Pricing for Resource Allocation in Cloud Computing

Transcription

1 Internatonal Conference on Logstcs Engneerng, Management and Computer Scence (LEMCS 2015) Prcng for Resource Allocaton n Cloud Computng Zhengce Ca Department of Informaton Servce Anhu Insttute of Internatonal Busness Hefe, Chna @qq.co m Hujun Yang Department of Informaton Servce Anhu Insttute of Internatonal Busness Hefe, Chna @qq.co m Guolong Chen School of Informaton Engneerng Suzhou Unversty Suzhou, Anhu Provnce, Chna cglbox@sna.com Xanwe L* School of Informaton Engneerng Suzhou Unversty Suzhou, Anhu Provnce, Chna lxanwe163@163.com * Correspondng Author Abstract In cloud computng envronment, prcng s an effectve method for resource allocaton and t provdes effcent ncentve for cloud provders to provde cloud servces. In ths paper, the author nvestgates two prcng schemes for the allocaton of cloud resources n a monopoly cloud market subject to constraned capacty of the cloud provder. There are two man prcng schemes, on-demand and reserved prcng mechansms adopted by leadng cloud provders,.e., Amazon and Gogrd. The paper analyzes how cloud users make ther choce decsons to subscrbe to cloud resources under dfferent prcng schemes. Keywords-cloud computng; prcng schemes; resource allocaton; revenue; utlty I. ITRODUCTIO Cloud computng has receved a great deal of attenton n both research and engneerng felds, and the use of cloud servces has become more and more wde. Fg. 1 llustrates the applcaton of cloud servces [1]. The defnton of cloud computng s an open topc and t can be defned by several ways, one popular recognzed defnton proposed by Buyya et al. [2] s: Computers that are dynamcally provsoned and presented as one or more unfed computng resources based on a cloud s a type of parallel and dstrbuted system consstng of a collecton of nterconnected and vrtualzed servce-level agreements establshed through negotaton between the servce provder and the consumers. Cloud servces can be categorzed nto three man types [3][4], Infrastructure as a Servce (IaaS), Software as a Servce (SaaS) and Platform as a Servce (PaaS), among whch IaaS and SaaS are more commonly used, therefore, most of the current works focus on study resource allocaton n IaaS and SaaS clouds. In IaaS cloud context, such as Amazon EC2, physcal resources (memory, dsk, and CPU et al) are vrtualzed nto dfferent types of vrtual machnes (VMs), and the computatonal resources are leased to cloud users n the form of VM nstances, as shown n Fg. 2. Table I shows some confguratons of VM nstances n Amazon EC2. In PaaS cloud context, such as Google App Engne, cloud users can develop and run ther applcatons on a computng platform. In SaaS cloud context, cloud users can access the applcatons whch are delvered over the Internet. Fgure 1. The uses applcaton of cloud servces [1]. Fgure 2. An llustraton of IaaS cloud The authors - Publshed by Atlants Press 921

2 In cloud computng envronment, prcng s an effectve method for resource allocaton and t provdes effcent ncentve for cloud provders to provde cloud servces. There are two prcng schemes,.e., on-demand and reservaton prcng schemes that are wdely adopted by leadng cloud provders, lke Amazon (Elastc Cloud) EC2 [5] and Gogrd [6]. The prces of some VM nstances n US East (. Vrgna) are shown n Table II wth the operatng system Lnux. Table III shows the prces of some Gogrd VM nstances under on-demand and reservaton prcng schemes. Besdes the two prcng schemes, other types of prcng schemes have also been studed. The authors n [7] [8] nvestgated aucton-lke prcng mechansms. The works of [9] [10] studes competton-based prcng scheme. The rest of the paper s organzed as follows. In the second secton, t studes optmal prcng for revenue maxmzaton by makng use of game theory to nvestgate the relatonshp between cloud provders and users. The author does smulatons to verfy the analyss n the thrd secton. Conclusons and future works are gven n the last secton. TABLE I. Instance Types TABLE II. TABLE III. COFIGURATIOS OF AMAZO EC2 VM ISTACES vcpu Storage (GB) Memory (GB) m1.small m1.large 2 2* m2.xlarge m3.xlarge c3.2xlarge Instance Types PRICES OF SOME AMAZO EC2 VM ISTACES On-demand prcng(hourly) Reservaton prcng(monthly) m1.small $0.048/h $21.9/m m1.large $0.385/h $89.79/m m2.xlarge $0.27/h $89.06/m m3.xlarge $0.293/h $152.57/m c3.2xlarge $0.462/h $234.33/m PRICES OF SOME GOGRID VM ISTACES Instance types Hourly Monthly X-Small $0.03 $16.43 Small $0.06 $32.85 Medum $0.12 $65.70 Large $0.24 $ X-Large $0.48 $ II. PRICIG FOR REVEUE MAXIMIZTIO The paper studes optmal prcng for revenue maxmzaton n a monopoly cloud market n ths secton. Frst, the author analyzes how to make choce decson gven dfferent prces and prcng schemes of VM nstances. Then, the paper studes how to set optmal prces n order to maxmze the revenue of cloud provders whle meetng cloud users satsfactons. A. Cloud Users Choce wth Dfferent Prcng Schemes As llustrated n Table II and Table III, even for the same type of nstance, cloud users have to make a decson about how to choose the sutable prcng schemes. In order to help cloud users make rght decsons, the paper frst analyzes whch prcng scheme cloud users should choose. Suppose that a cloud user wants to buy t hours to process hs/her servce requests. Take m1.small VM nstance of Amazon EC2 as an example, the prce that he/she has to pay s $0.048t, and the reservaton prce per month s $21.9. By settng 0.048t=21.9, then t 456hours, whch means that f total tme of the usage of the m1.small VM nstance are less than 456 hours n one month, t s better for ths cloud users to adopt on-demand prcng scheme, otherwse, t s better for ths cloud user to adopt reservaton prcng scheme. If ths cloud user chooses to buy the smlar type of VM nstance n Gogrd, for example, X-Small, the total money that he/she has to pay s 0.03t under on-demand prcng scheme, and the reservaton prce s $16.43 per month, by settng 0.03t=16.43, then, t 548 hours, whch means that f total tme of the usage of the X-Small VM nstance are less than 548hours n one month, t s better for ths cloud user to adopt on-demand prcng scheme, otherwse, t s better for ths cloud user to adopt reservaton prcng scheme. The author summarzes the above analyss results n Table IV. Fg. 3 further llustrates the adopton opton under on-demand and reservaton prcng schemes. T ABLE IV. CHOICE DECISIO FOR CLOUD USERS Instance Hourly Monthly types m1.small Usage <456hours Usage 456hours X-Small Usage <548 hours Usage 548 hours Medum Usage <456hours Usage 456hours Large Usage <581hours Usage 581hours X-Large Usage <546hours Usage 546hours B. Cloud Users Decson Choces Then the paper studes how to set optmal prces n order to maxmze the revenue of cloud provders whle meetng cloud users satsfactons. Assume that there s a cloud provder wth total capacty C sellng cloud resources n the form of VM nstances to a potental number of cloud users, the prce of per VM nstance s charged wth p $/h under on-demand prcng scheme. Each cloud user s denoted by θ, whch s unformly dstrbuted n [0, 1]. 922

3 Fgure 3. Illustraton the adopton opton. Fgure 5. How cloud users utltes vary wth dfferent values of α. change of demand to the percent change of prce, and cloud users wll get more utlty f the value of the elastc parameter s hgher. It s known that the elastcty of the above utlty functon s 1/(1-α). For the cloud users, they wll choose to subscrbe cloud resources f and only f ther net benefts are nonnegatve, whch mples that, θx α px 0, (3) Fgure 4. Stakelberg game n the monopoly cloud market. The paper models the nteractons between cloud provders and users as a stakelberg game [10], whch s llustrated n Fg. 4. In the frst stage, cloud provder makes ther prce decsons, and n the second stage, cloud users make ther selecton decson choces. The backward method s used and the author frstly analyzes cloud users decson choces. Gven the prce of that VM nstance p, a cloud user that requres x VM nstances wll pay px, and hs/her net beneft can be expressed as θu(x ) px (1) where u(x ) s the utlty that ths cloud user gets. The paper models u(x ) by the followng utlty functon whch s wdely used n the lterature [11], u(x )= x α where α s an elastcty parameter,whch les n (0,1). Fg. 5 llustrates how users utltes vary wth dfferent values of α. From ths fgure t can be observed that α reflects the elastc demand of ths cloud user, that s, the percentage (2) from whch a crtcal value θ 0 can be obtaned and the cloud users whose values are dstrbuted n [0, θ 0 ] wll not subscrbe to the cloud resources, and the users whose values are dstrbuted n [θ 0, 1] wll choose to use the cloud servces. The cloud users problem can be expressed by max[ u x px] (4) s.t. x 0 C. Cloud Provder s Prng Decson The paper studes how to set optmal prces n order to maxmze the revenue of cloud provders whle meetng cloud users satsfactons n ths subsecton. Prcng provdes an economc ncentve for cloud provders and t ensures the success of cloud computng. For the cloud provder, ts objectve s to maxmze ts revenues, whch s the total pay from cloud users. The cloud provder s problem can be formulated as follows, max p x (5) s.t. 1 x 1 C px 0 u x x 0 The frst constrant of problem (5) ensures that the total number of VM nstances should not be over the capacty of ths cloud provder, and the second constrant s to make sure that cloud users net beneft s nonnegatve. From the observaton of the second constrant of problem (5), t can 923

4 px u x be found that should be satsfed to be optmal. Otherwse, the cloud provder can ncrease the prce of ths type of VM nstance. Therefore, transform the problem (5) nto an equvalent problem, 1 max u x (6) s.t. 1 x C x 0 ow, get the cloud provder s revenue maxmzaton problem and do smulatons to verfy the analyss n the next secton. III. SIMULATIO RESULTS In ths secton, do smulatons to verfy the analyss n the prevous secton. The frst step s to analyze users decson choces, and then analyze cloud provder s revenue problem. A. Cloud Users Utltes The frst step s to analyze how cloud users are senstve to the prces of cloud resources. Fg. 6 llustrates how cloud users net benefts vary wth dfferent values of θ wth x=2, p=0.2 and α=1/2. It can be observed from Fg. 6 that not all the cloud users can get net beneft, therefore, some cloud users may not choose to subscrbe to the cloud resources. The parameter θ reflects cloud users wllng to pay, whch means that users wth hgher value of θ wll be more wllng to use cloud servces. Fg. 7 llustrates how cloud users net benefts vary wth the prce charged by cloud provder wth θ and other parameters are set the same as n Fg. 6. It can be observed that wth prce ncreasng, the net beneft of ths cloud user wll get less net beneft, and ths mples that n order to encourage cloud users to use cloud servces, cloud provders should set prces of cloud resources properly, otherwse, hgher prces wll dscourage cloud users to pay for usng cloud servces. Fgure 7. How cloud users net benefts vary wth prce of cloud resources p. B. Cloud Provder s Revenue Problem The next step s to analyze how the cloud provder sets ts prces n order to maxmze ts revenue. From Eqs.(5) and (6), t s known that the revenue of cloud provder s affected by cloud users choces, then transform the revenue functon nto a functon assocated wth cloud users utltes. Fg. 8 shows that the revenue of the cloud provder vares wth dfferent number of VM nstances, and the revenue wll be hgher f the prce s set hgher wth the same number of VM nstances. Fg. 9 shows that cloud users are more wllng to subscrbe cloud servces f they have hgher values for usng cloud servces, and f cloud users have more elastc demand for cloud servces, cloud provder wll get more revenue. The above analyss mply that cloud provder can set hgher prces for these cloud users who are more wllng to pay and who have hgher elastc demands. Fgure 6. How cloud users net benefts vary wth dfferent values of θ. Fgure 8. The revenues of cloud provder vary wth dfferent number of VM nstances. 924

5 ACKOWLEDGMET Ths work s partly supported by the key project of Anhu Provnce (S ), and the Major project of nature scence of Department of Educaton of Anhu Provnce (KJ2014ZD31). Fgure 9. The revenues of cloud provder vary wth dfferent cloud users types. IV. COCLUSIOS AD FUTURE WORKS The paper studes resource allocaton n a monopoly cloud market. It analyzes the choce decsons of cloud users n the Amazon EC2 and Gogrd clouds, and ponts out the rght choce for cloud users when face on-demand and reservaton prcng schemes. The paper does not only analyze how cloud users utltes and net benefts vary wth dfferent types of cloud users and dfferent number of VM nstances, but also analyzes how the revenue of cloud provder vares wth dfferent prces and dfferent number of VM nstances. Future works wll nclude resource allocaton n a duopoly or olgopoly cloud market where there are more than one cloud provders. REFERECES [1] J. Me, K. L, A. Ouyang et al. A Proft Maxmzaton Scheme wth Guaranteed Qualty of Servce n Cloud Computng, n press. [2] R. Buyya, C.S. Yeo, and S. Venugopal, Market Orented Cloud Computng: Vson, Hype, and Realty for Delverng t Servces as Computng Utltes, Proc. 10th IEEE Conference on Hgh Performance Computng and Communcatons (HPCC 2008), Dalan, Chna, pp. 5-13, Sep [3] M. Armbrust, A. Fox, R. Grffth, A. D. Joseph, R. Katz, A. Konwnsk,G. Lee, D. Patterson, A. Rabkn, I. Stoca, and M. Zahara. A vew of cloud computng. Commun. ACM, 53(4):50 58, [4] S. K. Garg, S. Versteeg, and R. Buyya. A framework for rankng of cloud computng servces. Future Gneraton Computer Systems, 29: , [5] Amazon EC2. [6] GoGrd Prcng. [7] Q. Wang, K. Ren, and X. Meng. When cloud meets ebay: Towards [8] effectve prcng for cloud computng. In IEEE IFOCOM, [9] H. Xu and B. L. Dynamc cloud prcng for revenue maxmzaton. [10] IEEE Transactons on Cloud Computng, 1(2): , July [11] Y. Feng, B. L, and B. L. Prce competton n an olgopoly market wth multple aas cloud provders. IEEE Transactons on Computers, 63(1):59 73, Jan [12] D. Fudenberg and J. Trole, Game Theory, MIT Press, Cambrdge, USA, [13] S.Y. Yun, Y. YI, D. H. Cho, et al. The economc effects of sharng femtocells. IEEE Transactons on Selected Areas n Communcatons, 30(3): , Aprl