Content Multi-homing: an Alternative Approach

Transcription

1 Content Muti-homing: an Aternative Aroach Technica Reort HKUST-CS14-01 Jason Min Wang 1, Jun Zhang 2, Brahim Bensaou 1 1 Deartment of Comuter Science and Engineering, The Hong Kong Universit of Science and Technoog 2 Network and Comuter Science Deartment, Teecom ParisTech [email protected], [email protected], [email protected] Abstract The CDN serves as an essentia eement in roviding content deiver services on the Internet; however, imited b its footrint and infuenced b variations of network conditions and user demands, no individua CDN can quaitative fufi deiver tasks antime and anwhere. As such, arge content roviders often use mutie CDNs. Nevertheess, this aroach is not on cumbersome to negotiate mutie business contracts, but aso economica inefficient, esecia for sma content roviders. A simer aternative aroach woud be to et each content rovider on sign one contract with an authoritative CDN, sa, and et hande the otentia erformance tra of individua CDN. To fufi its business commitment, coud either use its own infrastructure or rent services from other CDNs, which is sometimes indisensabe. To make an otima oerating an for oerator, we roose a new robem, caed MCDN-CM, whose objective is to minimize CDN- 0 s oerating cost. MCDN-CM is a concave minimization robem and we take advantage of the secia form of the ractica CDN-ricing function iece-wise inear concave to arrive at an otima soution through an iterative rocedure. We conduct numerica eeriments under reaistic settings and show via the eerimenta resuts that can achieve a tremendous costsaving b using our roosed agorithm. I. INTRODUCTION B moving content coser to end users, content deiver networks (CDNs) great reduce the content distribution cost and significant imrove the content access eerience. Increasing, CDNs are recognized to a a fundamenta roe in suorting the arge-scae content deiver over the Internet. Nowadas, arge content roviders (CPs) re on the CDN to deiver their content in the goba scae. For eame, YouTube uses Googe s rivate CDN to deiver videos; Netfi [1] and Huu [2] rovide their services via third-art CDNs, incuding Akamai, LimeLight, and Leve-3. The ever-growing demand for videos drives the continua u-scaing of the CDN infrastructures. From the content rovider ersective, it is desirabe that its content can be deivered to users with high quait, regardess of the geograhica ocation of the users and the ISP network the attach to. However, two facts make this requirement difficut to achieve. First, it is hard for an singe CDN rovider, even the argest one ike Akamai, to eand its footrint to ever corner of the word. Tica a CDN resents distinct erformances at different geograhica areas. Second, due to the dnamics of network conditions and the variation of server oads, the erformance of a CDN, even at the same area, fuctuates over time [1] [4]. As a consequence, content roviders ike Netfi [1] and Huu [2] use mutie Cost v r 1 v r 2 v r 3 CDN-r (a) Voume Cost 2 1 CDN-s (b) CDN-r Voume Fig. 1. (a) The iecewise inear concave ricing function of CDN-r, f r( ). (b) Motivating eame: when invoving two CDNs (CDN-r and CDN-s), the content deiver erformance gets imroved but the tota cost aid b the sma content rovider is greater than that using on CDN-r: >. CDNs to rovide high quait services; this is referred to as content muti-homing [3]. Content muti-homing enabes a content rovider to avoid the quait of eerience (QoE) tra of an singe CDN, whereas it coud resut in economic inefficienc for sma or medium content roviders. Such economic inefficienc arises from the wide-adoted charging oic of CDN: i) ou a as ou go, and ii) the more ou use, the cheaer the average rice ou get. Secifica, the CDN ricing function has a iecewise inear concave shae, as shown b Fig. 1(a). Under current charging oicies, a sma CP, when using mutie CDNs, has to a the ortions of traffic at a high charging rate for individua CDNs. This is iustrated b the eame in Fig. 1. Note that for a arge CP this robem is aeviated, since its charging voume at each CDN can easi arrive at the highest voume-rice segment, thus making the ament at a ower average rice. In addition, content muti-homing entais each CP to negotiate and sign business contracts with mutie CDN roviders, which is cumbersome. Motivation. To mitigate the above diemma, an aeaing aroach consists in etting sma CPs contact and dea with on one authoritative CDN, sa. As such, CPs no onger suffer from the negative effects of ament discount oic brought b muti-homing. It is now s resonsibiit to fufi the erformance commitment, stiuated in the service eve agreement (). To this end, must re on other CDNs in rocuring content muti-homing transarent to the CP. This new aroach is iustrated b Fig. 2. acts as a ro, aggregating demands from registered CPs and acquiring the maimum discounts from other CDNs as a giant CP. Overview. Deivering an content item to a secific area can either use s own servers or emo other CDNs. Two factors imact the decisions. One is that can not satisf the service quait requirement of certain items, restricted b its footrint and regiona service caabiities. In this case, it has

2 CP-1 CP-2... CP-N CoudFront MaCDN N CDN-K US US EU Sain HK/SG JP Austria S/A China AU Jaan US/EU/SA Brazi A/P Austraia Fig. 2. Mutie content roviders sign business contracts with one authoritative CDN with various ; the authoritative, as a customer, rents services from other CDNs, besides using its own infrastructure. to resort to other CDNs that are better imanted regiona. The other is that deivering some content items to certain areas, coud be more cost-effective in renting other CDNs services than doing it on its own network. For eame, the average cost of running one reica server in a secific area coud be so high that it hinders from running a ortion of its reica servers there. Consequent, the oerator of is insired to carefu make an oerating an: how to reaize the business commitments, in articuar the QoE requirements, b using either its own infrastructure or other CDNs services, whist aiming to minimize its oerating cost. In this aer, we he oerator make the oerating an otima, b modeing it as a concave minimization robem, referred as MCDN-CM. We sove the robem otima b invoking an iterative rocedure. Contributions. First, to the best of our knowedge, we are the first to roose the MCDN-CM robem, which has a strong motivation for the oerator of and aso benefits the content roviders, esecia smaer ones, in both rocedura and economica asects. Second, we give an agorithm to sove MCDN-CM otima. The soution can be direct transated into s oerating an. Third, this work embraces the emerging trend of CDN-interconnection [5]. Outine. Section II describes the necessar background on CDN and formuates the MCDN-CM robem. We derive the otima soution to MCDN-CM in Section III and resent the eerimenta resuts in Section IV. Fina, we concude the aer in Section V. II. CONTENT MULTI-HOMING MODEL We now resent the new content muti-homing mode. After introducing some basic terminoog and notations, we forma define the MCDN-CM robem. A. Preiminaries CDN rovider. A CDN rovider deos reica servers at strategica chosen edge ocations, aka oint of resences (PoPs), scattered across the Internet. We view each PoP as an entit that hosts servers and has a massive amount of comuting and caching ower. Different CDNs have different andscaes in terms of deoed PoPs and service caacities. We denote P the set of PoPs owned b. Content rovider. Each content rovider (e.g., YouTube) services a set of objects to users at different areas via the CDN infrastructure. Suose the set of content roviders N have signed business contracts with, shown in Fig. 2. For each CP n N, I n reresents the set of served content objects. In view of the icense issues, it is reasonabe to US : CDN S charging region, r R China : request s ocation area, a A Fig. 3. The maing from request ocation area a A to charging region r R k of two CDNs: CoudFront and MaCDN. assume that content sets of different roviders are disjoint, i.e., I n1 I n2 =, n 1 n 2. For convenience, et I = n N I n. Content object. Each content object (e.g.,, a video) ossesses various roerties [3]. For content distribution, ke roerties invove the object size, the content ouarit, and the erformance requirement. Let o i be the size of object i I. Since an object i can be requested b users in different areas, we denote A the set of geograhica areas. Let d ai be the number of times that object i has been requested b the users in area a during a eriod. Obvious, d ai refects the content ouarit for this object. Note that d ai s coud be estimated according to historica access records. Thus, we assume these arameters are avaiabe to use in our robem. The roert of erformance requirement is discussed ater. CDN ricing. Some CDN roviders (e.g., Amazon CoudFront and MaCDN) offer their cometitive rices in ubic, whereas other CDN roviders (e.g., Akamai, Limeight, and Leve3) do not ubish their ricing information. Nevertheess, the ricing oicies in the CDN market genera obe the rue that ou a as ou go and the more traffic ou use, the ower the average rice ou get. The CDN ricing has the foowing three roerties: (1) regiona-based ricing, with a rice that varies across different regions; (2) voume-based charging, where charging is based on the voume of traffic, originating from ocation areas of a secific charging region, during the biing eriod (e.g., one month); and (3) quantitative discount, where the arger the voume is consumed, the arger the reative discount is given. For eame, Amazon CoudFront divides its ricing into si charging regions [6], shown in Fig. 3. Among the si, the regiona rice of US is the cheaest; it charges 0.12$/GB for ow voume and 0.02$/GB for high voume. Let K be the set of CDNs that everages to fufi its business commitments. Let R k be the set of charging regions of CDN-k. Cear, R k1 R k2 =, k 1 k 2. For simification, et R = k K R k. Further, we denote fk r ( ), as in Fig. 1.(a), the voume ricing function of CDN-k over region r. QoE guarantee. The business contract stiuates the serviceeve-agreement () that outines the eected QoE and costs associated with the business arrangement. The meaning of QoE, for different tes of objects, varies. For eame, the QoE with resect to a Web age or image coud sim mean access atenc, whie for a YouTube video it coud ertain to the bit-rate. Instead of secifing distinct QoE metrics for diverse objects, we adot a sime unified characterization [3], the fraction of times that requests for an object can be served with sufficient QoE. We use ˆq ai to denote the erformance target set b the CP. For eame, for video i,

3 ˆq ai = 90% means that 90 ercent requests at area a shoud be served at the video s encoding rate. On the other hand, we use q ai, P and qr ai, r R k 1 to characterize the abiit (fraction of times) of PoP of and the servers in region r of CDN-k in serving requests at area a for object i with the targeted QoE, resective. To refect the QoE constraints, we define Q ai = { P, q ai ˆq ai } and Q ai = {r r R, q r ai ˆq ai}. Note that, it is ossibe that Q ai = Q ai =. In this case, the best or r wi be added. B. Cost Mode and Probem Formuation We mode PoP as a coection of reica servers used to cache content and serve cient requests. As the ufront investment, we assume has deoed M servers at PoP P. Given the demands from customers N, the CDN- 0 oerator needs to figure out how requests for objects are served. To this end, we introduce two decision variabes: i) ai, the fraction of requests at area a for object i to be directed to PoP of ; and ii) r ai, r R k, the fraction of requests to be served b servers in region r of CDN-k. To suort { ai }, we assume m servers have to be rovisioned at PoP. The goa is to minimize s oerating cost that consists of two arts: i) the running cost of its infrastructure, {m } servers; ii) the cost aid to other CDNs in K. Running cost of P. In ractice, the running cost of PoP deends on severa factors, ike eectricit, bandwidth, and ta. Cost ike eectricit even varies temora. To simif, we use h to reresent the average hosting cost er server at PoP. Then the running cost of PoP becomes m h. Abeit sime, it has catured the fundamenta asects of CDN s oerating cost, i.e., the cost increases with m ; h varies across different areas. Further, we use b to denote the average rocessing ower of one server at PoP ; b is normaized to be the average number of requests each server can resond to. Note that this simified mode was used in [7], [8] as we. Cost aid to other CDNs. The ortions of requests redirected to other CDNs aggregate to be the charging voume that CDN- 0, as the customer, as to other CDNs. The cost aid to CDNk is r R k fk r( a A i I d aio i r ai ). Probem formuation. Given the above cost mode, the goa is to minimize the tota oerating cost of. We ca this the Mutie CDNs Cost Minimization (MCDN-CM) robem, defined as: min,m s.t. k,r f r k ( d ai o i r ) ai + m h (1) ai + r ai = 1, a A, i I (2) Q ai r Q ai ai 0, a A, i I, Q ai (3) r ai 0, a A, i I, r Q ai (4) r ai = 0, a A, i I, r / Q ai (5) d ai ai m b, P (6) 0 m M, P (7) 1 In ractice, {q ai } can be estimated based on the access ogs of ; {qai r } can be estimated from the that has signed with CDN-k. (1) is s oerating cost. (2) ensures that an user request for object i at area a is served. The QoE requirements are catured via Q ai and Q ai, encasuated in (3), (4), and (5). (6) states that the eected tota oad of servers in PoP shoud not eceed the service caacit. (7) imits the number of active servers of PoP. Athough m is integra in essence, we ma rea it to be continuous in MCDN-CM, in view of: i) a PoP coud comrise hundreds of servers; and ii) b and h er se are rough estimates. Aart from the service caacit constraint (6), we coud aso add constraints ike the bandwidth caacit constraint, d aio i ai m u. The soution discussed hereinafter sti works. MCDN-CM is a concave minimization robem [9]. Since decision variabes are we bounded and constraints are inear, the feasibe set D is a bounded ohedron. We assume D is non-emt. B Weierstrass Theorem, MCDN-CM has a goba otima soution, which is attained at an etreme oint of D [9]. However, instead of using a genera aroach to sove a concave minimization robem, we wi take advantage of the secia structure of fk r ( ) iecewise inear concave. C. Discussion Liu et a. studied content muti-homing [3] from the ersective of arge content roviders. Their aroach requires each content rovider to sign mutie CDN contracts and is not economica efficient for sma content roviders. In this aer, we advocate the secia roe of the authoritative CDN- 0. Thus, the muti-homing robem in [3] and MCDN-CM differ in the articiation of, with a different objective function and additiona constraints. Athough Liu et a. gave a secia and efficient agorithm in soving the muti-homing robem, we cannot use their aroach to sove MCDN-CM. This is because the etra server caacit constraints (5) (or the otentia bandwidth caacit constraints) rohibit transforming MCDN-CM into the so-caed assignment robem [3] in the first ste, thus making the aroach in [3] infeasibe. III. GLOBAL OPTIMIZATION To reach an otima soution to MCDN-CM, we transform the concave minimization robem into a biinear rogram b eoiting the secia structure of the CDN ricing function and sove the biinear rogram in an iterative manner. A. Eiminating m Coser observation to MCDN-CM reveas that the constraint (7) must be tight in the otima soution (, m ). That is, d ai ai = m b, P. With this roert, we can eiminate the decision variabe m from MCDN-CM, and get an equivaent robem MCDM-CM-E: min f r ( k d ai o i r ) ai + c d ai ai (8) k,r s.t. (2), (3), (4), (5) d ai ai s, P (9) where c = h /b and s = M b. Note that c can be viewed as the normaized er request service cost in PoP and s is the maimum service caacit of PoP.

4 B. Biinear Transformation Tabe I demonstrates the concrete ricing functions of CoudFront and MaCDN. The ricing function is iece-wise inear concave (see Fig. 1(a)). Secifica, fk r ( ) can be written in the foowing form u 1 r r + e 1 r, r [vr 0 = 0, vr) 1 fk r u 2 ( r ) = r r + e 2 r, r [vr, 1 vr) 2 (10) u nr r r + e nr r, r [vr nr 1, ) where u 1 r > u 2 r > > u nr r. n r is the number of charging intervas and u r(1 n r ) refects the average rice (er GB) in the voume interva [vr 1, vr). Equivaent, f r k ( r ) = min {u r r + e r }. (11) 1 n r For brevit, et r = d aio i r ai reresent the charging voume of region r R. Given the voume interva in which r fas, fk r ( ) turns into a inear function, whie MCDF-CM- E becomes a inear rogram. For this urose, we introduce for each region r a set of binar variabes r (1 n r ), indicating whether r fas in [vr 1, vr). That is, { 1, if r r [vr 1, v = r) (12) 0, otherwise. We reformuate the robem MCDN-CM-E: i) modif the objective function (8) using binar variabes r, fk r( r) = [u r r + e r]r; ii) add etra constraints, r = 1, v 1 r r r v rr, and r = {0, 1}. Reaing the integer constraint of rs eads to the foowing robem, referred to as MCDN-CM-ER, r( u r r + e ) r + c d ai ai (13) min, k,r s.t. (2), (3), (4), (5), (9) vr 1 r r vr r, r R (14) r = 1, r R (15) r 0, r R, 1 n r (16) Athough we rea the integer constraint of r, Theorem 1 (see roof in Aendi) estabishes the equivaence of MCDN- CM-ER and MCDN-CM-E. Therefore, we devote to soving MCDN-CM-ER instead. Theorem 1: (, ) is an otima soution to MCDN-CM- ER, if and on if is an otima soution to MCDN-CM-E. C. Agorithm for Soving MCDN-CM-ER MCDN-CM-ER is a biinear rogram with joint constrained feasibe region. Aong the ine of Dnamic Cost Udating Procedure (DCUP) [10], we resent an eact and continuous agorithm, Ag. 1, to sove MCDN-CM-ER. DCUP rocedure is based on the observation that the feasibe sets of variabes { r ai } and { r} are joint constrained on b constraint (14). If we fi one te of variabes, the remaining Agorithm 1 DCUP for MCDN-CM-ER 1: Initiaization: et r (0) be the initia vector of { r} where 1 r(0) = 1 and r(0) = 0, 1; et t 1; 2: Iteration-t: 2.1: Sove MCDN-LP ( (t 1) ) : (t) arg min { MCDN-LP ( (t 1) )} ; 2.2: Sove MCDN-LP ( (t) ) : (t) arg min { MCDN-LP ( (t) )} ; 3: If (t) = (t 1), then sto; otherwise, et t t + 1 and go to Ste 2; robem becomes an otimization with resect to the other te of variabes and consists in a inear rogram. Secifica, b fiing, we get the foowing inear robem MCDN-LP(), min r u rr + c d ai ai k,r (17) s.t. (2), (3), (4), (5), (9) Simiar, b fiing the variabe, we get the other inear robem MCDN-LP(), ) min r( u r r + e r k,r (18) s.t. (14), (15), (16) Ag. 1 roceeds b soving two (coued) inear rograms iterative. It is worth noting that MCDN-LP() itsef does not incude the constraint (14). But when Ag. 1 terminates, the constraint (14) wi be satisfied, because this constraint aread aears in MCDN-LP(). Theorem 2 estabishes the correctness of Ag. 1 in soving MCDN-CM-ER and Theorem 3 estabishes the convergence of Ag. 1 (see roof in Aendi). Theorem 2: The fina soution (, ỹ) given b Ag. 1 is an otima soution to MCDN-CM-ER. Theorem 3: The Ag. 1 stos in a finite number of iterations. IV. PERFORMANCE EVALUATION MCDN-CM-ER aims to minimize the oerating cost of, whist fufiing its business commitment, that requests from cients for content rovided b registered CPs shoud be satisfied with sufficient QoE secified in the s. It is natura to observe the cost achieved from different oerating ans. A. Eerimenta Setu Datasets. To make the numerica eeriments as reaistic as ossibe, we used the Youtube Dataset rovided b [11]. We ran the eeriments on 5 grous of datasets. Since simiar resuts were observed, we on reort resuts of one grou for brevit. Each grou dataset consists of 5 das records. We random distribute them to N = 10 content roviders (CPs). Tica, a 5-da dataset corresonds to severa thousands of TB traffic, which we beieve is a medium size 2 and is aroriate for our eeriments. Imortant fieds of the dataset 2 The mathematica mode of mutie-cdn cost minimization (MCDN-CM) er se does not deend on the fideit of an inut arameters.

5 TABLE I. REGIONAL PRICING FUNCTIONS USED IN THE EXPERIMENTS CDN Region [0, 10TB) [10TB, 50TB) [50TB, 150TB) [150TB, 500TB) [500TB, 1PB) [1PB, 5PB) [5PB, ) US $0.12 /GB $0.08 /GB $0.06 /GB $0.04 /GB $0.03 /GB $0.025 /GB $0.02 /GB EU $0.12 /GB $0.08 /GB $0.06 /GB $0.04 /GB $0.03 /GB $0.025 /GB $0.02 /GB CoudFront HK/SG $0.19 /GB $0.14 /GB $0.12 /GB $0.10 /GB $0.08 /GB $0.07 /GB $0.06 /GB JP $0.201 /GB $0.148 /GB $0.127 /GB $0.106 /GB $0.085 /GB $0.075 /GB $0.065 /GB S/A $0.25 /GB $0.20 /GB $0.18 /GB $0.16 /GB $0.14 /GB $0.13 /GB $0.125 /GB AU $0.19 /GB $0.14 /GB $0.12 /GB $0.11 /GB $0.095 /GB $0.090 /GB $0.085 /GB MaCDN US/EU/SA $0.07 /GB $0.06 /GB $0.05 /GB $0.04 /GB $0.035 /GB $0.03 /GB $0.02 /GB A/P $0.10 /GB $0.074 /GB $0.064 /GB $0.053 /GB $0.043 /GB $0.037 /GB $0.032 /GB invove the video id, the views, the ength, and the video rate (KB/s). The roduct of ength and rate ieds the video size. Based on the rate vaue, the videos are categorized in two tes: ow bit-rate and high bit-rate. We distinguish these two tes, as each te has different QoE requirements. Pricing and QoE settings. We deiberate choose CoudFront () and MaCDN () to form the set K, as their regiona ricing is ubic avaiabe, thereb eading to a reaistic setting of ricing functions fk r ( ). The concrete ricing function is iustrated in Tabe I. On average, the ricing of MaCDN is ower than that of CoudFront. Liu et a. in [3] conducted eeriments via PanetLab and measured the CDN s erformance in servicing requests from 7 ocation areas (as are shown in Fig. 3). To make the settings of QoE arameters {qai r } reaistic, we reuse their coected data and set A to hod those 7 areas as we. The detaied information on QoE arameter settings is summarized in Tabe II. In genera, CoudFront resents a high quait in servicing both ow bit-rate and high bit-rate videos, whie MaCDN resents varing erformances in serving different tes of videos at distinct areas. Fina, the QoE target q ai is set to 90%, which determines the vaues of Q ai and Q ai in turn. Setting of. To mode the footrint of, we assume 3 PoPs have been deoed at each area in A. For eame, P 1, P 2, and P 3 are three PoPs to serve requests from the US area. In tota contains P = 21 PoPs. We assume that three PoPs at the same area resent simiar erformance, i.e., q 1 ai = q2 ai = q3 ai. The concrete vaues are given in Tabe II. Furthermore, the genera cost of running an active server, h, shoud refect the regiona cost variations. To this end, we set the vaues of {h }, referring to the ricing for Virtua Machines of Amazon EC2 [12]. The setting of {h } is summarized in Tabe III, where different grous corresond to different eves of hosting rices. Last, we set M, the quota of servers in, between [20, 35] random. B. Evauation Methodoog The soution given b Ag. 1, referred as OPT, offers the detaied oerating an of. An feasibe oerating an invoves two asects: i) PoP activation, that m servers of PoP wi be activated; and ii) request assignments 3, that r ai (r R k) ortion of requests for object i at area a wi be directed to region r of CDN-k and ai ortion wi be redirected to PoP of. Together {m }, { r ai }, { ai } determine the oerating cost. To evauate the erformance of 3 The requests redirection ma either use eisting DNS-based aroach or emo the emerging technique of software defined networking (SDN). TABLE II. MEASURED CDN PERFORMANCE SETTINGS US Sain Austria China Jaan Brazi Austraia 99 a b a The first row corresonds to the erformance in servicing ow bit-rate videos. b The second row corresonds to the erformance in servicing high bit-rate videos. TABLE III. AVERAGE HOSTING PRICE OF SERVER IN POP OF h grou US Sain Austria China Jaan Brazi Austraia Grou c Grou Grou Grou c in US doars er month. Costs (Kio US Doar) OPT QoE-on Random Greed Grous of { h } Fig. 4. The gross oerating cost of using different methods, with varing grous of {h }. Ag. 1 in minimizing the oerating cost, we comare it with three aternatives: i) QoE-on, which awas choose the region r or PoP that can rovide the best QoE (maimum qai r or q q ai ); ii) random, which icks an one among those regions or PoPs that satisf the QoE requirements; and iii) greed, which seects from the QoE-satisfied candidates the one that eads to the owest cost after current assignment. Note that the above three aternatives a roceed b making assignments for requests sequentia in a uniform random order.

6 Traffic (TB) OPT QoE-on Random Greed Traffic (TB) Grou-1 Grou-2 Grou-3 Grou-4 Fig. 5. Traffic distribution of four methods under Grou-1 {h }. Fig. 6. Traffic distribution using OPT, under four grous of {h }. We use the Pthon interface of Gurobi-5.1 (under the academic icense) to sove MCDN-LP(). With around thousands of ocation-objects, Gurobi-5.1 can sove MCDN- LP() in about 10 minutes under a machine with 4 AMD Oteron 844 (1.8GHz) CPU and 8GB RAM. In a our eeriments, Ag. 1 terminates with ess than 3 iterations. C. Eerimenta Resuts First, we observe the cost aid b for accomishing its business commitment with fu QoE grantees. We comare the vaues of the oerating cost, resuting from the four different agorithms mentioned above. Fig. 4 shows the resuts with varing grous of {h }. As eected, OPT eads to the east month cost. In genera, the greed method erforms much better than the other two aternatives: QoE-on and random. This is because, these two methods do not take into consideration at a the cost when making request assignments. Abeit, the curve of greed seems to be cose to that of OPT, this atter sti brings a considerabe saving. For eame, under this articuar arameter settings, OPT saves , , , and US doars for each month under the four grous of h searate, comared with greed. Net, we dissect how ortions of traffic are distributed using different methods. From Fig. 5, we can see that OPT rioritize using s own infrastructure under Grou- 1 {h }, since Grou-1 s hosting rices are reative sma. Further, OPT refers to, since the average rice of is ower than that of in genera. But it sti has to seek he from, since cannot satisf the erformance target in areas ike China, Brazi, and Austraia. This oint is further refected b the traffic distribution of greed. From Tabe II, we observe that rovides the best erformance across a the areas, which arises from the far-fung footrint of CoudFront as a goba CDN rovider. B virtue of this fact, QoE-on heavi reies on. On the other hand, random equa uses the three CDNs and wi suffer from the negative effects of using mutie CDNs caused b the ament discount oic, when the tota traffic is of medium size, as in this case. Fina, we see how the traffic distribution changes when the average hosting rice of increases. As shown in Fig. 6, when the hosting costs of PoPs increase, OPT begins Fig. 7. Traffic (TB) Grou-1 Grou-2 Grou-3 Grou-4 Traffic distribution using greed, under four grous of {h }. to re more on other CDNs, articuar, in servicing requests. The greed aroach refects such change as we, but not as evident as does OPT, as shown in Fig. 7. V. CONCLUSION This aer is motivated b the content muti-homing robem in [3]. Content muti-homing is economica inefficient, articuar for the mriad of sma content roviders. We roose an aternative aroach where each content rovider on signs the contract with the authoritative, and takes charge of handing the otentia QoE tra of an singe CDN, b utiizing other CDNs to fufi its business commitment. We identif the MCDN-CM robem that hes the oerator of make an otima oerating an in terms of minimizing its oerating cost. Under reaistic settings, the eerimenta resuts show that our agorithm for soving MCDN-CM resuts in considerabe amount of mone saving. In the future work, we an to stud the imacts of renting other CDNs services on defining the ricing an of CDN- 0. For eame, can raise its rice without oosing otentia customers? VI. ACKNOWLEDGMENTS This work was in art suorted b UGC grant FS- GRF14EG24.

7 REFERENCES [1] V. Adhikari, Y. Guo, F. Hao, M. Varveo, V. Hit, M. Steiner, and Z.- L. Zhang, Unreeing netfi: Understanding and imroving muti-cdn movie deiver, in INFOCOM, 2012 Proceedings IEEE, March 2012, [2] V. Adhikari, Y. Guo, F. Hao, V. Hit, and Z.-L. Zhang, A tae of three cdns: An active measurement stud of huu and its cdns, in Comuter Communications Workshos (INFOCOM WKSHPS), 2012 IEEE Conference on, March 2012, [3] H. H. Liu, Y. Wang, Y. R. Yang, H. Wang, and C. Tian, Otimizing cost and erformance for content mutihoming, in Proceedings of the ACM SIGCOMM 2012 Conference on Aications, Technoogies, Architectures, and Protocos for Comuter Communication, ser. SIGCOMM 12. New York, NY, USA: ACM, 2012, [4] A.-J. Su, D. R. Choffnes, A. Kuzmanovic, and F. E. Bustamante, Drafting behind akamai: inferring network conditions based on cdn redirections, IEEE/ACM Trans. Netw., vo. 17, no. 6, , Dec [5] N. B. Ben Niven-Jenkins, Francois Le Faucheur, Content distribution network interconnection (cdni) robem statemen-rfc6707, htt://datatracker.ietf.org/doc/draft-ietf-cdni-robem-statement/, [6] Amazon. Amazon coudfront ricing. htt://aws.amazon.com/coudfront/ricing/. [7] P. X. Gao, A. R. Curtis, B. Wong, and S. Keshav, It s not eas being green, in Proceedings of the ACM SIGCOMM 2012 Conference on Aications, Technoogies, Architectures, and Protocos for Comuter Communication, ser. SIGCOMM 12. New York, NY, USA: ACM, 2012, [8] Q. Zhang, Q. Zhu, M. F. Zhani, and R. Boutaba, Dnamic service acement in geograhica distributed couds, in Proceedings of the 2012 IEEE 32nd Internationa Conference on Distributed Comuting Sstems, ser. ICDCS 12, 2012, [9] R. Horst and H. Tu, Goba Otimization: Deterministic Aroaches. Sringer, [10] P. M. Nahaetan, A. Pardaos, A biinear reaation based agorithm for concave iecewise inear network fow robems, Journa of Industria and Management Otimization, vo. 3, no. 1, , [11] X. Cheng, C. Dae, and J. Liu, Dataset for statistics and socia network of outube videos, Simon Fraster Universit, Canada. htt://netsg.cs.sfu.ca/outubedata/, [12] Amazon. Amazon ec2 ricing. htt://aws.amazon.com/ec2/ricing/. APPENDIX Proof of Theorem 1: To rove the theorem, we wi show that an otima soution to one of the two robems is a feasibe soution to the other with identica objective vaue. Suose is an otima soution to MCDN-CM-E. We ma construct the vector ỹ according to (12). That is, for each r R, if r [vr 1, vr), et ỹr = 1; and, 1 n r, et ỹr = 0. Since satisfies constraints (2), (3), (4), (5), and (9), and ỹ satisfies constraints (14), (15), and (16), (, ỹ) is a feasibe soution to MCDN-CM-ER. Further, fk r( r) = u r r + e r, where r [vr 1, vr). Thus, the objective vaue of MCDN- CM-ER given b the feasibe soution (, ỹ) is identica to the otima objective vaue of MCDN-CM-E. Net, we show the oosite direction. Suose (, ỹ) is an otima soution to MCDN-CM-ER. First, it is eas to check that is aso feasibe to MCDN-CM-E. Second, we need to show that the objective vaues of the two robems are identica. Note that the objective functions of the two (8) and (13) differs on in the first art. Thus, we on need to check whether fk r( r) equas r( ỹ u r r + er). Or ut in another wa, we eamine whether ỹr resects (12). B fiing the vaue of vector as, the MCDN-CM-ER robem reduces to a inear rogram with resect to, that is, the robem LP( ). Note that LP( ) can be fu searated into R subrobems for each r R. Hence, in the foowing, we on focus on a secific region r. Since (, ỹ) is an otima soution to MCDN-CM-ER, ỹ must be the otima soution to LP( ) as we. On the other hand, we assume that r [vr 1, vr]. That is, in the otima soution, the vaue r ies in the segment indicated b. Reca (11) and thus fr( r ) = min {u r r + e r} = u r r + e r. Based on this, we 1 n r construct a new vaue ŷ r of vector r : et ŷr = 1; and for an, et ŷr = 0. Then the new constructed vector ŷ r satisfies: i) the constraint (14), because r [vr 1, vr]; and ii) ŷ r = arg min{ r(u r r + e r) r = 1, r 0}. Hence, ŷ r is an otima soution to the subrobem of LP( ) with resect to r. A simiar resut hod for an other r R. Therefore, ŷ is an otima soution to LP( ). Since ỹ is aso an otima soution to LP( ), we concude (, ŷ) is aso an otima soution to MCDN-CM-ER 3. These two facts: i) fr( r ) = r( ŷ u r r + er), according to how we construct ) = ỹ r( u r r + e r), because ŷ r ; and ii) r( ŷ u r r + e r both and ŷ are otima to LP( ), aow us to concude that fk r( r) is equa to r( ỹ u r r + er). So we finish roving that the objective vaue of MCDN-CM-E given b equas the objective vaue of the otima soution (, ỹ) of MCDN- CM-ER. Proof of Theorem 2: Let (, ỹ) be the returned soution of Ag. 1. For notationa simification, et g(, ) reresent the objective function (13) of MCDN-CM-ER and et D be the feasibe region. B virtue of the stoing condition in Ste 3 of Ag. 1, we get: (i) = arg min{mcdn-lp(ỹ)}; and (ii) ỹ = arg min{mcdn-lp( )}. (ii) eads to ỹ = arg min g(, ). Since ỹ satisfies the constraint (14) aread (even though (14) is miss- (,) D ing in MCDN-LP(ỹ)), combined with (i), we get = arg min (,ỹ) D g(, ỹ). The above two equations show that (, ỹ) = arg min g(, ). Therefore, the soution (, ỹ) (,) D returned b Ag. 1 is an otima soution of MCDN-CM-ER. Proof of Theorem 3: Theorem 3 can be roven in the same aroach as Theorem-6 in [10]. 3 Note that in this roof, we don t care whether ỹ = ŷ.