliear ad complex. Istead, we preset the CEA heuristic algorithm to fid the miimum total cost by solvig oliear costraied optimizatio problems uder various icurred costs ad user behavior variatios. CAE heuristic algorithm Iput Data: 1. Arrival rate λ. 2. Potetial balkig ad reegig factors [Ub, Ur]. 3. Cost matrix [C1, C2, C3, C4, C5, C6, C7, C8]. 4. The umber of servers R. 5. The upper boud of service rate ad buffer size i the cloud server farm, deoted by μp ad βd. 6. The loss probability guaratees x i the SLA costrait. Output: μ *, β * ad F (μ *, β * ) Step1. For i= 1; i = p; i++ Set μ i curret service rate; For j = 1; j = d; j++ Set βj curret buffer size; Step2. Calculate Lq ad λb usig Eq. (5) - Eq. (9) Calculate P ad λ usig Eq. (2) ad Eq. (10-12) λm λ λb λ ; Step3. Set λm arrival rate at the middle ode queue; Calculate Lq *, q * ad λr usig Eq. (13)-Eq. (19) λf λm λr ; Step4. Set λf expected fial throughput rate; Calculate ρf usig Eq. (20)- Eq. (21) PL (λ λf)/ λ; If PL < x, the Brig all cost parameters ito the developed cost model ad begi to calculate F (μi, βj) Else Retur to step 1 ad begi to test a ext idex. Ed Step5. If the joit value of (μi, βj) ca obtai the miimum cost value i all tests, the, Output (μi, βj) ad F(μi, βj) Else Retur to step 1 ad begi to test a ext idex. Ed 5 NUMERICAL VALIDATION 5.1 System Performaces To gai more isight ito the desiged system behavior, first of all we provide several experimets to observe the effect of resources provisioig o performaces. Numerical simulatios are demostrated by assumig λ=2500 request/mi, Ur= Ub=0.01, R=64 ad the buffer size is made variable from 0, 16 to 32 i three steps. All computatioal programs are developed by usig MATLAB. Arrival rate at the MN queue β=0 β=16 β= Fig. 5 Arrival rate at the MN queue uder various μ ad the give β values. Loss probability β=0 β=16 β= Fig. 6 Loss probability uder various μ ad the give β values. Fig. 5 ad Fig. 6 demostrate the variatio of the request arrival rate at the MN queue ad the loss probability distributio uder differet service rates ad buffer sizes, respectively. It s observed that icreasig the service rate ca certaily improve the arrival rate at the MN queue. However, icreasig the buffer size does ot ecessarily improve the arrival rate at the MN queue. It ca be see that it will cause the highest loss probability if there has o buffer available ad it does ot cotribute to reducig the loss probability through buffer overprovisioig. Both performace gaps betwee differet β values become smaller ad coverge to early equal as

8 8 IEEE TRANSACTIONS ON SERVICES COMPUTING, TSC R1 the service rate further icreases. 5.2 Experimetal Results The experimets have bee coducted to validate that the optimal resources provisioig ca be obtaied by applyig the heuristic algorithm ad show that the CEA policy is practical. It s assumed that λ=5200 request/mi, Ur=Ub=0.006, R=100, while the loss probability costrait is 0.5%, deoted by SLA(0.5%). Sice a server provisioig cost is mostly determied by the ret/purchase cost ad power cosumptio cost, the server provisioig cost ca be roughly estimated accordig to differet requiremets. Here, we assume [C1, C2, C3, C4, C5, C6, C7, C8] = [200, 30, 20, 60, 50, 10, 5, 5] i experimets. The effect of varyig μ ad β values to fid the miimum cost is show i Fig. 7. It s oted that the miimum cost of ca be obtaied at the optimal solutio (μ*, β*) = (62, 12). The loss probability distributios uder various μ ad β values are demostrated i Fig. 8. The effect of the service rate o the loss probability variatio is larger tha the buffer size. As ca be see, reducig the loss probability at begiig 29,500 ca lower the cost (correspods to Fig. 7). However, as the loss probability further reduces, it leads to o more cost reductio. This behavior is due to the fact that, maitaiig a extremely low loss probability requires more resources provisioig, which directly results i high cost burde. The correspodig loss probability at the optimal solutio is 0.29%. Simulatio results have verified that the system ca satisfy the SLA costrait ad simultaeously obtai the miimum operatioal cost by applyig the CEA policy. I the ext experimets, system blockig probabilities uder various μ ad β values are show i Fig. 9. As ca be expected, the system blockig probabilities ca be reduced by icreasig either the service rate or the buffer size. The lower blockig probability of 0.1% ca be obtaied at the optimal solutio. After excludig the balkig ad the system blockig rate, the remaiig arrival rates at the MN queue is show i Fig. 10. The effect of the buffer size o the arrival rate at the MN queue is larger whe the service rate is low; however, it becomes virtually udetectable whe the service rate is high Cost 29,000 28,500 28,000 F(62, 12)= Loss probability % 27, Fig. 7 Cost distributios uder various μ ad β values Fig. 8 Loss probability distributios uder various μ ad β values. 2 System blockig probability 1% 0.8% 0.6% 0.4% 0.2% % Fig. 9 System blockig probabilities uder Fig. 10 Arrival rates at the MN queue uder various μ ad β values. various μ ad β values. The higher arrival rates at the MN queue of also ca be achieved by adoptig the CEA policy. The reegig rate ad the system throughput rate distributios are show i Fig. 11 ad Fig. 12, respectively. It s oted Arrival rate at MN queue

9 AUTHOR ET AL.: TITLE 9 that the reegig rate ca be reduced by icreasig the service rate or lesseig the buffer size. Besides, the impact of the buffer size becomes virtually udetectable whe the system operates at a higher service rate. The same tedecy ca be foud i the throughput rate, as show i Fig. 12. Throughput rate Reegig rate Fig. 11 Reegig rates uder various μ ad β values 5,190 5,180 5,170 5,160 5,150 5,140 Fig. 12 Throughput rates uder various μ ad β values. 5.3 Compariso of Results A geeral approach, which implies that a solutio is calculated oly by cosiderig a absolute performace guaratee is used as a basis for compariso sice most of the previous works [31], [32], [33] had adopted this approach to maage cloud resources. For the sake of simplicity, here it s referred to as a o-cea policy sice o system loss evaluatios or cost optimizatio aalyses are cosidered. Next, we try to show that the CEA policy is also applicable for a system with a fixed buffer size. Experimets are coducted by assumig that λ=500 request/mi, R=20 ad both policies eed to comply with the same loss probability guaratee of SLA(5%). Naturally, users react variously to differet degrees of latecy. I additioal, may potetial factors such as idividual feeligs, satisfactio, delay tolerat, etc. caot be igored sice it may also ifluece user's decisio. I the desiged system, the abadomet iformatio will be recorded at per plaig period. For a existig cloud computig service, the balkig ad reegig potetial factors ca be obtaied from a actual historical statistic. Here both parameters are radomly chose ad three differet cases are performed. Both policies are evaluated by assumig potetial balkig/reegig factors (Ub; Ur) = (0.005; 0.005), (0.005; 0) ad (0; 0.005) i order to study ad compare the ifluece of differet impatiet situatios o the operatioal costs ad performaces. Besides, differet buffers of size 1, 10 ad 20 are assiged. - (Ub; Ur) = (0; 0.005), i order to study the behavior of both policies whe a system without balkig but has the threat of reegig users. - (Ub; Ur) = (0.005; 0), i order to study the behavior of both policies whe a system without reegig but has the threat of balkig users. - (Ub; Ur) = (0.005; 0.005), i order to study the behavior of both policies whe there have both threats of balkig ad reegig users i the system. Comparisos of the cotrolled service rates are show i Fig. 13. As ca be see, it will result i a higher service rate for reducig system losses whe the give buffer size is less. The results show that the service rates determied by the o-cea policy are lower tha the CEA policy sice the former tries to reduce resources provisioig cost as more as possible. However, the lower operatioal cost ca be achieved by applyig the CEA policy, as show i Fig. 14. It s oted that the system will result i higher cost uder a larger give buffer size whe there has the threat of reegig No-CEA policy CEA policy (0; 0.005) (0.005; 0) (0.005; 0.005) ad (Ub; Ur) Fig. 13 Compariso of the service rate.

10 10 IEEE TRANSACTIONS ON SERVICES COMPUTING, TSC R No-CEA policy CEA policy Fially, we measure the cost improvemet ratio, which calculates the relative value of improvemets to the origial value istead of the absolute value; the results are show i Fig 16. The relative improvemet rate is up to 46% i terms of cost reductio. The compariso of results has show that more cost-savig ad throughput rate ehacemet ca be achieved by applyig the CEA policy. 6 CONCLUSION AND FUTURE OR Cost (0; 0.005) (0.005; 0) (0.005; 0.005) ad (Ub; Ur) Fig. 14 Compariso of the operatioal cost. Nevertheless, the costs ca be reduced by applyig the CEA policy ad they also ca be maitaied relatively stable as compared to the o-cea policy. Comparisos of the throughput rate are show i Fig. 15. It s oted that the throughput rate ca be improved sigificatly by applyig the CEA policy No-CEA policy CEA policy Developig a successful service system ecessitates takig ito accout ot oly system cotrol factors but also user behaviors. However, most existig studies fail to offer a effective system cotrol to capture optimizatio opportuities whe facig impatiet users ad various icurred costs. To tackle the problem, the effect of resources provisioig o system losses ad the throughput rate are studied i our work. A cost model is developed to coduct the costs/performaces tradeoff accordig to the icurred costs, system losses, resources provisioig ad system performaces. The proposed CEA policy cotributes to addressig the optimal service rate ad buffer size cotrols i a system with a fiite buffer ad impatiet users. Experimet results have show that realizig cost-effective resources provisioig withi a loss probability guaratee ca be obtaied by applyig the CEA policy. As compared to a system without applyig our approach, the beefit of reducig cost is up to 46 percet. As for future works, we pla to aalyze more challegig issues such as traffic load cotrol mechaisms, fiite populatio cocers, etc. for coductig a comprehesive cotrol strategy. Throughput rate (0; 0.005) (0.005; 0) (0.005; 0.005) (Ub; Ur) Fig. 15 Compariso of the throughput rate. Cost improvemet rate(%) (0; 0.005) (0.005; 0) (0.005; 0.005) ad (Ub; Ur) Fig. 16 Cost improvemet rate. REFERENCES [1] S. Sivathau, L. Liu, M. Yiduo, ad X. Pu, "Storage maagemet i virtualized cloud eviromet," 2010 IEEE 3rd Iteratioal Coferece o Cloud Computig (CLOUD), pp , [2] R. Zhag, ad L. Liu, "Security models ad requiremets for healthcare applicatio clouds," IEEE 3rd Iteratioal Coferece o Cloud Computig (CLOUD), pp , [3]. ag, N. Li, ad Z. Jiag, Queueig System with Impatiet Customers: A Review, IEEE Iteratioal Coferece o Service Operatios ad Logistics ad Iformatics (SOLI), pp , [4] J. Li, T. Dai, J. Huo, ad Q. Su, A Method of Service Quality Moitorig i Cotact Ceters with Impatiet Customers, 9th Iteratioal Coferece o Service Systems ad Service Maagemet (ICSSSM), pp , [5] N. Mehdi, A. Mamat, H. Ibrahim ad S. Symba, Virtual machies cooperatio for impatiet jobs uder cloud paradigm, Iteratioal Joural of Iformatio ad Commuicatio Egieerig, vol. 7, o. 1, pp.13-19, [6] C. Cardoha, M. D. Assução, M. A. Netto, R. L. Cuha, ad C. Queiroz, "Patiece-aware schedulig for cloud services: Freeig users from the chais of boredom," Spriger Berli Heidelberg I Service-Orieted Computig," pp , [7] M. Mazzucco ad D. Dyachuk, "Balacig electricity bill ad performace i server farms with setup costs," Future Geeratio Computer Systems, vol. 28, o. 2, pp , [8] N. A. Mehdi, A. Mamat, H. Ibrahim, ad S.. Subramaiam, "Impatiet task mappig i elastic cloud usig geetic algorithm," Joural of Computer Sciece, 7(6), 877, [9] T. eski, ad N. Taski, "A pricig model for cloud computig service," Hawaii Iteratioal Coferece o System Scieces (HICSS), pp , [10]. M. Sim, Aget-Based Cloud Computig, IEEE Trasitios o Services Computig, vol. 5, o. 4, pp , 2012.

11 AUTHOR ET AL.: TITLE 11 [11] Y. J. Chiag ad Y. C. Ouyag, "Profit Optimizatio i SLA- Aware Cloud Services with a Fiite Capacity Queuig Model." Mathematical Problems i Egieerig, [12] Y. Q. Zhao ad A. S. Alfa, Performace aalysis of a telephoe system with both patiet ad impatiet customers, Telecommuicatio Systems, pp , [13] A. Madelbaum ad S. Zelty, The impact of customers patiece o delay ad abadomet: some empirically-drive experimets with the M/M/+G queue, OR Spectrum, vol. 26, o. 3, pp , [14] D. Dora, L. Lipsky ad S. Thompso, Cost-based Optimizatio of Buffer Size i M/G/1/N Systems Uder Differet Servicetime Distributios, Proceedigs of 9th IEEE Network Computig ad Applicatios (NCA), pp , [15] A. P. Ghosh, ad A. P. eerasighe, Optimal buffer size ad dyamic rate cotrol for a queueig system with impatiet customers i heavy traffic, Stochastic Processes ad their Applicatios, pp , [16] B. Yag, F. Ta, Y. S. Dai, ad S. Guo, Performace Evaluatio of Cloud Service Cosiderig Fault Recovery, Cloud Computig. Spriger Berli Heidelberg, pp , [17] H. hazaei, J. Misic, ad V. B. Misic, Performace Aalysis of Cloud Computig Ceters Usig M/G/m/m+r Queuig Systems, IEEE Trasactios o Parallel ad Distributed Systems, pp , [18] J. Cappos, I. Beschastikh, A. rishamurthy, ad T. Aderso, "Seattle: a platform for educatioal cloud computig," ACM SIGCSE Bulleti, vol. 41, o. 1, pp [19] C. Shouraboura ad P. Bleher, "Placemet of applicatios i computig clouds usig Vorooi diagrams, Joural of Iteret Services ad Applicatios, vol. 2, o.3, pp , [20] B. P. Lim, P.. Chog, E.. aruppiah, Y. M. Yassi, A. Nazir,ad M. F. N. Batcha, "FARCREST: Euclidea Steier Treebased cloud service latecy predictio system," Cosumer Commuicatios ad Networkig Coferece (CCNC), pp , [21] S. Selvarai ad G. S. Sadhasivam, Improved cost-based algorithm for task schedulig i cloud computig, IEEE Iteratioal Coferece o Computatioal Itelligece ad Computig Research (ICCIC), pp.1-5, [22] Z. Yag, C. Yi, ad Y. Liu, A Cost-based Resource Schedulig Paradigm i Cloud Computig, 12th Iteratioal Coferece o Parallel ad Distributed Computig, Applicatios ad Techologies, pp , [23] M. Hadji ad D. Zeghlache, Miimum Cost Maximum Flow Algorithm for Dyamic Resource Allocatio i Clouds, IEEE Fifth Iteratioal Coferece o Cloud Computig, pp , [24] R. Hwag, C. Lee, Y. Che, ad J. D. Zhag, Cost Optimizatio of Elasticity Cloud Resource Subscriptio Policy, IEEE Trasitio o Services Computig, [25] D. Gross, J. F. Shortle, J. M. Thompso ad C. M. Harris. Fudametals of Queuig Theory (Fourth editio), A Joh iley & Sos, Ic., New York, [26] J. Cao et al., Social attribute based web service iformatio publicatio mechaism i Delay Tolerat Network, IEEE 14th Iteratioal Coferece o Computatioal Sciece ad Egieerig (CSE), pp , [27] M. Armoy ad C. Maglaras, Cotact Ceters with a Call-Back Optio ad Real-Time Delay Iformatio, Operatios Research, vol. 52, o. 4, pp , [28] P. Guo ad P. Zipki, Aalysis ad Compariso of Queues with Differet Levels of Delay Iformatio, Maagemet Sciece, vol. 53, o. 46, pp , [29] Amazo EC2 O-Demad Istace Prices, [30] M. Y. Luo ad C. S. Yag, Costructi.g zero-loss eb services, IEEE Computer ad Commuicatios Societies Coferece, pp , [31] J. Shao, ad Q. ag, "A performace guaratee approach for cloud applicatios based o moitorig," IEEE 35 th Aual Computer Software ad Applicatios Coferece orkshops (COMP- SAC), pp , [32] R. Nathuji, A. asal, ad A. Ghaffarkhah, "Q-clouds: maagig performace iterferece effects for qos-aware clouds," ACM Proceedigs of the 5th Europea coferece o Computer systems, pp , [33] R. N. Calheiros, R. Raja,ad R. Buyya, "Virtual machie provisioig based o aalytical performace ad QoS i cloud computig eviromets," Iteratioal Coferece o Parallel Processig (ICPP), pp , Yi-Ju Chiag received her BS ad MS degrees from the Departmet of Electrical Egieerig (EE) at Natioal Chug-Hsig Uiversity of Taiwa i 2011 ad 2013, respectively. She is curretly workig toward the PhD degree i Departmet of Electrical Egieerig (EE) at Natioal Chug- Hsig Uiversity. Her research iterests iclude cloud computig, optimal cotrol algorithm, performace evaluatio, queuig theory ad gree computig system. She is a IEEE studet member. Ye-Chieh Ouyag (S 86 M 92) received the BSEE degree i 1981 from Feg Chia Uiversity, Taiwa, ad the MS degree i 1987 ad the PhD degree i 1992 from the Departmet of Electrical Egieerig, Uiversity of Memphis, Memphis, Teessee. He joied the Faculty of the Departmet of Electrical Egieerig at Natioal Chug Hsig Uiversity, Taiwa, i August He curretly is a professor ad the departmet chair i the Departmet of Electrical Egieerig, NCHU. His research iterests iclude cloud computig, hyperspectral image processig, medical imagig, commuicatio etworks, etwork security i mobile etworks, multimedia system desig, ad performace evaluatio. He is a member of the IEEE.

12 12 IEEE TRANSACTIONS ON SERVICES COMPUTING, TSC R1 Professor Chig-Hsie (Robert) Hsu is a professor i departmet of computer sciece ad iformatio egieerig at Chug Hua Uiversity, Taiwa; ad distiguished chair professor i school of computer ad commuicatio egieerig at Tiaji Uiversity of Techology, Chia. His research icludes high performace computig, cloud computig, parallel ad distributed systems. He has published 200 papers i refereed jourals, coferece proceedigs ad book chapters i these areas. He has bee ivolved i more tha 100 cofereces ad workshops as various chairs ad more tha 200 cofereces/workshops as a program committee member. He is a IEEE seior member.