Profit-Maximizing Virtual Machine Trading in a Federation of Selfish Clouds

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1 Proft-Maxmzng Vrtual Machne Tradng n a Federaton of Selfsh Clouds Hongxng L, Chuan Wu, Zongpeng L and Francs CM Lau Department of Computer Scence, The Unversty of Hong Kong, Hong Kong, Emal: hxl, cwu, fcmlau}@cshkuhk Department of Computer Scence, Unversty of Calgary, Canada, Emal: zongpeng@ucalgaryca Abstract The emergng federated cloud paradgm advocates sharng of resources among cloud provders, to explot temporal avalablty of resources and dversty of operatonal costs for ob servng Whle extensve studes exst on enablng nteroperablty across dfferent cloud platforms, a fundamental queston on cloud economcs remans unanswered: When and how should a cloud trade VMs wth others, such that ts net proft s maxmzed over the long run? In order to answer ths queston by the federaton, a number of mportant, correlated decsons, ncludng ob schedulng, server provsonng and resource prcng, need to be dynamcally made, wth long-term proft optmalty beng a goal In ths work, we desgn effcent algorthms for nter-cloud resource tradng and schedulng n a federaton of geo-dstrbuted clouds For VM tradng among clouds, we apply a double auctonbased mechansm that s strategyproof, ndvdual ratonal, and ex-post budget balanced Couplng wth the aucton mechansm s an effcent, dynamc resource tradng and schedulng algorthm, whch carefully decdes the true valuatons of VMs n the aucton, optmally schedules stochastc ob arrvals wth dfferent SLAs onto the VMs, and udcously turns on and off servers based on the current electrcty prces Through rgorous analyss, we show that each ndvdual cloud, by carryng out our dynamc algorthm, can acheve a tme-averaged proft arbtrarly close to the offlne optmum I INTRODUCTION The emergng federated cloud paradgm advocates sharng of dsparate cloud servces (n separate data centers) from dfferent cloud provders, and nterconnectng them based on common standards and polces to provde a unversal envronment for cloud computng Such a cloud federaton explots temporal and spatal avalablty of resources (eg, vrtual machnes) and dversty of operatonal costs (eg, electrcty prces): when a cloud experences a burst of ncomng obs, t may resort to VMs of other clouds havng dle resources; when the electrcty prce for runnng servers and VMs s hgh at one data center, the cloud can schedule obs onto other data centers wth lower electrcty charges In ths way, the aggregate ob processng capacty of the cloud federaton can potentally be hgher than the summaton of the capactes of separate clouds operatng alone, leadng possbly to a larger overall proft To realze such a federated cloud paradgm, fundamental problems on cloud economcs need to be resolved Naturally, a cloud n the real world s selfsh, and would try every mean to maxmze ts own proft e, ts ncome from handlng obs and leasng VMs to other clouds, mnus ts operatonal costs and expenses n VM rental from other clouds Only f ts proft can be maxmzed and n any case not lower than when operatng alone, can a cloud be ncentvzed to on a federaton Ths ncentve s materalzed f an effcent mechansm to carry out resource tradng and schedulng among federated clouds, thus achevng proft maxmzaton for ndvdual clouds, can be put n place To ths end, several correlated, practcal decsons need to be made: (1) VM prcng: what mechansm should be advocated for VM sale and purchase among the clouds, and at what prces? (2) Job schedulng: gven tme-varyng ob arrvals at each cloud, havng dfferent resource and SLA requrements, should a cloud serve the obs rght away or later, and use ts own resources or others, n order to take advantage of lower electrcty prces? (3) Server provsonng: s t more benefcal for a cloud to keep many of ts servers runnng to serve obs of ts own and those from others, or to swtch some of them off to save electrcty costs? These decsons should be effcently and optmally made n an onlne fashon, whch n turn provde a guarantee for long-term optmalty of ndvdual cloud s profts In ths paper, we desgn effcent algorthms for nter-cloud resource tradng and schedulng, n a federaton consstng of dsparate cloud data centers A double aucton-based mechansm s appled for the sell and purchase of avalable VMs across cloud boundares, whch s strategy-proof, ndvdual ratonal, and ex-post budget balanced Closely combned wth the aucton mechansm s an effcent, dynamc VM tradng and schedulng algorthm, whch carefully decdes the true valuatons of VMs to partcpate n the aucton, optmally schedules randomly-arrvng obs wth dfferent resource requrements (eg, number of VMs) and SLAs (eg, maxmum ob schedulng delay) onto dfferent data centers, and udcously turns on and off servers n the clouds based on the current electrcty prces The contrbutons of ths work are summarzed as follows Frst, we address selfshness of ndvdual clouds n a cloud federaton, and desgn effcent mechansms to maxmze the net proft of each partcpatng cloud Ths proft s not only guaranteed to be larger than that when the cloud operates alone, but also maxmzed over the long run, n the presence of tme-varyng ob arrvals and electrcty prces Second, we novelly combne a truthful double aucton mechansm wth stochastc Lyapunov optmzaton technques, and desgn an onlne VM tradng and schedulng algorthm for a cloud to optmally prce the VMs and udcously schedule the VM and server usages Each cloud values dfferent VMs based on the back pressure n ts ob queues, and bds for them n the aucton for effectve VM acquston Thrd, we demonstrate that by applyng the dynamc algorthm wth double aucton, each cloud can acheve a tmeaveraged proft arbtrarly close to ts offlne optmum (obtaned f the cloud has complete knowledge of the ncomng

2 obs and electrcty prces over the entre tme span) In the rest of the paper, we dscuss related lterature n Sec II, present the system model n Sec III, ntroduce the detaled resource tradng and schedulng mechansms n Sec IV, and conclude the paper n Sec V II RELATED WORK A Optmal Schedulng n Cloud Computng Exstng lterature ([1] [3] and references theren) on resource schedulng n cloud systems focuses manly on a sngle cloud that operates alone A common theme s to mnmze the operatonal costs (manly consstng of electrcty blls) n one or multple data centers of the cloud, whle provdng certan performance guarantee for ob schedulng, eg, n terms of average ob completon tmes [1] [3] Dfferent from these studes, ths work nvestgates bounded schedulng delay for each ob even n the worst cases, and proft maxmzaton for ndvdual selfsh clouds n a cloud federaton B Resource Tradng Mechansms There s a large body of lterature devotng to resource tradng n computng grds [4] and wreless spectrum leasng [5] [6] Varous mechansms have been studed, eg, barganng [4], fxed or dynamc prcng based on a contract or the supplydemand rato [7], and auctons [5], [6] A typcal barganng mechansm [4] tends to have unacceptable complexty when negotatng between each par of traders Fxed prcng, eg, Amazon EC2 on-demand nstances, has been shown to be neffcent n proft maxmzaton gven there are system dynamcs [8] Dynamc prcng, such as Amazon EC2 spot nstances, could be neffcent too, as the partcpants may quote the resources untruthfully [9] Aucton stands out as a promsng mechansm, for whch there are many solutons ([5], [6] and references theren) wth truthful desgn and polynomal complexty Although some recent works [8], [9] am to desgn an aucton mechansm wth ndvdual ratonalty (non-negatve proft gan) for tradng n federated clouds, they do not explctly address ndvdual proft maxmzaton over the long run Moreover, there s very lttle dscusson n the lterature on auctons about methods to quanttatvely calculate the true valuaton n each bd, whch s usually assumed as known Our desgn addresses these ssues III SYSTEM MODEL AND AUCTION FRAMEWORK A Federaton of Clouds We consder a federaton of F clouds, each of whch assgned to a dfferent geometrc locaton and operates autonomously to gan proft by servng ts customers ob requests, managng server provsonng and tradng resources wth other clouds Servce demands: Each ndvdual cloud [1, F] has a front-end proxy server, whch accepts ob requests from ts customers There are S types of obs beng servced at each cloud, each specfed by a three-tuple < m s,g s,d s > Here, m s [1,M] refers to the type of the requred VM nstances, where M s the maxmum number of VM types, and each type corresponds to a dfferent set of confguratons of CPU, storage and memory; g s s the number of type-m s VMs that the ob needs smultaneously (see Amazon EC2 API [7]); and d s stands for the SLA (Servce Level Agreement) of ob type s [1, S], evaluated by the maxmal response delay for schedulng a ob, e, the tme-span from when the ob arrves to when t starts to run on the scheduled VMs In a real cloud, t s common to buy servers of the same confguraton and provson the same type of VMs on one machne [10] Therefore, we suppose each cloud has N m homogeneous servers to provson VMs of type m [1,M], each of whch can provde a maxmum of C m VMs of ths type; the total number of servers n cloud s M m=1 Nm The system runs n a tme-slotted fashon At the begnnng of each tme slot t, r s [0,Rs ] obs arrve at cloud, for each ob type s R s s an upper-bound on the number of type-s obs submtted to cloud n a tme slot The arrval of obs s an ergodc process at each cloud We assume the arrval rate s gven, and how a customer decdes whch cloud to use s not a concern n ths study Let p s [0,ps(max) ] be the gven servce charge to the customer by cloud, for acceptng a ob of type s n tme slot t, whch remans fxed wthn a tme slot, but may vary across tme slots Here, p s(max) s the maxmum possble prce for p s Job schedulng: Each ncomng ob to cloud enters a FIFO queue of ts type a cloud mantans a queue to buffer unscheduled obs of each type s, wth Q s as ts length n t When the requred VMs of a ob are allocated, the ob departs from ts queue and starts to run on the VMs A cloud may schedule ts obs on ether ts own VMs or VMs leased from other clouds, whchever yelds the best economc benefts Let µ s be the number of type-s obs of cloud that are scheduled for processng n cloud at the begnnng of slot t When a ob s maxmum response tme (the SLA) cannot be met, probably because of system overload, the ob s dropped A penalty s rased n ths case, to compensate for the customer s loss Let D s [0,D s(max) ] (1) be the number of type-s obs dropped by cloud n t, where D s(max) s the maxmum value of D s Let ξs ps(max) be the penalty to drop one such ob, whch s at least equal to the maxmum prce charged to the customer f the ob were accepted Hence, the number of unscheduled obs buffered at each cloud can be updated wth the followng the queueng law: F Q s (t+1) =maxq s µ s D,0} s +r, s s [1,S], [1,F] (2) Job schedulng should satsfy the followng SLA constrant: Each type-s ob n cloud s ether scheduled or dropped (subect to a penalty) before ts maxmum response delay d s, s [1,S] (3) To satsfy ths SLA constrant, we seek to bound the lengths of ob queues and the followng vrtual queues Z s, each assocated wth a ob queueq s The vrtual queues are created based on the ǫ persstence queue technque [11] =1

3 F Z(t+1) s = maxz+1 s Q s >0} [ǫ s µ s ] D s F C ms N ms 1 Q s =0},0}, [1,F],s [1,S] (4) g s =1 Here, ǫ s > 0 s a constant 1 Q s >0} and 1 Q s =0} are ndcator functons such that 1 Q s >0} = =1 1 f Q s > 0 ; 1 Q s 0 Otherwse =0} = 1 f Q s = 0 0 Otherwse Length of a vrtual queue reflects the cumulated response delay of obs from the respectve ob queue Server provsonng: We consder the electrcty cost, for runnng and coolng the servers [12], as the man component of the operatonal cost n a cloud Other costs, eg, space rental and labour, reman relatvely fxed for a long tme, and therefore are of less nterest Gven that electrcty prces vary at dfferent locatons and from tme to tme [1], we model the operatonal cost β n each cloud as a general ergodc process over tme, varyng across tme slots between β (mn) and β (max) Each cloud strategcally decdes the number of actve servers at each tme, to optmze ts proft Let n m be the number of actve servers provsonng type-m VMs at cloud n t The avalable server capactes constran any feasble ob schedulng strategy at tme t as follows: [1,F] s:m s=m,s [1,S] g sµ s C m n m, m [1,M], [1,F], (5) n m N m, m [1,M], [1,F] (6) (5) states that the overall demand for type-m VMs n cloud from tself and other clouds should be no larger than the maxmum number of avalable type-m VMs on the actve servers n cloud Here g s µ s s the total number of VMs needed by type-s obs scheduled from cloud to cloud n t Consderng practcal ob executon effcency, we only consder the schedulng of a ob to VMs n a sngle cloud, but not to VMs across dfferent clouds (6) ensures that the number of actve servers s lmted by the total number of on-premse servers of the correspondng VM confguraton at each cloud B Inter-cloud VM Tradng wth Double Aucton In an nter-cloud resource market, VMs are the tems for tradng For each type of VMs, multple clouds may have them on sale whle multple other clouds can request them A double aucton s a natural ft to mplement effcent tradng n ths case, allowng both sellng and buyng clouds to actvely partcpate n prcng to strve for ther own benefts In our dynamc system, a mult-unt double aucton s carred out among the clouds at the begnnng of each tme slot, to decde the VM trades wthn that tme slot Buyers & Sellers: A cloud can be both a buyer and a seller A buy-bd < b m,γm > records the unt prce and maxmum quantty for whch cloud s wllng to buy VMs of type m, n t Smlarly, a sell-bd < s m,ηm > records the unt prce and maxmum quantty for whch cloud s wllng to sell VMs of type m n t Let b m and sm be cloud s true valuatons of buyng and sellng a type-m VM respectvely (the max/mn prce t s wllng to pay/accept) Smlarly, let γ m and ηm be cloud s true valuatons of the quanttes to buy and sell VMs of type m respectvely (the maxmum number of VMs t s wllng to purchase/sell) A cloud may strategcally manpulate the bd prces and volumes, n the hope of maxmzng ts proft Auctoneer: We assume that there s a broker n the cloud federaton, assumng the role of the auctoneer After collectng all the buy and sell bds, the auctoneer executes a double aucton to decde the set of successful buy and sell bds, ther clearng prces and the numbers of VMs to trade n each type Let ˆb m be the actual charge prce for cloud to buy one type-m VM, and ˆγ m be the actual number of VMs purchased Smlarly, let ŝ m be the actual ncome cloud receves for sellng one type-m VM, and ˆη m be the actual number of VMs sold Let α m be the number of type-m VMs that cloud purchases from cloud n t, as decded by the auctoneer: ˆγ m = α m, m [1,M], [1,F], (7) ˆη m = [1,F], [1,F], α m, m [1,M], [1,F] (8) Snce VMs are purchased for servng obs, the ob schedulng decsons µ s at each cloud, [1,F],s [1,S], are related to the number of VMs t purchases: g s µ s = α m, s:s [1,S],m s=m m [1,M],, [1,F], (9) Three economc propertes are desrable for the auctoneer s mechansm () Truthfulness: Bddng true valuatons s a domnant strategy, and consequently, both bdder strateges and aucton desgn are smplfed () Indvdual Ratonalty: Each cloud obtans a non-negatve proft by partcpatng n the aucton () Ex-post Budget Balance: The auctoneer has a non-negatve surplus, e, the total payment from all wnnng buy-bds s no less than the total charge for all wnnng sellbds n each tme slot Detaled desgn of an aucton wth these propertes s gven n our techncal report [13] C Indvdual Selfshness Each cloud n the federaton ams to maxmze ts tmeaveraged proft (revenue mnus cost) over the long run of the system, whle strvng to fulfl the resource and SLA requrements of each ob Revenue: A cloud has two sources of revenue: ) ob servce charges pad by ts customers, and ) the proceeds from VM sales The tme-averaged revenue of cloud by undertakng dfferent types of obs from ts customers s Φ 1 1 = lm Ep s r}, s [1,F] (10) t=0 s [1,S]

4 We assume the front-end charges, p s, from a cloud to ts customers, are gven Hence, ths part of the revenue s fxed n each tme slot The tme-averaged ncome of cloud from sellng VMs to other clouds s: Φ 1 2 = lm t=0 m [1,M] Eŝ m ˆη m }, [1,F] (11) Cloud can control ths ncome by adustng ts sell-bds, e, s m and ηm, m [1,M], at each tme Cost: The cost of cloud conssts of three parts: ) operatonal costs ncurred for runnng ts actve servers, ) the penaltes for droppng obs, and ) the expendture on buyng VMs from other clouds The tme-averaged cost for operatng servers s decded by the number of actve servers n each tme, e, Ψ 1 M 1 = lm Eβ n m }, [1,F] (12) t=0 m=1 The tme-averaged penalty s determned by the number of dropped obs over tme, e, D s, s [1,S], t [0,]: Ψ 1 2 = lm Eξ s D s }, [1,F] (13) t=0 s [1,S] The tme-averaged expendture for VM purchase s decded by the actual VM tradng prces and numbers, as decded by the buy-bds (b m,γm ) from cloud : Ψ 1 M 3 = lm E ˆbm ˆγ m } (14) t=0 m=1 Proft Maxmzaton: The proft maxmzaton problem at cloud [1,F] can be formulated as follows: max Φ 1 +Φ 2 Ψ 1 Ψ 2 Ψ 3 (15) st Constrants (1)-(9) IV DYNAMIC ALGORITHMS We next present a dynamc algorthm for each cloud to trade VMs and schedule obs/servers, whch s n fact applcable under any truthful, ndvdual-ratonal and ex-post budget balanced double aucton mechansm Fg 1 llustrates the relaton among these algorthm modules Fg 1 Key algorthm modules The goal of the dynamc algorthm at each cloud s to maxmze ts tme-averaged proft, e, to solve optmzaton (15), by dynamcally makng decsons n each tme slot We apply the drft-plus-penalty framework n Lyapunov optmzaton theory [14], and derve (from (15)) the followng one-shot optmzaton problem to be solved by cloud n each tme slot t (detaled dervaton n our techncal report [13]): where max ϕ 1+ϕ 2+ϕ 3 (16) st Constrants (1), (5)-(9) ϕ 1 = V ϕ 2 = ϕ 3 = m [1,M] s= [1,S] [1,F] s [1,S] [ŝ m ˆη m ˆb m ˆγ m β n m ], µ s [Q s +Z s ], D s [Q s +Z s V ξ s ], and V > 0 s a user-defned parameter for gaugng the optmalty of the tme-averaged proft In solvng the one-shot optmzaton, cloud observes the states of ob and vrtual queues (Q (s),z s ), ob arrval rates, the current cost for server operaton (β ), and then decdes the optmal values of varables for optmal decsons on ) buy/sell bds for dfferent types of VMs, ) schedulng of actve servers and obs to these servers, and ) obs to drop 1 VM Valuaton and Bd: Optmzaton (16) s related to the actual chargesˆb m and ŝm ( m [1,M]) and traded VM numbers ˆγ m and ˆηm ( m [1,M]), from the double aucton These values are determned by the auctoneer accordng to buy-bds (b m,γm ) and sell-bds (sm,ηm ) submtted by all clouds, and ts double aucton mechansm When a truthful double aucton s employed, sellers and buyers bd ther true values of the prces and quanttes, n order to maxmze ther ndvdual utltes (16) s the utlty maxmzaton problem for each cloud If we can fnd true values of each cloud, b m, γm, sm and ηm, and let the cloud bd usng these values, the acheved proft n (16) s guaranteed to be the largest, as compared to bddng other values The true values of the buy/sell prces for cloud are derved as follows (detaled dervaton s presented n the techncal report [13]): bm = Qs m, (17) V g s m and s m Q s m f Q s m > β = V g s V g s /C m m, β /C m Otherwse (18) respectvely, where W s s m = arg max W s s [1,S],m s =m }, (19) and W s = Qs +Z s (20) denotes the weght for schedulng one type-s ob (to run on type-m s VM(s)) by cloud n t, and s m specfes the ob type wth the largest weght (tes broken arbtrarly), among all types of obs requrng type-m VMs The true values of the number of type-m VMs to buy and to sell at cloud are γ m = C m N m, (21) [1,F] g s and η m = C m N m (22) They state that the maxmum number of type-m VMs cloud s wllng to buy (sell) at the prce n (17) (n (18)), s the number of all potental type-m VMs n the federaton (the number can provson)

5 Algorthm 1 Dynamc Proft Maxmzaton Algorthm at cloud n Tme Slot t Input: r s, Q s, Z s, g s, m s, ξ s, C m, N m and β, s [1,S] Output: b m, s m, γ m, η m, D s, µ s and n m, m [1,M],s [1,S], [1,F] 1: VM valuaton and bd: Decde b m, s m, γ m and η m wth Eqn (17)-(22); 2: Server provsonng, ob schedulng and droppng: Decde µ s, D s and n m wth Eqn (23), (25) and (26); 3: Update Q s and Z s wth Eqn (2) and (4) To conclude, n each tme slot t, cloud submts ts bds as b m = b m, sm = sm, γm = γm and ηm = η m, for each type of VMs m [1,M] 2 Server Provsonng, Job schedulng and Droppng: After recevng results of the double aucton (actual charges and VM allocaton α ms, s [1,S], [1,F]), cloud schedules ts obs on ts local servers and (potentally) purchased VMs from other clouds, decdes whch obs to drop and the number of actve servers to provson, by solvng the one-shot optmzaton n (16) Detaled steps can be found n our techncal report [13] The derved number of type-s obs scheduled to run on the local servers s C ms N ms αms µ s g s f Qs +Zs V g s > β /C ms = and s = s m s, 0 Otherwse (23) and the number of type-s obs to run at cloud ( ) s µ s α ms = /gs f s = s m s 0 Otherwse (24) The number of type-s obs dropped by cloud n t s D s D s(max) f Q s = +Z s > V ξ s (25) 0 Otherwse The number of actvated servers at cloud to provson typem VM s calculated as n m = ( α m )/C m (26) s [1,S],m s=mµ s g s + These many servers can provde enough type-m VMs for servng local obs and sellng to other clouds Alg 1 summarzes the dynamc algorthm at each cloud We next analyze the performance guarantee provded by our dynamc algorthm Due to space lmt, all detaled proofs can be found n [13] Lemma 1: Let Q s(max) = Vξ s+rs and Zs(max) = Vξ s+ ǫ s If D s(max) maxr s,ǫ s}, each ob queue Q s and each vrtual queue Z s are upper-bounded by Qs(max) and, respectvely, n t [0,T 1], [1,F],s [1,S] Z s(max) Theorem 1 (SLA Guarantee): Each ob of type s [1,S] s ether scheduled or dropped wth Alg 1 before ts maxmum response delay d s, f we set ǫ s = Qs(max) +Z s(max) d s Theorem 2 (Indvdual Proft Optmalty): Let Ω be the offlne-optmal tme-averaged proft of cloud [1, F], obtaned wth a truthful, ndvdual-ratonal, ex-post budgetbalanced double aucton, wth complete nformaton about ts own ob arrvals and prces n the entre tme span [0,T 1] The dynamc Algorthm 1 can acheve a tme-averaged proft Ω for cloud wthn a constant gap B /V to Ω, e, Ω Ω B /V, where V > 0 and B = 1 2 s [1,S] [[ F =1 Cms N ms /g s + D s(max) ] 2 +[R] s 2 +[ǫ s] 2 +[D s(max) + F =1 Cms N ms /g s] 2 ] s a constant The gap B /V can be close to zero by fxng ǫ s and ncreasng V Detaled proof s ncluded n [13] V CONCLUSION Ths paper nvestgates proft maxmzaton strateges at ndvdual selfsh clouds n a cloud federaton where VM tradng happens across cloud boundares We adopt a truthful, ndvdual-ratonal, ex-post budget-balanced double aucton as the nter-cloud tradng mechansm, and desgn a dynamc algorthm for each cloud to decde the best VM valuaton and bddng strateges, and to schedule ob servce/drop and server provsonng n the most economc fashon, under tme-varyng ob arrvals and operatonal costs The proposed algorthm can obtan a tme-averaged proft for each cloud wthn a constant gap from ts offlne maxmum, based on sold theoretcal analyss ACKNOWLEDGEMENTS The research was supported n part by a grant from Hong Kong RGC under the contract HKU E REFERENCES [1] L Rao, X Lu, L Xe, and W Lu, Mnmzng electrcty cost: Optmzaton of dstrbuted nternet data centers n a mult-electrctymarket envronment, n Prof of IEEE INFOCOM 10, 2010 [2] R Urgaonkar, U Kozat, K Igarash, and M Neely, Dynamc resource allocaton and power management n vrtualzed data centers, n Prof of IEEE/IFIP NOMS 10, 2010 [3] Y Yao, L Huang, A Sharma, L Golubchk, and M Neely, Data centers power reducton: A two tme scale approach for delay tolerant workloads, n Proc of IEEE INFOCOM 12, 2012 [4] R Buyya, D Abramson, and J Gddy, Nmrod/g: An archtecture of a resource management and 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