SOAR: Strategy-Proof Auction Mechanisms for Distributed Cloud Bandwidth Reservation

SOAR: Strategy-Proof Aucton Mechansms for Dstrbuted Cloud Bandwdth Reservaton Yang Gu, Zhenzhe Zheng, Fan Wu, Xaofeng Gao, and Guha Chen Shangha Key Laboratory of Scalable Computng and Systems Department of Computer Scence and Engneerng Shangha Jao Tong Unversty, Chna Abstract Bandwdth reservaton s envsoned to be a valueadded feature for the cloud provder n the followng years. We consder the bandwdth reservaton tradng between the cloud provder and tenants as an open market, and desgn practcal mechansms under an aucton-based market model. To the best of our knowledge, we propose the frst famly of Strategy-prOof Aucton mechansms for cloud bandwdth Reservaton (SOAR). Frst, we present SOAR-VCG that acheves both optmal socal welfare and strategy-proofness when the tenants accept partally flled demands. Then, we propose SOAR-GDY that guarantees strategy-proofness and acheves good socal welfare when the tenants do not satsfy wth partal bandwdth reservatons. We do not only theoretcally prove the propertes of SOAR famly of aucton mechansms, but also extensvely show that they acheve good performance n terms of socal welfare, bandwdth satsfacton rato, and bandwdth utlzaton n the smulaton. I. INTRODUCTION One of the most mportant busness paradgms brought by cloud computng s Infrastructure as a Servce (IaaS), by whch vrtual machnes that abstract bundles of computaton, storage, and network resources, are provded to applcatons/tenants. More and more Internet applcatons move ther platform to cloud provders. For example, Netflx movets data storage system, streamng servers, encodng engne, and other major modules to Amazon Web Servces (AWS) n 2. A number of such applcatons that provde onlne streamng servces need guaranteed bandwdth to mantan ther qualty of servce (QoS) at requred level. However, n contrast to the CPU or storage resources, the bandwdth resource currently provded by major cloud provders does not have any quanttatve guarantee. Fortunately, recent developments of data center networkng technques make t possble to offer bandwdth reservatons for tenants [], [2]. Therefore, we beleve that there wll be a newly emerged market, n whch the tenants purchase bandwdth reservatons from cloud provders to guarantee ther QoS requrements. Recently, Nu et al. [3] elegantly ntroduced a proft makng broker to negotate the bandwdth reservaton prce wth the tenants and lead the system to converge to a unque Nash equlbrum (NE). However, NE may not be an deal soluton to the problem of cloud bandwdth reservaton due to three reasons [4]: Frst, NE s not a very strong soluton concept n game theory. NE does not hold when the players do not have belef on the others behavors. Second, NE usually cannot guarantee optmal socal welfare. Ths work was supporten part by the State Key Development Program for Basc Research of Chna (973 project 24CB3433 and 22CB362), n part by Chna NSF grant 642228, 6472252, 6272443 and 6336, n part by Shangha Scence and Technology fund 2PJ449 and 2ZR449, ann part by Program for Changjang Scholars and Innovatve Research Team n Unversty (IRT58, PCSIRT) Chna. The opnons, fndngs, conclusons, and recommendatons expressen ths paper are those of the authors and do not necessarly reflect the vews of the fundng agences or the government. F. Wu s the correspondng author. We consder the bandwdth reservaton tradng between a cloud provder and a number of tenants as an open market, anntroduce aucton to strengthen the marketng mechansm. Desgnng a practcal aucton mechansm for cloud bandwdth reservaton has two major challenges. One major challenge s strategy-proofness, whch guarantee that only reportng true valuaton as a bd can maxmzes one s utlty and no partcpant can beneft herself by manpulatng.the other major challenge s the optmalty of the aucton outcome, whch s an allocaton of the cloud bandwdth. In general case, fndng the optmal cloud bandwdth reservaton s a combnatoral problem that cannot be solven polynomal tme and classc strategy-proof aucton mechansms cannot be appled. In ths paper, we model the problem of cloud bandwdth reservaton as a sealed-bd aucton, and carry out n-depth study of mechansm desgn on the problem. We propose SOAR, whch s the frst famly of Strategy-prOof Aucton mechansms for cloud bandwdth Reservaton. SOAR contans two aucton mechansms, SOAR-VCG and SOAR-GDY. SOAR-VCG s a VCG-based aucton mechansm for cloud bandwdth reservaton, achevng both optmal socal welfare and strategy-proofness when the tenants accept partally flled demands. When the tenants are sngle-mnded, meanng that they cannot be satsfed by partal bandwdth reservatons, SOAR-GDY can be appled to guarantee strategy-proofness and to acheve good socal welfare n most cases. Fnally, we mplement these two aucton mechansms and extensvely evaluate ther performance. Our evaluatons results show that they acheve good performance n terms of socal welfare, bandwdth satsfacton rato, and bandwdth utlzaton. We note that SOAR can also be appled to provsonng other knds of cloud resources, e.g., CPU, memory, and storage. The rest of ths paper s organzed as follows. We present techncal prelmnares n Secton II. We consder the tenants who would lke to pay for every unt of bandwdth reserved up to her maxmum demand and present SOAR-VCG n Secton III. In Secton IV, we present SOAR-GDY, for the case that each tenant can only be satsfed when all her demanded bandwdth s reserved. We show evaluaton results and related works Secton V and Secton VI, respectvely. The concluson and possble future work are gven n Secton VII. II. TECHNICAL PRELIMINARIES In ths secton, we present our aucton model for the problem of cloud bandwdth reservaton, and revew some useful soluton concepts from classc mechansm desgn. A. Aucton Model As shown n Fg., we consder an open market for cloud bandwdth reservaton, n whch there s a cloud provder havng multple data centers and a number of cloud tenants rentng cloud bandwdth to provde ther onlne streamng

2 servces, such as onlne vdeo. The data centers of the cloud provder are geographcally located, and have dfferent capactes of bandwdth. The cloud tenants, especally the provders of onlne vdeo streamng servces, need to compete wth each other to reserve bandwdth to guarantee ther requrements on qualty of servce (QoS) of data rate. The cloud provder manages the allocaton of avalable bandwdth of the data centers, accordng to the cloud tenants bandwdth demands. Fg.. An open market for cloud bandwdth reservaton wth m data centers and n tenants. We model the problem of cloud bandwdth reservaton as a sealed-bd aucton, n whch all the buyers smultaneously submt sealed bds perodcally, so that no buyer knows the bd of any of the other partcpants. The cloud provder s assume to be trustworthy, and let t make the decson on the allocaton of reserved cloud bandwdth and the charge to each tenant. The aucton s carred out perodcally (e.g., every hour or day) or on demand (e.g., one of the cloud provder rase a request for bandwdth adjustment). Cloud Provder: A cloud provder (e.g., Azure, Amazon EC2, and Google AppEngne) possesses a number of data centers geographcally located all over the world, denoted by M = {,2,...,m}. Each data center l M may have a dfferent outgong bandwdth capacty of, and a servng # cost of c l per unt of bandwdth. B = (B,B 2,...,B m ) and # c = (c,c 2,...,c m ) denote the vector of bandwdth capactes and per unt bandwdth costs, respectvely. Tenant: There s a set of tenants, denoted by N = {, 2,..., n}, who are onlne streamng servce provders (e.g., Netflx, Hulu, and Youku). The tenants compete to reserve bandwdth from the cloud provder to serve ther customers. Each tenant N demands to reserve bandwdth to satsfy her requrement on QoS, and has a valuaton of v on each unt of bandwdth reserved. Ths valuaton can be derved from the revenue obtaned by a tenant for servng her subscrbers, ans the prvate nformaton to the tenant. We denote the valuaton profle of the tenants by # v = (v,v 2,...,v n ). In the aucton, the tenants smultaneously submt ther sealed bds # b = (b,b 2,...,b n ), whch are not necessarly equal to ther valuatons, the bandwdth demands # d = (d,d 2,...,d n ), to the cloud provder. In Secton III, we consder the case that each tenant would lke to pay for every unt of bandwdth reserved up to her maxmum demand. In Secton IV, we consder the case, n whch each tenant can only be satsfed when all her demanded bandwdth s reserved. The cloud provder determnes the set of wnnng tenants W, bandwdth reserved for the tenants A = (a l ) N,l M, and the charge to the tenants # p = (p,p 2,...,p n ). Here, a l denotes the bandwdth reserven the data center l for the tenant, and p denotes the per unt bandwdth charge for the tenant. To guarantee the proft of the cloud provder, we requre that the charge must be no less than a predefned constant p > (e.g., p = max l M (c l ) ). The utlty u of the tenant s defned to be the dfference between her valuaton on the reserved bandwdth and the charge, namely u = a (v p ), where a = a l s the total amount of bandwdth reserved for the tenant. We assume that the tenants are ratonal, that means the only objectve of each tenant s to maxmze her own utlty. A tenant has no preference over dfferent outcomes, f the utlty s same to the tenant herself. The tenants may try to manpulate ther bds n order to seek for hgher utltes, but do no cheat about ther bandwdth demands. We also assume that the tenants do not collude wth each other. In contrast to the tenants, the aucton s objectve s to maxmze socal welfare, whch s defned as follows. Defnton (Socal Welfare). The socal welfare n an aucton for cloud bandwdth reservaton s the dfference between the sum of tenants valuatons and the sum of costs on the reserved bandwdths: SW = W (v c l )a l. B. Soluton Concepts A strong soluton concept from mechansm desgn s domnant strategy. Defnton 2 (Domnant Strategy [5]). Strategy (bn ths paper) s s the player (tenant n ths paper) s domnant strategy, f for any strategy s s and any other players strategy profle s : u (s,s ) u (s,s ). Intutvely, a domnant strategy of a player/tenant s a strategy/bd that maxmzes her utlty, regardless of what strategy/bd profle the other players/tenants choose. The concept of ncentve-compatblty means that there s no ncentve for any player/tenant to le about her prvate nformaton, and thus revealng truthful nformaton s the domnant strategy for every player/tenant. An accompanyng concept s ndvdual-ratonalty, whch means that for every player/tenant partcpatng the game/aucton s expected to gan no less utlty than stayng outsde. Now we ntroduce the defnton of Strategy-Proof Mechansm. Defnton 3 (Strategy-Proof Mechansm [5]). A mechansm s strategy-proof when t satsfes both ncentve-compatblty anndvdual-ratonalty. The objectve of our work s to desgn strategy-proof aucton mechansms for cloud bandwdth reservaton. III. VCG-BASED AUCTION In ths secton, we consder the case that each tenant would lke to pay for every unt of bandwdth reserved up to her maxmum demand. We present SOAR-VCG, a VCG-based aucton mechansm for cloud bandwdth reservaton, whch acheves both optmal socal welfare and strategy-proofness. SOAR-VCG s composed of optmal bandwdth reservaton and VCG-based chargng. A. Optmal Bandwdth Reservaton Gven the bandwdth capacty profle # B and per unt bandwdth cost profle # c of the data centers, and demand profle # d and bd profle # b from the tenants, we model the problem of socal welfare maxmzng bandwdth reservaton as a lnear program LP. The objectve s to maxmze the socal welfare. Here, we use b nstead of v to calculate socal welfare, because the strategy-proof mechansm shown n Secton III-B

3 wll guarantee that bddng b = v s the domnate strategy of each tenant N. Constrant () ndcates the bandwdth capacty lmtaton on the data centers. Constrant (2) ndcates the maxmal demands from the tenants. Constrant (3) guarantees that each bandwdth reservaton s non-negatve. Objectve: Maxmze SW = (b c l )a l. N Subject to: a l, l M () N l M a l, N (2) a l, N, l M (3) We can get the optmal bandwdth reservaton A to acheve optmal socal welfare by solvng the above lnear program n polynomal tme. B. VCG-Based Chargng When there exsts a polynomal-tme algorthm to compute the optmal soluton for an allocaton problem, the celebrated VCG mechansm [6] can be appled to calculate the charge to acheve the strategy-proofness. Suppose A and A be the bandwdth reservaton outcome matrx when the tenant partcpates the aucton or not, respectvely. Then the VCG charge p of the wnnng tenant s (b j c l )a l j (b j c l )a l j c l a l j l M j j l M j p = a l Intutvely, the VCG charge p of the wnnng tenant s the dfference between the two socal welfare excludng herself, when she partcpates the aucton or not. It cannot happen that < p < p, because b p, N. Then, the charge p for the wnnng tenant s p = max{p,p }. For the losers, they are free of any charge. Snce SOAR-VCG has an optmal allocaton and calculates the charge based on VCG, we have the followng concluson. Theorem. SOAR-VCG s a strategy-proof and optmal aucton mechansm for cloud bandwdth reservaton. IV. GREEDY AUCTION In realty, some tenants may have strct requrement on QoS, and they can only be satsfed and would lke to pay for the reserved bandwdth, when all of the demanded bandwdth s reserved. In ths secton, we consder the stuaton that each tenant pays for the reserved bandwdth only when her demand s fully flled, and model the socal welfare maxmzaton problem as the followng bnary programm BP. Objectve: Maxmze SW = (b c l )a l. N Subject to: a l, l M (4) N a l = x, N (5) x {,}, N (6) The above bnary programm verson of the socal welfare maxmzaton can be reduced to the Generalzed Assgnment Problem (GAP), whch has been proven to be NP-hard [7]. Consderng the computatonal ntractablty of the problem of socal welfare maxmzaton annfeasblty of VCG mechansm, we propose SOAR-GDY, an alternatve greedybased aucton mechansm for cloud bandwdth reservaton.. A. Desgn of SOAR-GDY Smlar to SOAR-VCG, SOAR-GDY also contans two components: greedy bandwdth reservaton and chargng. ) Greedy Bandwdth Reservaton: Intutvely, SOAR-GDY tres to greedly reserve the bandwdth for the tenants that may brng hgher socal welfare. Snce the part of socal welfare acheved by the bandwdth reservaton of the tenant depends on the outcome of bandwdth allocaton, whch s not known before runnng the algorthm, we approxmate the socal welfare that mght be acheved by the tenant by M ntroducng a vrtual bd ˆb = d ( b ) l M c l l M SOAR-GDY sorts the tenants by ther vrtual bds n nonncreasng order, and then greedly reserves bandwdths accordng to the tenants demands followng the orderng. Algorthm shows the pseudo-code of SOAR-GDY s bandwdth reservaton algorthm. After calculatng the vrtual bd of each tenant (Lne 2-4), SOAR-GDY sorts the tenants accordng to ther vrtual bds n non-ncreasng order (Lne 5) β. Then, SOAR-GDY checks the tenants one by one followng the order β to see whether each tenant s demand can be satsfed by the rest of the bandwdth. If yes, SOAR-GDY adds the tenant to the set of wnners, and allocates the bandwdth wth the smallest cost to the tenant. Otherwse, SOAR-GDY smply gnores the tenant (Lnes 6-5). Fnally, SOAR-GDY outputs the set of wnnng tenants W and the matrx of bandwdth reservaton A. The runtme of Algorthm s O(mn). Algorthm : SOAR-GDY Bandwdth Reservaton Input: Vector of bandwdth capactes B #, vector of per unt bandwdth costs # c, vector of bds # b, vector of demands # d. Output: Set of wnnng tenants W, matrx of bandwdth reservaton A. W ; A n,m ; 2 foreach N do 3 ˆb M 4 end ( b c l ) ; 5 Sort ˆb, N n non-ncreasng order β : ˆb ˆb 2... ˆb n ; 6 for = to n do 7 f then 8 W W {} ; 9 whle > do l argmn (c l ) ; M M \{l} ; a l mn(, ) ; 2 3 end a l ; a l ; 4 end 5 end 6 return W and A ; 2) Chargng: The charge s calculated by fndng crtcal compettor frst, whch s defned as follow. Defnton 4 (Crtcal Compettor). The crtcal compettor cc() N of tenant W s the frst tenant, after whch has been selected as a wnner by Algorthm gven N\{}, such that the tenant s demand can no longer be satsfed by the remanng bandwdths. Now we can show the method to calculate the charge for the tenant by dstngushng three cases: ) If tenant loses n the aucton, then her charge s. 2) If tenant W and cc() does not exst (denoted by cc() = ), then her charge s p. 3) If tenant W and there exsts a crtcal compettor cc(), the charge p of the tenant s set to p =.

4 max{ˆb cc() M c l,p }. Algorthm 2 shows the pseudo-code of SOAR-GDY s chargng algorthm, and the runtme s O(mn). Algorthm s called once to determne the set of wnner and bandwdth reservaton, and we need to call Algorthm 2 O(n) tmes to calculate the charge for each of the wnnng tenants. Therefore, the total runtme of SOAR-GDY s O(mn 2 ). Algorthm 2: SOAR-GDY Chargng for Tenant W Input: Vector of bandwdth capactes # B, vector of demands # d, sorted lst β. Output: p. p p ; 2 for j = to n do 3 f j and l M j d j then 4 whle d j > do 5 l argmn l M j (c l ) ; M j M j \{l} ; 6 a l j mn(,d j ) ; 7 d j d j a l j ; a l j ; 8 end 9 f < then p max{ˆb j M cc() j ; break; 2 end 3 end 4 end 5 return p ; c l,p } ; B. Analyss In ths secton, we prove the strategy-proofness. Theorem 2. SOAR-GDY s a strategy-proof aucton mechansm for cloud bandwdth reservaton. Proof: We frst show that for each tenant N, bddng truthfully s her domnant strategy. We dstngush two cases: The tenant wns n the aucton and gets utlty u when bddng truthfully,.e., b = v. If she manpulates her bd b v, the followng two cases may happen: The tenant stll wns n the aucton. Her utlty does not change, because her crtcal compettor and charge are ndependent on her bd. The tenant turns to loss n the aucton. Then, her utlty becomes, whch s defntely no more than u (u ). The tenant loses n the aucton when bddng truthfully. Then she must have a crtcal compettor, and we have ˆb ˆb cc(). Then, her utlty u =. If she stll loses when manpulatng her bd, her utlty cannot change. We consder the case that she cheats the bd b v and becomes a wnner. Her utlty stll cannot be postve: u = v p ˆbcc() M = v v ˆb M c l c l = v b =. Therefore, the tenant cannot ncrease her utlty by bddng any other value than v, namely, bddng truthfully s her domnant strategy. So, SOAR-GDY s ncentve-compatblty. Second, we show that for each tenant, truthfully partcpatng the aucton s always better than stayng outsde, whch results n a utlty of. It s clear that f tenant loses n the aucton and gets utlty u =, ths s not worse than stayng outsde. If the tenant wns n the aucton and gets utlty u = v p, we further consder two cases: The tenant s crtcal compettor does not exst, and thus p = p b = v. The tenant has a crtcal compettor cc(). Her charge p s no larger than v. p = ˆbcc() M ˆb M c l c l = b = v. Therefore, SOAR-GDY provdes ndvdual-ratonalty. Therefore, SOAR-GDY s strategy-proof because t s both ncentve-compatblty anndvdual-ratonalty. V. EVALUATION RESULTS We mplemented SOAR and gave a smlar expermental setup wth [8] to evaluate the performance n ths secton. Consder a cloud provder wth a number of data centers provdes bandwdth reservaton to multple tenants, the data center s cost of per unt bandwdth s normalzed and unformly dstrbuted over nterval (, ] whle the tenant s valuaton on per unt of bandwdth s unformly dstrbuted over (,2]. Smlarly, each tenant s bandwdth demans normalzed and range from to, and we assume that the bandwdth capacty of each data center s randomly selecten the range of (, ]. We fx the number of data centers at 5 and 5, respectvely, and evaluate the performance of SOAR wth the number of tenants vary from 2 to 3. For each smulaton settng, we calculate the results averaged over rounds. The followng three metrcs are used to evaluate performance of SOAR. As shown n Fg. 2 and 3, SOAR outperforms Nash Equlbrum (NE) methon terms of the three performance metrcs. We also compare SOAR-GDY wth the suboptmal soluton of bnary programm BP shown n Secton IV acheve by nteger programmng tools 2. Socal welfare: The defnton s gven n Defnton. Bandwdth satsfacton rato: Bandwdth satsfacton rato s the percentage of tenants bandwdth demands that can be satsfen the aucton. Bandwdth utlzaton: Bandwdth utlzaton s rato of the total bandwdth that s utlzen the aucton. In Fg. 2, we show the performance of SOAR-VCG as a functon of the number of tenants. We can see that the socal welfare and bandwdth utlzaton ncreases wth the number of tenants, and bandwdth satsfacton rato decrease. When there are 5 datacenters and less than 2 tenants, bandwdth satsfacton rato exceeds 9%, and the bandwdth utlzaton rato of SOAR-VCG s hgher than 9% when there are more than 8 tenants n the aucton. That pont ndcates the bandwdth satsfacton tends to be saturated. Fg. 3 shows evaluaton results acheved by SOAR-GDY as the number of tenants ncreases. Whch s smlar to SOAR- VCG, when the number of datacenter s 5 and the number of The ranges of the number of data center can be dfferent from the ones used here. However, the evaluaton results of usng dfferent ranges are dentcal. Therefore, we only show the results of the above ranges n ths paper. 2 Snce fndng the optmal soluton for the SOAR-GDY case s NP-hard and the computaton tme of rounds s more than an hour, we only calculate the optmal soluton wth small-scale bdders.

5 Fg. 2. Socal Welfare 9 8 7 6 5 4 3 2 SOAR-VCG (m=5) SOAR-VCG (m=5) 2 4 6 8 2 4 6 8 2 22 24 26 28 3 (a) Socal Welfare Bandwdth Satsfacton Rado.8.6.4.2 SOAR-VCG (m=5) SOAR-VCG (m=5) 2 4 6 8 2 4 6 8 2 22 24 26 28 3 (b) Bandwdth Satsfacton Rato Performance of SOAR-VCG by varyng the number of bdders and datacenters (m). Bandwdth Utlzaton Rado.8.6.4.2 SOAR-VCG (m=5) SOAR-VCG (m=5) 2 4 6 8 2 4 6 8 2 22 24 26 28 3 (c) Bandwdth Utlzaton Fg. 3. Socal Welfare 8 6 4 2 2 4 6 8 2 4 6 8 2 22 24 26 28 3 (a) Socal Welfare Bandwdth Satsfacton Rado.8.6.4.2 2 4 6 8 2 4 6 8 2 22 24 26 28 3 (b) Bandwdth Satsfacton Rato Performance of SOAR-GDY by varyng the number of bdders and datacenters (m). Bandwdth Utlzaton Rado.8.6.4.2 2 4 6 8 2 4 6 8 2 22 24 26 28 3 (c) Bandwdth Utlzaton tenants s less than 8, bandwdth satsfacton rato SOAR- GDY exceed 9%, and after that the bandwdth utlzaton rato of t s hgher than 8%. We also use lnes wthout pont plots the suboptmal soluton n Fg. 3. Compared to suboptmal soluton of bnary programm BP, SOAR-GDY can get more than 93.58% of the optmal soluton n general case. The socal welfare acheved by SOAR-GDY s closely approxmated to that of suboptmal solutons, whch demonstrates that the greedy-based bandwdth reservaton algorthm has a hgh socal welfare n most cases. VI. RELATED WORKS A number works such as SecondNet [2], Oktopus [], PRO- TEUS [9] and Seawall [], have been proposed to address the problem of cloud bandwdth allocaton and reservaton. Popa et al. propose three allocaton polces to navgate tradeoffs between mn-guarantee, hgh utlzaton and payment proportonalty requrements for cloud networks sharng []. Snce the tradtonal pay-as-you-go model [2] can not satsfy the needs of onlne streamng servce applcatons, new approaches are proposed for the cloud bandwdth allocaton problem. Broker or allocator s proposed to processes requests and negotate the bandwdth prces n [8], [3]. Several prcng schemes [4] [6] are also proposed for cloud resource allocaton. In coupled systems wthout complcatng message-passng, a new teratve approach to dstrbuted resource allocaton was proposen [7]. A truthful onlne aucton was desgn n cloud computng where users wth heterogeneous demands could come and leave on the fly [8]. The rgorous cooperatve game framework has also been appled to share mult-tenant data center networks [9]. In contrast to ther work, we propose a famly of strategyproof aucton mechansms for cloud bandwdth reservaton. Our approaches not only acheve strategy-proofness, but also provde guaranteed performance n most of the cases. VII. CONCLUSION In ths paper, we have modeled the problem of cloud bandwdth reservaton as a sealed-bd aucton and propose SOAR, a famly of strategy-proof aucton mechansms for cloud bandwdth reservaton. 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