Revenue Maximization Using Adaptive Resource Provisioning in Cloud Computing Environments

Transcription

1 202 ACM/EEE 3th nternatonal Conference on Grd Coputng evenue Maxzaton sng Adaptve esource Provsonng n Cloud Coputng Envronents Guofu Feng School of nforaton Scence, Nanng Audt nversty, Nanng, Chna nufgf@gal.co Saurabh Garg, akuar Buyya CODS aboratory, Dept. of Coputng and nfo. Systes Melbourne, Australa {sgarg, ra}@csse.unelb.edu.au enzhong State Key ab for Novel Software Technology, Nanng nversty, Nanng, Chna lwz@nu.edu.cn Abstract Keywords-. NTODCTON Cloud coputng represents the delvery of coputng as a servce, whereby such resources as CP, software, nforaton, and devces are provded to end-users as a etered servce over the nternet. Cloud coputng provdes a vastly effcent, flexble, and cost-effectve way for T to eet escalatng busness needs: T as a Servce. Ths study consders two scenaros. Frst, soe ultnatonal corporatons rent the T nfrastructure and servces fro a Cloud provder to buld a vrtual datacenter/cluster for ther branches all over the world. Second, a Cloud datacenter provdes transacton servces of electronc coerce for soe sall copanes. nder both these scenaros, the Cloud provders a to obtan the revenues by leasng the resources as servces and the custoers rent servces to eet ther applcaton requreents. The custoers only rent the requred servces and only pay for the consued ones. The busness odel based on Servce evel Agreeents (SA) plays a crucal role n Cloud paradg and t s the key pont to dstngush Cloud coputng fro conventonal dstrbuted coputng paradgs such as grd coputng and cluster coputng []. Partcularly, SAs facltate the transactons between custoers and servce provders by provdng a platfor for consuers to ndcate ther requred servce level or Qualty of Servce (QoS) [2]. SA usually specfes a coon understandng about responsbltes, guarantees, warrantes, perforance levels n ters of avalablty, response te, etc. A chargng odel, ncludng the chargng echans and penaltes n case of non-coplance of SA, s also specfcally defned. Servce provders usually charge custoers accordng to the acheved perforance level. For exaple, Aazon EC2 offers three types of copute servces (.e., on-deand, spot and reserved) at dfferent prces based on ther servce/ perforance levels. SA s also the fundaental bass for servce provders to provson ther Cloud resources. The servce provder usng a ult-tenant odel assgns pooled copute resources n the for of a vrtual achne to ultple consuers. The pooled physcal resources can be assgned and reassgned to the dfferent vrtual achnes dynacally based on consuers requests and avalable resources. e defne servce nstance as the cobnaton of a custoer and hs/her assgned vrtual achne (a certan type of rental resource or servce). A custoer ay belong to ore than one servce nstances snce a custoer ay request any types of servces. The servce nstances ay have dfferent attrbutes such as arrval rate, executon te, and prcng echans. Even for the sae servce nstance, ts request arrval rate can vary wth dfferent rando dstrbutons. The challenge s how uch underlne physcal resources ust be assgned to antan the prosed level of perforance as descrbed n SAs. Snce resource allocaton strateges have an pact on the servce perforance, a fundaental proble faced by any Cloud servce provder s how to axze ther revenues by allocatng resources dynacally aong the servce nstances and provdng dfferentated perforance levels based on SA and easurable perforance ndces. Generally, we should allocate ore resources for those nstances wth hgh arrval rate and hgh prce n order to obtan hgh revenues. However, soe nstances ay have hgh throughput rate (hgh arrval rate) and low prce, and vce versa. Thus, t s nontrval to allocate the resources /2 $ EEE DO 0.09/Grd

2 properly and precsely accordng to the heterogeneous paraeters. Therefore, ths paper focuses on how a Cloud data center can axzes the SA-based revenues by proper resource allocaton and presents optal allocaton algorths for dfferent prcng schees. The basc dea n ths paper s to schedule the Cloud resources aong dfferent servce nstances adaptvely based on the dynacally collected nforaton. Our an contrbutons n ths paper nclude: () Queung Theory based atheatcal forulaton for the resource allocaton proble. The forulaton odels the applcaton s requreent usng varous paraeters such as resource quantty, request arrval, servce te and prcng odel. (2) Optal SA-based resource allocaton algorths aong dfferent Cloud servce nstances, by whch Cloud provders can axze ther revenues. Our sulaton shows that they outperfor related work. The reander of ths paper s organzed as follows. Secton ntroduces two prcng odels n ters of response te. Secton forulates the proble of resource allocaton and provdes the optal solutons to these two probles. n Secton V, we have carred out several sulatons to verfy our solutons. Secton V presents soe related work. Fnally, Secton V concludes our paper.. MODES Cloud coputng as dscussed by Buyya et al. [2], should ncorporate autonoc resource anageent odels that effectvely self-anage changes n servce requreents to satsfy both new servce deands and servce oblgatons accordng to the sgned SA. n ths paper, we contrbute towards ths a of Cloud coputng and therefore, consder a slar scenaro where a Cloud provder offers varous servces to custoers at dfferent SA. Each servce s hosted wthn a datacenter usng certan aount of vrtual nfrastructure, whch can grow and shrnk on deand. The obectve s to fnd how any servers should be assgned for each servce nstance n order to acheve axu revenue for a gven a chargng/prcng odel. Fgure - llustrates the syste odel of a Cloud-coputng envronent. A. Matheatcal Model e assue that the Cloud datacenter s coposed of N hoogenous servers. The servers are grouped nto clusters dynacally and each server can only on one cluster sultaneously. Every servce nstance s apped to a server cluster. Each cluster s vrtualzed as a sngle achne. The users do not need to know the specfc detals of the operaton on vrtual achnes. A servce provder sgns longter SAs wth custoers. Every servce nstance s allocated to n, n 2,... n servers to provde servces. e assue that the capablty of every vrtual achne s proportonal to the nuber of assgned servers. Ths assupton s reasonable especally for those coputng tasks that can be dvded nto several peces and dspatched to any servers to execute concurrently. For exaple, any dynac web pages are coposed of any parts that should be coputed separately; or soe tasks can be decoposed for parallel coputng. e assue that the requests fro any servce nstance arrve at the syste n a Posson dstrbuton wth average arrval rate and the processng tes by one server follow a negatve exponental dstrbuton wth average servce rate / ( s the nuber of processed requests per unt te). Then the servce rate of a vrtual achne wth n servers s /n. Servce nstance Vrtual achne Scheduler n servce level Consuer Montor n operatng level e also assue that t costs uch for servers to shft ther runnng envronents. For exaple, t needs a long te to read the coercal data of a new custoer nto cache fro the external eory. Hence, the requests cannot be oved easly fro one vrtual achne to another. Each servce nstance, a vrtual achne assocated wth a user, can be odeled as a FFO (Frst n Frst Out) M/M/ queue. Here we defne servce ntensty as the rato of arrval rate to servce throughput of one server, The notatons used n ths paper are: Clouds Consuer Fgure - syste odel of Cloud Pooled resources Servce nstance ρ = λ / μ () Arrval rate of servce requests of each nstance Servce rate of servce nstance wth one server Servce ntensty Nuber of servce nstances n Varable of assgned servers to an nstance N Nuber of all the servers n resource pool b A constant of servce prce B Benchark to evaluate the servce perforance r Varable of response te ser requreent on response te n SA g Mean revenue fro a servce provson G Provder s revenue fro Cloud provson q Slope of prcng curve n Mean esponse Te (MT) F Perforance level of servce n MT 93

3 B. Prcng Model n ters of Mean esponse Te (MT) The prcng echans s usually defned n SA. t specfes how servce requests are charged. For nstance, requests can be charged based on subsson te (peak/offpeak), prcng rates (fxed/changng) or avalablty of resources (supply/deand) [2]. However, these echanss are servce provder-orented. Here we propose two custoer-orented prcng echanss MT and T, n whch the custoers are charged accordng to acheved servce perforance n ters of ean response te. Mean response te s a coonly used etrc to evaluate the servce perforance. Here we defne response te as the nterval fro when a request arrves at the syste to the nstant at whch the servce s copleted (gnorng the lnk latency). The response te can also be tered as the soourn te of a request n M/M/ queung odel. t s necessary for servce provders to dvde the whole provsonng te nto soe slots. e calculate the ean response te of every te slot ndependently because arrval rate vares over te. e frst propose a prcng odel called MT. e use F to denote an offset factor of actual response te to benchark. e defne F as, F = r/ (2) where r s the easured average response te durng a te slot and represents a benchark of response te defned n SA. Every servce nstance has dfferent, whch s deterned by custoer s actual requreent. For exaple, the recoended response te for transactons n e- coerce s 2-4 seconds. Ths prcng odel s also called servce deand drven odel [3]. Then we forulate the prcng echans as, B = b( F) (3) where B s the prce of each servce provson and b s the prce constant. As dsplayed n Fg. (a), the prce B actually s a lnear functon of ean response te r. hen ean response te s longer than the threshold, servce provder wll be penalzed. Fgure also shows us that b/ s the slope of prcng functon, q = b/ (4) C. Prcng Model n ters of nstant esponse Te (T) MT ay work well when the easureents are evenly dstrbuted over a narrow range. However, MT s not eanngful as a perforance etrc when the response te vares qute a bt over a large range. Therefore, we propose another prcng odel n ters of T. A request n T s charged accordng to the easured response te. That s, br, B = 0, r > The prcng odel T can be llustrated as Fg. (b). The bllng under ths odel s deterned by the nuber of servce provsons wth response te wthn requred. B. b (a) Prce odel n ters of MT r Fgure. Prce odels MATHEMATCA FOMATONS FO ESOCE AOCATON POBEM N CODS A. Optal Allocaton Based on MT Accordng to the research conclusons on Queung Theory of M/M/ odel, the average response te r of servce nstance at the steady syste state, r = n μ λ Then servce perforance level F s, F = ( nμ λ ) Accordng to (3), the ean revenue g brought by a servce provson s, g = b ( nμ λ ) The overall revenues durng a te slot fro servce nstance s, G = λg = λb ( nμ λ ) Then our optzaton proble can be forulated as, B b r (b) Prce odel n ters of T (5) (6) (7) (8) (9) 94

4 Obectve : Max λ b ( nμ λ ) = = = st.. n N (0) e resolve ths proble usng agrange Multpler Method n the followng. Constructng agrange coposte functon, n ( ) = b + N n λ λ = ( nμ λ ) () = where λ s a constant of agrange ultpler. ettng d / dn = 0, = 0,, 2..., λb μ λ = 0 ( n μ λ ) 2 (2) n = qρ + ρ (3) λ Substtutng (3) nto the constrant of the optzaton proble (0), λ < n μ (7) n > ρ (8) Moreover, Fgure shows us that the servce provders wll be penalzed once ean response te cannot et the servce deand. Therefore, our servce allocaton strategy guarantees that ean response te should be less than, r = n μ λ < (9) n > + ρ (20) μ Equaton (8) and (20) offer us the lower bound of assgned resources for each servce nstance. t s obvous that (8) holds once (20) s satsfed. B. Optal Allocaton Based on T Accordng to the conclusons on Queung Theory of M/M/ odel, the soourn te probablty dstrbuton s, () ω t μ λ e λ μ ( ) t = ( ) (2) λ = = (4) N = q ρ + ρ e assue that servce nstance s allocated to n servers. Then the ean revenue brought by a servce provson s, N ρ = = λ q ρ = (5) Substtutng (5) nto (3), we yeld the fnal answer,.e., the nuber of servers used for each servce nstance, n N ρ = = q ρ + q ρ = ρ (6) However, equaton (6) s correct on the prese that (6) holds. Equaton (6) s vald only when the request arrval rate of each servce nstance s less than servce processng rate accordng to the conclusons on Queung Theory of M/M/ odel. Otherwse, the length of request queue wth FFO wll not converge and the ean response te always ncreases as te elapses. Therefore, our concluson of (6) holds only f arrval rate s less than servce processng rate, () 0 0 ( λ nμ) = b ( e ) ( ) ( λ ) nμ t g = bω t dt = b μ λ e dt (22) Then the overall ean revenue fro servce nstance durng a te slot s, G = g = b e λ μ (23) ( ) ( n λ λ ) Thus, our optzaton proble can be forulated as, Obectve : Max λ b e = = st.. n = N ( λ nμ) ( ) Constructng agrange coposte functon, n ( ) = b e + N n = = (24) ( λ n μ ) λ ( ) λ (25) 95

5 where λ also s agrange ultpler. ettng d / dn = 0, = 0,, 2..., n ( n ) be λ μ λμ ( λμb) λ= 0 (26) ln ln n = λ ρ μ μ + (27) Substtutng (27) nto (24), ln ( λμ ) b ln λ ρ (28) N = + μ μ = = = ln λ = ln ( λμ b ) μ = = μ = + ρ N Substtutng (29) nto (27), we can obtan the result, ln ( λμb) ( λμ b ) = = = ρ + μ μ = μ ln μ + ρ N (29) (30) Because of the sae reason as prevous subsecton, the arrval rate should be larger than the servce rate (processng speed) of the vrtual achne coposed of all the assgned servers. Naely, the allocated resource n should be larger than servce ntensty. V. PEFOMANCE EVAATON n ths secton, we present our experental results on the valdty of our algorths for optzng the resource provsonng n the Cloud envronent. n the followng, we provde two types of experents, where requests are odeled usng synthetc dataset and traced dataset. e develop a C-based sulator based on a te-drven odel to conduct the experents. Sulaton clock ncreases at a constant rate of one llsecond. After each llsecond, we check and handle those events that happen at the current te slot. The events anly nclude four types: arrval, departure, resource reallocaton, and output the experent results. Snce our an goal s to axze the revenue of the Cloud provder, we use revenue fro servce provsonng as our an etrc to evaluate the strateges. n the evaluaton, we use a resource allocaton algorth proposed by Mchele n hs thess [4], as our base algorth to copare wth, because ths work s the ost recent work that s slar to ours. n the followng, we use MT, T, and Heurstc to denote our optal algorth based on ean response te, our optal algorth based on nstant response te, and the heurstc allocaton algorth proposed by Mchele [4] respectvely. The related paraeters and ther default values are lsted n Table. TABE. PAAMETES AND THE DEFAT VAES Paraeter Default Value Paraeter Default Value Arrval ate ando (20 30) Servce ate 0 ntercept b 20/60 ntercept ando (2 32)/60 custoers 20 evenue unt $ A. Sulatons wth Synthetc Data n ths secton, each sulaton runs for one hour. e partton the te nto slots. After each te slot, we calculate and output the revenue gan durng ths slot. Our results are derved fro the last te slot. N 3 N S VH YH V 057 +HX V F Fgure 2. evenue versus the nuber of servers 057QDZ5 057 E DG 5 +HX V F QD Z 5 +HX V F E DG 5 VH YH V Fgure 3. evenue versus the nuber of serves under dfferent q Fgure 2 s the coparson of revenue between MT and Heurstc wth dfferent servers. Te slot n ths sulaton s set 30 nutes. Fgure 2 shows that the revenue fro MT and Heurstc ncreases wth the ncrease of the server nuber. To calculate dg / dn n (9), 96

6 λbμ G = n ( μ λ ) 2 (3) G n (3) s always larger than zero, whch ples that the revenue always ncreases wth the ncrease of servers. However, G decreases wth the ncrease of n, whch eans that revenue ncreases ore and ore slowly wth the ncrease of server nuber. Fgure 2 shows us that our resource allocaton strategy of MT always outperfors Heurstc. Ths s because MT s the optal strategy n theory. Moreover, the superorty of MT s rearkable especally when the resources are relatvely rare. Therefore, MT s uch valuable to prove the revenue through proper allocaton when the resource s rare or the accepted requests are nuerous. Fgure 2 also shows us that Heurstc perfors well, ostly close to MT. Equaton (6) can explan ths result. The optal allocaton can be dvded nto two steps. Frst, each servce nstance s allocated accordng to. Second, the reanng resources are allocated accordng to and q. Thus, the servce ntensty ostly donates the optal allocaton. hat s ore, Heurstc actually acheves the sae optal allocaton as MT when q follows the sae dstrbuton as. Ths ay explan why MT and Heurstc are ostly close. Fgure 3 also can verfy ths vewpont. 3 S,57 +HX V F VH YH V Fgure 4. revenue versus the nuber of servers 057 +HX V F PH P Q Fgure 5. Evoluton of revenue durng 5 nutes over te wth traces Fgure 3 s the revenue coparson under the sulatons wth dfferent q between Heurstc and MT. Each servce nstance n the sulatons has the sae, b and dfferent response te deands. The revenue, both of Heurstc and MT, ncreases wth the ncrease of response te deand. However, MT rses rearkably especally when the resources are rare. hen all the b s fxed, q n sulatons wth broad s ore dverse. q has pact on the allocaton n our optal algorth, but has no pact on Heurstc accordng to (6). That s why revenue of MT ncreases ore than Heurstc when q changes fro a narrow dstrbuton to a broad dstrbuton. Fgure 4 s the coparson of revenue between T and Heurstc. Te slot n ths sulaton s set to 0 nutes. t shows us that, due to the sae reason as MT, both the revenue of T and Heurstc ncrease wth the ncrease of server nuber. T always outperfors Heurstc because T s optal n theory. Moreover, the superorty of T s rearkable especally when resources are relatvely rare. Therefore, T s uch valuable to prove the revenues through proper allocaton when the resource s rare or the accepted requests are nuerous. B. Sulatons wth Traced Data e use the traced data to sulate the requests and allocate the resources dynacally and adaptvely accordng to probed paraeters. Due to unavalablty of publc Cloud data, we used web applcaton data, whch are taken fro [5]. All the data are records of HTTP requests to servers. e ntercept consecutve request records of 8 hours fro the traces to sulate the arrval of a servce nstance. The detaled nforaton s shown n Table. TABE. METADATA ON TACED DATASET # source Date te #records EPA-HTTP 30 Aug :00-7: EPA-HTTP 30 Aug :00-24: SDSC-HTTP 22 Aug :00-7: SDSC-HTTP 22 Aug :00-24: NASA-HTTP 0 Jul :00-08: NASA-HTTP 0 Jul :00-7: NASA-HTTP 0 Jul :00-24: NASA-HTTP 25 Jul :00-08: NASA-HTTP 25 Jul :00-7: NASA-HTTP 25 Jul :00-24: e partton the te nto slots, each wth a length of 5 nutes. Durng the executon, we count the nuber of arrved requests at each te slot. Then we predct the average arrval rate of next te slot accordng to the records of prevous and current slot. The predctng algorth s forulated as, λ = λ + 0.5( λ λ ) (32) next current current prevous 97

7 where λprevous and λ current are the real nuber of requests durng the passed two slots. They can be counted easly. The servers are parttoned nto 0 groups, each wth a FFO (Frst n Frst Out) watng queue. At the end of each te slot, the syste re-allocates the resources to every servce nstance accordng to λ next. However, we do not adust the group sze edately after the calculaton, but after a te slot. Ths s because the current queue length s a consequence of prevous te slot. The specfc paraeters are lsted n Table. TABE. PAAMETES AND THE DEFAT VAES Paraeter Default Value Paraeter Default Value Servce Te Negatve ntercept Dstrbuton Exponental b ando (0 20)/60 Servce ate ando ando (0 30)/60 ntercept (0 5) ns custoers 0 Fgure 5 depcts the evoluton of revenues every 5 nutes. Eghty servers are deployed n ths sulaton. The overall curve tendences, both of MT and Heurstc, anly depend on arrval rate. t can be seen fro Fg. 5 that MT outperfors Heurstc. The average revenues every 5 nutes of MT and Heurstc durng the 8 hours are and respectvely. The revenues of MT s 7.57% hgher than Heurstc. S,57 +HX V F 7 PH P Q Fgure 6. \ F Q H F H Evoluton of revenues durng 5 nutes over te,57 +HX V F PH P Q Fgure 7. Evoluton of effcency durng 5 nutes over te Fgure 6 and Fgure 7 llustrate the perforance coparson of T and Heurstcs. There are 60 servers deployed n the sulatons. Fgure 6 s the revenues of both T and Heurstc over te. t shows us that T s better than Heurstc. The average revenues every 5 nutes of T and Heurstc durng the 8 hours are and respectvely. The revenues of T s 65.9% hgher than Heurstc. Fgure 6 ndcates that T s better n provng revenues than Heurstc. However, t does not reflect the real perforance levels of these two strateges. For exaple, aybe both algorths are at a very low level copared wth other algorths. Fgure 7 s the effcency evoluton of T and Heurstc over te. Here effcency s defned as the rato of actual revenues to the axu revenues n theory, naely the whole revenues when all the requests are responded wthn ther requred response te deand. Effcency reflects the real perforance ore obectvely wth the overall benchark and standard. Fgure 7 shows us that T ostly closes to the revenues upper bound n theory, wth and average effcency of 93.89%. Heurstc has a low and fluctuant effcency, wth an average effcency of 62.24%. The effcency of T s uch hgher than Heurstc wth 3.65%. Nuber of requests Te (5nutes) Fgure 8. Evoluton of total arrval requests over te Sultaneously, both Fgure 5 and Fgure 6 show us that the revenues of MT and T durng the 47 th te slot decreases sharply. e beleve that t results fro the extree fluctuaton of arrval rate. As dsplayed n Fgure 8, the arrval rate decreases sharply fro 42 nd to the 45 th te slot, whle t rses quckly after the 46 th te slot. Thereby, the predcton of arrval rate by Equaton (32) s not correct, whch sleads the resource allocaton. The revenues of MT and T also decrease sharply at the 26 th te slot because of the sae reason. Therefore, a ore precse predcton of arrval rate has a postve pact on the valdty of our resource allocaton strateges durng ther practcal applcatons. V. EATED OK The busness odel s the key characterstc to dstngush Cloud coputng fro prevous typcal 98

8 coputng paradgs []. As a brdge, SA plays a vtal role n facltatng the realzaton of an econoc-based Cloud syste. SA provdes echanss and tools that allow servce provders and end users to express ther requreents and constrants such as response te and prce schee. t s very natural but challengng for servce provders to allocate the resources dynacally aong the end-users based on the agreeent, thereby to axze the revenues. There s an extensve lterature on resource anageent technques for coercal data centers. tlty s often adopted as a etrc for resource allocaton. alsh et al. [6] dscuss a dstrbuted archtecture wth the a of solvng the resource allocaton proble for dedcated data center archtecture wth dynac vrtual pool. The ephass of these papers s on the use of utlty functons as fundaental fraework to optze resource usage rather than the utlty of data center. tlty functons provde crtera for tradng off between ultple copetng syste obectves. akuar et al. [7] propose a QoS-aware resource allocaton odel Q- AM. The obectve of Q-AM s to axze the utlty derved fro concurrent applcatons under the ultdensonal QoS constrants. Ghosh et al. [8] and Hansen et al. [9] further extend Q-AM, where the scalablty and ablty to ake resource trade-off decsons are enhanced. Many works llustrate how to eet the QoS and SA requreents by the proper resource allocaton. Menascé et al. [0, ] propose an approach based on hll clbng technques to gude the search for the best cobnaton of confguraton paraeters of a ultlayered archtecture. t uses the exstng resources best n a anner that the desred QoS levels are et to cope wth short ter fluctuatons n the workload. Chandra et al. [2] present technques for dynac resource allocaton n shared web servers. sng a cobnaton of onlne easureent, predcton and adaptaton, the technques can dynacally deterne the resource share of each applcaton based on QoS and easured workload. evy et al. [3] present an archtecture and prototype pleentaton of a perforance anageent syste, where cluster utlty s used to encapsulate busness value n the face of servce level agreeents. The syste dynacally allocates server resources, balances the load aong ultple classes accordng to perforance deand. et al. [4] take the nzaton of resource consupton as the obectve and propose a strategy for autonoc coputng to eet SA requreents n ters of response te and server utlzaton. However, the aorty of prevous work does not take the econoc ssues related to SAs nto account. Zhang and Ardagna [5] propose a resource allocaton controller for autonoc coputng data center. The obectve s to axze the provder s revenues assocated wth ult-class Servce evel Agreeent. n the syste, the revenue depends on dscrete QoS levels and the revenue ganed per request ncreases wth the acheved perforance level. u et al. [6] propose a theoretcal odel to axze the revenues of a hostng platfor subect to ult-class SAs. T, et al. [7] presents a fraework that lnks techncal and econocal aspects to the anageent of coputatonal resources. t cobnes soe techncal ethods such as dynac prcng, dfferent ob prortes, and clent classfcaton nto an econocally enhanced resource anageent that ncreases revenue for the local resource stes. Vllella et al. [8] study how a servce provder should allocate the applcaton ter of an Ecoerce applcaton subect to QoS constrants. The paper odels each server as an M/G//PS queue, and derves three sple ethods that approxate the allocaton that axzes revenues. Anthony et al. [9] propose overbookng odels to fnd an deal overbookng lt that exceeds the axu Grd capacty wthout ncurrng greater copensaton cost. However, all the works adopt a flat-rate dscrete prce levels whle we adopt a contnuous prce functon n ths paper. e also provde the foral precse answer to the probles. There are several works sharng slar scenaros wth our work. Zhu et al. [3] proposes an allocaton strategy of server resources aong custoers to nze the ean response te. Nevertheless, ths work does not consder the econoc odel. n addton, the paraeter of weght q n optal soluton lacks the specfc practcal eanng. The work [4] s very slar to ours. t provdes two strateges for the resource allocaton, Heurstc and Greedy. Greedy s optal but t often costs an practcally long executon te whle the proved algorth does not always work well. Heurstc s sple but our work dsplays that ts valdty s affected by the envronent paraeters. V. CONCSONS AND FTE DECTONS Cloud coputng has eerged as a new busness odel for delverng varous T servces to custoers n a pay-asyou-go anner. The busness odel of Cloud coputng requres legal servce level agreeents to facltate the collaboraton between end-users and servce provders. Ths paper addresses how to axze provders revenues based on the perforance-aware prcng odel n SAs through the proper resource allocaton aong the custoers. Ths paper has forulated the optzaton proble and gven the optal results by the Method of agrange Multpler. Our experental results have shown that the proposed algorths n ths paper always outperfor the prevous work and they are of hgher sgnfcance especally when the Cloud envronents face wth coputng resource shortage. However, we consdered the server group servng each custoer as an M/M/ odel n ths paper. t s ore reasonable to odel the server group as an M/M/c odel when runnng envronents are easly ntated. Moreover, prcng odel s the foundaton of our work. But prcng odel can be very coplex. Therefore, t wll be nterestng to see how to apply technques proposed n ths paper to such scenaros. e wll further nvestgate these probles n the future work. ACKNOEDGMENTS Ths work was supported by the Natonal Basc esearch Progra of Chna (Grant No. 2009CB320705), the Natonal Natural Scence Foundaton of Chna (Grant Nos , ), and the Jangsu Natural Scence Foundaton (Grant Nos. BK , BK200900). The frst author 99

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