Cost-Minimizing Dynamic Migration of Content Distribution Services into Hybrid Clouds

Transcription

1 The 31st Annual IEEE Internatonal Conference on Computer Communcatons: Mn-Conference Cost-Mnmzng Dynamc Mgraton of Content Dstrbuton Servces nto Hybrd Clouds Xuana Qu, Hongxng L, Chuan Wu, Zongpeng L and Francs C.M. Lau Department of Computer Scence, The Unversty of Hong Kong, Hong Kong, {xqu,hxl,cwu,fcmlau}@cs.hku.hk Department of Computer Scence, Unversty of Calgary, Canada, zongpeng@ucalgary.ca Abstract The recent advent of cloud computng technologes has enabled agle and scalable resource access for a varety of applcatons. Content dstrbuton servces are a maor category of popular Internet applcatons. A growng number of content provders are contemplatng a swtch to cloud-based servces, for better scalablty and lower cost. Two key tasks are nvolved for such a move: to mgrate ther contents to cloud storage, and to dstrbute ther web servce load to cloud-based web servces. The man challenge s to make the best use of the cloud as well as ther exstng on-premse server nfrastructure, to serve volatle content requests wth servce response tme guarantee at all tmes, whle ncurrng the mnmum operatonal cost. Employng Lyapunov optmzaton technques, we present an optmzaton framework for dynamc, cost-mnmzng mgraton of content dstrbuton servces nto a hybrd cloud nfrastructure that spans geographcally dstrbuted data centers. A dynamc control algorthm s desgned, whch optmally places contents and dspatches requests n dfferent data centers to mnmze overall operatonal cost over tme, subect to servce response tme constrants. Rgorous analyss shows that the algorthm ncely bounds the response tmes wthn the preset QoS target n cases of arbtrary request arrval patterns, and guarantees that the overall cost s wthn a small constant gap from the optmum acheved by a T-slot lookahead mechansm wth known nformaton nto the future. I. INTRODUCTION Cloud computng technologes have enabled rapd provsonng server utltes to users anywhere, anytme. To explot the dversty of electrcty costs and to provde servce proxmty to users n dfferent geographc regons, a cloud servce often spans multple data centers over the globe, e.g., Amazon CloudFront, Mcrosoft Azure. The elastc and on-demand nature of resource provsonng has made cloud computng attractve to provders of varous applcatons. More and more new applcatons are beng created on the cloud platform [1][2], whle many exstng applcatons are also consderng the cloud-ward move [3][4], ncludng content dstrbuton applcatons [5][6]. As an mportant category of popular Internet servces, content dstrbuton applcatons, e.g., vdeo streamng, web hostng and fle sharng, feature large volumes of content and demands that are hghly dynamc n the temporal doman. A cloud platform wth multple, dstrbuted data centers s deal to host such a servce, wth substantal advantages over The research was supported n part by a grant from Hong Kong RGC under the contract HKU E. a tradtonal prvate or publc content dstrbuton network (CDN) based soluton, n terms of more aglty and sgnfcant cost reducton. Two maor components exst n a typcal content dstrbuton applcaton, namely back-end storage for keepng the contents, and front-end web servce to serve the requests. Both can be mgrated to the cloud: contents can be stored n storage servers n the cloud, and requests can be dstrbuted to cloud-based web servces. Therefore, the key challenge for cloud-ward move of a content dstrbuton applcaton s how to effcently replcate contents and dspatch requests across multple cloud data centers and the provder s exstng on-premse servers such that good servce response tme s guaranteed and only modest operatonal expendture s ncurred. Some exstng work [3][4][5][6] have advocated to optmze applcaton mgraton nto clouds, but none focuses on guaranteeng overtme cost mnmzaton wth a dynamc algorthm. In ths paper, we present a generc optmzaton framework for dynamc, cost-mnmzng mgraton of content dstrbuton servces nto a hybrd cloud (.e., prvate and publc clouds combned), and desgn a ont content placement and load dstrbuton algorthm that mnmzes overall operatonal cost over tme, subect to servce response tme constrants. Our desgn s rooted n Lyapunov optmzaton theory [7][8], where cost mnmzaton and response tme guarantee are acheved smultaneously by effcent schedulng of content mgraton and request dspatchng among data centers. Lyapunov optmzaton provdes a framework for desgnng algorthms wth performance arbtrarly close to the optmal performance over a long run of the system, wthout the need for any future nformaton. It has been extensvely used n routng and channel allocaton n wreless networks [7][9], and has only recently been ntroduced to address resource allocaton problems n a few other types of networks [10][11]. We talor Lyapunov optmzaton technques n the settng of a hybrd cloud, to dynamcally and ontly resolve the optmal content replcaton and load dstrbuton problems. We demonstrate the optmalty of our algorthm wth rgorous theoretcal analyss. The algorthm ncely bounds the servce response tmes wthn the preset QoS target n cases of arbtrary request arrvals, and guarantees that the overall cost s wthn a small constant gap from the optmum acheved by a T-slot lookahead mechansm wth nformaton nto the future. In the rest of the paper, we present the optmzaton model n /12/$ IEEE 2853

2 TABLE I NOTATIONS Fg. 1. The system archtecture. Sec. II, desgn a ont content placement and load dstrbuton algorthm n Sec. III, analyze ts performance n Sec. IV, and conclude the paper n Sec. V. A. System Model II. THE SERVICE MIGRATION PROBLEM We consder a typcal content dstrbuton applcaton, whch provdes a collecton of contents (fles), denoted as set M, to users spreadng over multple geographcal regons. There s an on-premse server cluster (or prvate cloud) owned by the provder of the content dstrbuton applcaton, whch stores the orgnal copes of all the contents. Wthout loss of generalty, we use one server to represent the on-premse server cluster. The on-premse server has an overall upload bandwdth of b unts for servng contents to users. There s a publc cloud consstng of data centers located n multple geographcal regons, denoted as set N. One data center resdes n each regon. There are two types of nterconnected servers n each data center: storage servers for data storage, and computng servers that support the runnng and provsonng of vrtual machnes (VMs). The provder of the content dstrbuton applcaton (applcaton provder) wshes to provson ts servce by explotng a hybrd cloud archtecture, whch ncludes the geo-dstrbuted publc cloud and ts on-premse server. The maor components of the content dstrbuton applcaton nclude: () back-end storage of the contents and () front-end web servce that serves users requests for contents. The applcaton provder may mgrate both servce components nto the publc cloud: contents can be replcated n storage servers n the cloud, whle requests can be dspatched to web servces nstalled on VMs on the computng servers. An llustraton of the system archtecture s gven n Fg. 1. We suppose that the system runs n a tme-slotted fashon. Each tme slot s a unt tme whch s enough for uploadng any fle m M wth sze v (m) (bytes) at the unt bandwdth. In tme slot t, a (m) (t) requests are generated for downloadng fle m M, from users n regon. We assume that the request arrval s an arbtrary process over tme, and the number of requests arsng from one regon for a fle n each tme slot s upper-bounded by A max. M Fle set N Regon set v (m) Sze of fle m, n bytes a (m) (t) No. of requests for fle m from regon at tme slot t (t) Request queue for fle m n regon A max Max. no. of requests for fle m from regon n a tme slot (t) No. of requests dspatched from to on-premse server at t (t) No. of requests dspatched from to data center at t (t) Bnary var: store fle m on data center or not at t. b Max. no. of requests the on-premse server can process n a tme slot µ max Max. no. of requests dspatched from each request queue to a data center n a tme slot,.e., (t) µ max g Charge for uploadng a byte from the data center o Charge for downloadng a byte nto data center f Charge for rentng one VM nstance n data center r No. of requests a VM n data center can serve n a tme slot p Charge for storng a byte on data center q (m) Charge for uploadng fle m from data center h Tme-averaged charge for uploadng a byte from the on-premse server w (m) Charge for mgratng fle m to data center W (m) Bound of queueng delay of requests n queue ɛ (m) Preset constant for controllng queueng delay n d round-trp delay between regon and the on-premse server e round-trp delay between regon and data center α Bound of tme-averaged round-trp delay G(t) Vrtual queue for boundng tme-averaged round-trp delay (t) Vrtual queue for boundng queueng delay n The cost of uploadng a byte from the on-premse server s h. The charge for storage at data center s p per byte per unt tme. g and o per byte are charged for uploadng from and downloadng nto data center, respectvely. The cost for rentng a VM nstance n data center s f per unt tme. These charges follow the chargng model of leadng commercal cloud provders, such as Amazon EC2 [12] and S3[13]. We assume that the storage capacty n each data center s suffcent for storng contents from ths content dstrbuton applcaton. We also assume that each request s served at one unt bandwdth, and the number of requests that a VM n data center can serve per unt tme s r. B. Cost-Mnmzng Servce Mgraton Problem We next develop an optmzaton framework to characterze the optmal content dstrbuton servce mgraton problem. Important notatons are summarzed n Table I. The decson varables n our optmzaton framework are formulated as follows: (1) For content replcaton, bnary varable (t) ndcates whether fle m s stored n data center n tme slot t or not. If (t 1) = 0 and (t) =1, fle m s coped from the on-premse server to the data center at t; f (t 1) = 1 and (t) =0, fle m s removed from data center. In other cases, the storage status reman the same. (2) For dspatchng requests from regon for fle m, let (t) be the number of requests to be served by the on-premse server n tme slot t, and (t) denote the 2854

3 number dspatched to data center n tme slot t, wth an upper bound of µ max. Requests for fle m can only be dspatched to data center when t stores the fle,.e., (t) > 0 only f (t) =1. We assume that a data center can serve a fle to users n the tme slot when the fle s beng coped to the data center, snce replcatng the fle from the on-premse server and servng chunks of the fle can be carred out n parallel. To buffer requests for fle m generated from users n regon over tme, a queue The backlog sze of queue s updated n each tme slot as follows: (t + 1) = max[ s mantaned, N,m M. at tme t, denoted as (t), (t) (t) N (t), 0] + a (m) (t). (1) Our framework focuses on mnmzng the recurrng operatonal cost n the content dstrbuton system. Let q (m) f = r + v (m) g denote the unt cost to serve each request for fle m on data center and let w (m) denote the mgraton cost to copy fle m nto data center, whch ncludes costs of upload and download bandwdths from the on-premse server to data center,.e., w (m) = v (m) (h + o ). The overall operatonal cost to the applcaton provder n tme slot t s M(t) = (v (m) (t)h + (t)q (m) ) (2) m M N N + N m M [ m M v (m) (t)p + N where the frst row corresponds to the charge for uploadng contents to users from the on-premse server and the cloud data centers, the second row computes the storage cost for cachng replcated contents at all the data centers, and the thrd row s the mgraton cost for copyng fles from the on-premse server to the data centers. Here [x] + = x f x 0 and [x] + =0f x<0. We wll not consder any recurrng storage cost on the on-premse server, and the removal of contents from a data center s cost-free. On the other hand, our framework enforces pre-set QoS constrants. The servce qualty experenced by users s e- valuated by request response delay, consstng of two maor components: queueng delay n the request queue, and roundtrp delay from when the request s dspatched from the queue to the tme the frst byte of the requested fle s receved. We gnore the processng delay nsde a data center. Let d and e denote the round-trp delay between regon and the on-premse server, and between regon and data center, respectvely. Let α be the upper-bound of the average roundtrp delay per request, whch the applcaton provder wshes to enforce n ths content dstrbuton applcaton. We reasonably assume α > e, N,.e., ths bound s larger than the round-trp delay between a user and the data center n the same regon. The optmzaton pursued by our dynamc algorthm s formulated as follows, whch mnmzes the tme-averaged operatonal cost whle guaranteeng servce qualty. We use (t) (t 1)] + w (m), 1 x(t) = lm T T value of x(t). subect to: m M N 0 (t)+ N ( N m M T 1 t=0 x(t) to represent the tme-averaged mn M(t) (3) (t) b, t, (4) (t) µ max (t), N, N,m M, t,(5) (t) (t), m M, N, t, (6) (t)d + N <α N m M (t)e ) ( (t)+ N (t)), (7) (t) 0, N,m M, t, (8) (t) {0, 1}, N,m M, t. (9) (4) corresponds to the upload bandwdth lmt at the onpremse server. (5) states that requests for a fle are only dspatched to data centers storng ths fle, and the maxmum number of requests dspatched from each request queue to a data center n each tme slot s no larger than µ max. (6) states that the number of requests dspatched from queue cannot be larger than the current queue sze. Constrant (7) specfes that the average round-trp delay per request should be bounded by α. Though queueng delay s not explctly modeled n the constrants, we show n Sec. IV that our algorthm can smultaneously solve ths optmzaton and bound the queueng delay of each request wth a pre-set threshold. III. DYNAMIC MIGRATION ALGORITHM We next desgn a dynamc control algorthm usng Lyapunov optmzaton technques, whch solves the optmal mgraton problem n (3) and bounds the tme-averaged roundtrp delays and queueng delays for each request. A. Boundng Delays To satsfy constrant (7), we resort to the vrtual queue technques n Lyapunov optmzaton [8]. We ntroduce a vrtual queue G, wth arrval rate of N m M (s(m) (t)d + N c(m) (t)e ),.e., the overall round-trp delay experenced by all requests n t, and departure rate of α N m M (s(m) (t)+ N c(m) (t)),.e., the total number of requests n t multpled by the round-trp delay bound α. G s updated as follows: G(t + 1) = max[g(t)+ ( (t)d + (t)e ) N m M N α ( (t)+ (t)), 0]. (10) N m M N If queue G s stable, ts tme-averaged arrval rate should not exceed ts tme-averaged departure rate [8],.e., constrant (7) s satsfed. Therefore, we can adust the request dstrbuton strateges (t) s and (t) s n each tme slot to guarantee that the vrtual queue s always stable, n order to satsfy constrant (7). 2855

4 To bound the worst-case queueng delay of each request n all queues, N,m M, the ɛ-persstent servce queue technque [14] can be appled. In partcular, we assocate wth a vrtual queue, updated by: (t + 1) = max[ (t) where ɛ (m) (t)+1 (m) {Q (t)>0} (ɛ(m) (t)) 1 (m) {Q µmax, 0], (11) (t)=0} N > 0 s a constant that can be gauged to control the queueng delay bound, whch further renders a tradeoff between the queueng delay bound and the cost optmalty acheved by our algorthm (to be dscussed n Sec. IV). The ratonale behnd (11) can be explaned ntutvely: If request queue of arrvals ɛ (m) s not empty n tme slot t, then a constant number are added nto vrtual queue, whle the (t)+ N c(m) (t), departure rate from the vrtual queue, s the same as the departure rate from request queue. If the request queue s empty n t, the length of the vrtual queue decreases by µ max. We strategcally decde (t) s and (t) s to keep the vrtual queue stable; n ths way, requests are expedently dspatched from the request queue, resultng n lmted queueng delay per request. B. Dynamc Algorthm Desgn Next we desgn a dynamc algorthm whch stablzes all queues and solves optmzaton (3). Let Θ(t) =[Q(t), G(t), Z(t)] be the vector of all queues n the system. Defne our Lyapunov functon as L(Θ(t)) = 1 2 [ m M N The one-slot condtonal Lyapunov drft s ( (t) 2 + (t)) 2 + G(t) 2 ]. (12) (Θ(t)) = E{L(Θ(t + 1)) L(Θ(t)) Θ(t)}. Followng the drft-plus-penalty framework n Lyapunov optmzaton (Chapter 5 n [8]), we can mnmze the tmeaveraged operatonal cost and stablze all queues by mnmzng an upper bound of the followng tem n each tme slot: (Θ(t)) + VM(t), where V s a non-negatve parameter set by the applcaton provder to control the tradeoff between the operatonal cost and request response delays. Squarng the queueng laws (1), (10) and (11), we derve the followng nequalty: (Θ(t)) + VM(t) B +1 {Q (m) [ m M N (t)[ (t)+(α d )G(t) (t)>0} Z(m) (t) v (m) Vh] (t)+(α e )G(t)+1 (m) {Q + V [v (m) (t)p +[ + m M N m M N + m M N (t)[1 (m) {Q (t)>0} ɛ(m) (t)a (m) (t), m M N N (t) (t)>0} Z(m) (t) Vq (m) ] (t) (t 1)] + w (m) ] 1 (m) µmax] {Q =0} (13) Algorthm 1: Control Algorthm on the Control Center Intalzaton: Set up request queue, vrtual queues G and, N,m M, and ntalze ther backlogs to 0; In every tme slot t: 1. Enqueue receved requests to request queues ( s); 2. Solve optmzaton (14) to obtan optmal content placement and load dstrbuton strateges (t), (t), (t),, N,m M; 3. Update content placement table wth (t) s, and mgrate fles as follows: for N,m M do f (t 1) = 0 and (t) = 1 then nstruct on-premse server to upload fle m to data center ; f (t 1) = 1 and (t) = 0 then sgnal data center to remove fle m; 4. Dspatch (t) requests from queue to on-premse server, (t) requests to data center,, N,m M; 5. Update vrtual queue and G accordng to Eqn. (11) and (10); where B = 1 2 M N [A2 max + ɛ 2 max + 2(b + Nµ max ) 2 ]+ + 1 ( M N 2 µ max e max + bd max ) α2 ( M N 2 µ max + b) 2 s a constant, wth d max = max{d N }, e max = max{e N, N }, and ɛ max = max{ɛ (m) N,m M}. We smplfy the notaton by defnng (t) = (t)+1 (m) {Q whch s a constant n tme slot t, and γ (m) η (m) (t) = (t)+1 (m) {Q whch s also a constant n t, and φ (m) (t)>0} Z(m) (t) Vv (m) h+(α d )G(t), (t)>0} Z(m) (t) Vq (m) +(α e )G(t), (t) =V (v (m) p +1 (m) {y (t 1)=0} w(m) ), whch s a constant n t as well, when (t 1) s gven. Mnmzng the rght-hand-sde of (13) s equvalent to: max F (t) = (t)γ (m) (t)+ m M N N m M N (t)η (m) (t) m M N φ (m) (t) (t) (14) subect to: constrants (4) (6) (5) (8) (9). Ths problem s an nteger lnear program (ILP), whch can be solved by optmzaton tools such as GLPK [15]. In summary, our complete dynamc, ont content placement and request dstrbuton algorthm s gven n Algorthm 1. The algorthm can be mplemented by the applcaton provder on a control center. The control center mantans a content placement table wth entres, whch are ntalzed to be 0. In each tme slot, t receves user requests and places the requests for fle m orgnated from regon n request queue. Vrtual queues and G are mantaned smply as counters. The control center observes the lengths of the queues and request arrval rates, and calculates the optmal content placement and load dstrbuton strateges usng Algorthm 1. It then sgnals the cloud data centers to replcate/remove fles and dspatches requests across the hybrd cloud accordngly. 2856

5 IV. PERFORMANCE ANALYSIS We next analyze the performance guarantee provded by our dynamc algorthm. Detaled proofs to all the theorems can be found n our techncal report [16]. A. Bound of Queueng Delay Theorem 1: (Bound of Queue Length) Defne max = V (v (m) pĩ + w (m) + q (m) )+A ĩ ĩ max, where (15) ĩ = argmn {v (m) p + w (m) + q (m) α e > 0, N }. (16) Then max (m) s the maxmum sze of queue Q at any tme t,.e., (t) max, N, m M. Theorem 2: (Bounded Queueng Delay): For each request queue, N, m M, defne = V (v(m) pĩ + w (m) + q (m) )+ max ĩ ĩ W (m) where ĩ s defned as n (16). The queueng delay of each request n ɛ m s bounded by W (m). B. Optmalty aganst the T-Slot Lookahead Mechansm Snce request arrval rates are arbtrary n our system, t s dffcult to fnd the global cost optmum, wth whch to compare the tme-averaged cost M(t) acheved by our algorthm. Therefore we utlze a local optmum target, whch s the optmal (obectve functon) value of a smlar cost mnmzaton problem wthn known nformaton (e.g., request arrvals) for T tme slots nto the future,.e.,at-slot lookahead mechansm [8]. In the T-slot lookahead mechansm, tme s dvded nto successve frames, each consstng of T tme slots. Denote each frame as F k = {kt, kt +1,..., kt + T 1}, where k =0, 1,.... In each tme frame, consder the followng optmzaton problem on varables N, N,m M, t F k : subect to: m M N mn 1 T kt +T 1 (t) b, t F k, (t), (t), (t), M(t) (17) 0 (t) µ max (t), N, N,m M,t F k, (t)+ N kt +T 1 kt +T 1 [a (m) (t) (t), m M, N, t F k, (t) (t) N m M( N N kt +T 1 <α (t)] 0, N,m M, (t)e + (t)d ) m M( N N (t) 0, N,m M,t F k, (t)+ (t)), (t) {0, 1}, N,m M,t F k. Theorem 3: (Optmalty of Cost) Let M k denote the optmal obectve functon value n the T-slot Lookahead problem (17) n tme frame F k. The mnmum operatonal cost derved wth our algorthm s M(t) n tme slot t. Suppose the tme lasts for KT tme slots, where K s a constant. We have 1 KT KT 1 t=0 M(t) 1 K K 1 k=0 M k + BT V, (18).e., our algorthm acheves a tme-averaged cost wthn constant gap BT V from that by assumng full knowledge n T tme slots n the future. Theorems 2 and 3 show that when V ncreases, worstcase queueng delay W (m) ncreases, whle the gap between the operatonal cost of our algorthm and that of the T-Slot lookahead mechansm s reduced. ɛ (m) has a smlar effect: when ɛ (m) ncreases, the worst-case queueng delay W (m) decreases, and B ncreases such that the gap to optmalty ncreases. V. CONCLUSION Ths paper nvestgates optmal mgraton of a content dstrbuton servce to a hybrd cloud consstng of prvate onpremse servers and publc geo-dstrbuted cloud servces. We propose a generc optmzaton framework based on Lyapunov optmzaton theory, and desgn a dynamc, ont content placement and request dstrbuton algorthm, whch mnmzes the operatonal cost of the applcaton wth QoS guarantees. We theoretcally show that our algorthm approaches the optmalty acheved by a mechansm wth known nformaton n the future T tme slots by a small constant gap, no matter what the request arrval pattern s. We ntend to extend the framework to specfc content dstrbuton servces wth detaled requrements, such as vdeo-on-demand servces or socal meda applcatons, n our ongong work. REFERENCES [1] Mcrosoft Offce Web Apps, [2] Google docs, [3] M. Haat, X. Sun, Y. E. Sung, D. Maltz, and S. Rao, Cloudward Bound: Plannng for Benefcal Mgraton of Enterprse Applcatons to the Cloud, n Proc. of IEEE SIGCOMM, August [4] H. Zhang, G. Jang, K. Yoshhra, H. Chen, and A. Saxena, Intellgent Workload Factorng for a Hybrd Cloud Computng Model, n Proc. of the Internatonal Workshop on Cloud Servces (IWCS 2009), June [5] H. L, L. Zhong, J. Lu, B. L, and K. Xu, Cost-effectve Partal Mgraton of VoD Servces to Content Clouds, n Proc. of IEEE CLOUD, July [6] X. Cheng and J. Lu, Load-Balanced Mgraton of Socal Meda to Content Clouds, n Proc. of NOSSDAV, June [7] L. Georgads, M. J. Neely, and L. Tassulas, Resource allocaton and cross-layer control n wreless networks, Foundatons and Trends n Networkng, vol. 1, no. 1, pp , [8] M. J. Neely, Stochastc Network Optmzaton wth Applcaton to Communcaton and Queueng Systems. Morgan & Claypool, [9] M. J. Neely, Energy optmal control for tme varyng wreless networks, IEEE Tran. on Informaton Theory, no. 7, pp , July [10] M. M. Amble, P. Parag, S. Shakkotta, and L. Yng, Content-Aware Cachng and Traffc Management n Content Dstrbuton Networks, n Proc. of IEEE INFOCOM, Aprl [11] M. J. Neely and L. Golubchk, Utlty Optmzaton for Dynamc Peer-to-Peer Networks wth Tt-For-Tat Constrants, n Proc. of IEEE INFOCOM, Aprl [12] Amazon Elastc Compute Cloud, [13] Amazon Smple Storage Servce, [14] M. J. Neely, Opportunstc Schedulng wth Worst Case Delay Guarantees n Sngle and Mult-Hop Networks, n Proc. of IEEE INFOCOM, [15] GLPK (GNU Lnear Programmng Kt), [16] X. Qu, H. L, C. Wu, Z. L, and F. C. M. Lau, Cost-Mnmzng Dynamc Mgraton of Content Dstrbuton Servces nto Hybrd Clouds, The Unversty of Hong Kong, Tech. Rep., Jan