HiFi: A Hierarchical Filtering Algorithm for Caching of Online Video

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1 HiFi: A Hirarchical Filring Algorihm for Caching of Onlin Vido Shahid Akhar Vlocix Alcal-Lucn Plano, TX, USA shahid.akhar@alcallucn.com Andr Bck Bll Labs Alcal-Lucn Naprvill, IL, USA andr.bck@alcal-lucn.com Ivica Rimac Bll Labs Alcal-Lucn Sugar, Grmany rimac@bll-labs.com ABSTRACT Onlin vido prsns nw challngs o radiional caching wih ovr a housand fold incras in numbr of asss, rapidly changing populariy of asss and much highr hroughpu rquirmns. W propos a nw hirarchical filring algorihm for caching onlin vido HiFi. Our algorihm is dsignd o opimiz hira, rplacmn ra and cach hroughpu. I has an associad implmnaion complxiy comparabl o ha of LRU. Our rsuls show ha undr ypical opraor condiions, HiFi can incras dg cach by hi-ra by 5-24% ovr an LRU policy, bu mor imporanly can incras RAM or mmory by hi-ra by 80% o 200% and rduc rplacmn ra by 90%! Ths wo facors combind can dramaically incras hroughpu for mos cachs. If SSDs ar usd for sorag, h much lowr rplacmn ra may also allow subsiuion of lowr cos MLC basd SSDs insad of SLC basd SSDs. W x prvious muli-ir analyical modls for LRU cachs o cachs wih filring. W dvlop a ralisic simulaion nvironmn for onlin vido using saisics from opraor racs. W show ha HiFi prforms wihin a fw prcnag poins from h opimal soluion which was simulad by Blady s MIN algorihm undr ypical opraor condiions. Cagoris and Subjc Dscripors B.3.2 [Mmory Srucurs]: Dsign Syls Cach mmoris; C.2.4 [Compur-Communicaion Nworks]: Disribud Sysms Clin/srvr. Gnral Trms Algorihms, Prformanc, Dsign. Kywords Hirarchical cach, onlin vido, hi-ra, LRU, LFU, GDSF. 1. INTRODUCTION Onlin vido is now h largs componn of Inrn raffic [20]. I is kp in small chunks of im of ypically bwn 2 and 10 sconds and ach vido may b ncodd ino mulipl vido qualiy lvls. This chunking chniqu can incras h numbr Prmission o mak digial or hard copis of all or par of his work for prsonal or classroom us is grand wihou f providd ha copis ar no mad or disribud for profi or commrcial advanag and ha copis bar his noic and h full ciaion on h firs pag. To copy ohrwis, or rpublish, o pos on srvrs or o rdisribu o liss, rquirs prior spcific prmission and/or a f. Rqus prmissions from Prmissions@acm.org. MM '15, Ocobr 26-30, 2015, Brisban, Ausralia 2015 ACM. ISBN /15/10 $15.00 DOI: hp://dx.doi.org/ / of fils ha can b rqusd by usrs in a caching sysm by a housand fold or mor. Incrasingly a significan par of h onlin vido is usd o rbroadcas rcn TV shows or nws rlad programs which ar iniially qui popular bu rapidly drop in populariy [2]. Th hug volum of onlin vido rquirs ha cachs b xrmly scalabl, which implis ha caching algorihms nd o b highly compu fficin. On mhod which is usd for high scalabiliy is SSD mmory, which has much fasr accss ims. Howvr SSD mmory is known o hav a limid numbr of wri cycls in is lifim. SSD mmory wih highr numbr of lifim wri cycls is ypically mor xpnsiv. Dspi a long hisory of caching rsarch only simpl schms lik Las Rcnly Usd (LRU), Grd Dual Siz Frquncy (GDSF) or Las Frqunly Usd wih Dynamic Aging (LFU- DA) hav bn implmnd in known caching sofwar such as Apach Traffic Srvr, Squid or Varnish [23][9]. Th ky impdimns o pracical us hav bn a prcivd implmnaion complxiy of h algorihms, which can impd hroughpu prformanc, and an xpcaion ha h valu of addiional caching prformanc may b ouwighd by facors such as abiliy o adap o ass populariy changs. In his papr, w propos a novl algorihm for onlin vido cachs HiFi, ha aims o addrss h abov rquirmns. I achivs nar opimal hi-ra and a low rplacmn ra, has low implmnaion complxiy which is comparabl o ha of LRU which allows i o scal for cachs ha hav vry larg numbr of asss. Th main conribuions of his papr includ: (i) a brif survy of caching schms wih focus on suiabiliy for handling onlin vido; (ii) h dsign and drivaion of h HiFi algorihm and is implmnaion wih O(1) compu complxiy; (iii) an xnsion of prvious work of an analyical modl of LRU cachs o rprsn h impac of using filring algorihms such as HiFi; (iv) a ralisic simulaion modl for onlin vido using saisics from opraors racs; (v) a prformanc valuaion of HiFi and comparison wih prominn sa-of-h-ar caching schms and opimal prformanc using Blady s MIN algorihm [3]. Th rmaindr of h papr is srucurd as follows. W provid background and a brif survy of caching algorihms in scion 2. W hn propos our nw algorihm and is implmnaion in scion 3, and is analyical modl in scion 4. W prsn h simulaion mhodology in scion 5; discuss h rsuls in scion 6 and our conclusions and fuur work in scion BACKGROUND Thr has bn a significan amoun of rsarch in making h righ or opimal dcision o plac an ass in a givn cach and whn o rmov i. Th righ dcisions can improv h cach prformanc in rms of hi-ra, by hi-ra, rplacmn ra 421

2 and how quickly h cach rsponds o changs in ass libraris. This rsarch can b organizd in hr main cagoris: cach vicion algorihms, hirarchical cach ass placmn algorihms and cach coopraion algorihms. Cach vicion algorihms apply o a singl cach and ry o opimiz h dcision of vicing h righ asss from h cach. Som wll known xampls ar LRU and LFU; LRU is mos ofn usd in oday s cachs. Hirarchical caching algorihms ar an nhancmn o h singl srvr cach vicion algorihms. Ths drmin whr o plac an ass givn a hirarchy of cachs and a s of dmands for ach ass a ach dg cach. Mos pracical hirarchis hav only fw lvls, ofn no mor han hr [21]. Cach coopraion algorihms conrol xchang of asss bwn cachs in h sam lvl of hirarchy [13][26]. Ths allow dg cachs o sor lowr amouns of daa han hirarchical cachs as hy can co-opra or ask a nighboring cach whn a cach dos no hav a givn ass. Howvr rsarch shows ha hirarchical cachs produc lowr lancy and consum lss ovrall bandwidh [18] han cach coopraion algorihms. In addiion, many opraors prfr o us hirarchical cachs sinc xising opraor ranspor and IP nworks ar ofn dsignd in a hirarchical fashion and hir opraions ar alignd wih h hirarchical naur of hs nworks. W discuss blow caching algorihms for singl and hirarchal cachs and how wll hy sui h rquirmns for onlin vido. 2.1 Singl Cach Algorihms Th work in [24] classifis cach vicion algorihms in four cagoris: rcncy focusd, frquncy focusd, rcncy and frquncy in qual focus and funcional algorihms which ypically also us h siz and cos of ach ass. Th cos is a paramr rprsning h ffor rquird o bring h ass o h cach running h vicion algorihm. Typically rcncy basd approachs lik LRU produc lowr hiras han ohr approachs. LRU allows all asss o b insrd in h cach whnvr hr is a cach miss. This allows unpopular asss o b insrd in h cach, which lowrs hi-ra. Prfc LFU, which racks h populariy of all asss is shown o produc h opimal hi-ra [5][22] whn ass populariy is saic. Wih dynamic changs in ass populariy, such as h cas wih onlin vido, Prfc-LFU dos no prform wll. Window- LFU [22], on h ohr hand can produc nar opimal rsuls if is window siz is opimizd for raffic dynamics. Howvr, Window-LFU nds a sord lis of all asss. Sinc h numbr of asss for onlin vido can b vry larg; 100 million asss or mor as w xplain lar, his is a significan issu, boh from a sorag prspciv and a compu prspciv as ach nw ass or ass populariy chang rquirs a las O(logN) im o find h righ plac in a sord lis. Window-LFU is an xampl of rcncy and frquncy basd approach sinc is window acs as a rcncy filr. Funcion basd approachs inroduc h concp of including h cos and siz of ach ass; GD [19] and GDSF [16] ar ky xampls. Howvr hy do no produc nar-opimal hi-ras and do no nd o rack all asss. Thr has bn som work o dvlop caching algorihms ha hav low compu rquirmns. In [1], h auhors show an LFU algorihm daa srucur ha can procss a nw ass in O(1) im only. Th algorihm is basd on a daa srucur ha kps all asss wih h sam coun in a lis and his lis is conncd o a masr lis which is sord according o ass coun. So whn h coun of an ass is incrasd or dcrasd by on, h algorihm only nds o look a h nighbor in h masr lis o drmin if h ass nds o b movd o h nx lmn in h masr lis. This algorihm braks down if h ass coun is don for a givn im window or if h soring is basd on a mor coninuous variabl such as xponnial moving avrag, whn h ass may nd o b movd o an arbirary locaion away from is currn locaion. In [5], h auhors us a bloom filr o rduc sorag rquirmns for a LFU soluion whn h numbr of asss o b rackd is vry larg. Bloom filrs allow rducion in sorag a h xpns of som rrors in ass populariy couns. Howvr, hy do rquir mulipl hashs o b calculad pr ass. Each hash is qui an xpnsiv opraion from a compu prspciv so i dos no appar o b a soluion for onlin vido whr minimizing compu rquirmn is also an objciv. Siz is usd in many of hs approachs o rmov asss of largr siz firs, which s o incras ovrall hi-ra as many smallr sizd asss can b accommodad in h cach du o h rmoval of on largr sizd ass. Howvr, his may no incras h by hi-ra. For onlin vido cachs, h individual asss ar chunks of vido ncodd a diffrn ransmission ras. Chunks ar gnrally in h 2 o 10 scond rang. If h cach prfrably rmovs chunks of largr siz, which ar likly o b for highr Vido Qualiy (VQ) lvls, hn h clin playr of h vido would ofn find ha chunks of h highr VQ lvls ar no availabl a h laf cach, and would hav o fch hs from h highr lvl cachs, which would likly rduc h ransmission spd of h largr chunks, and h clin may conclud ha h highr VQ lvls ar no susainabl. For his rason, h us of siz in h cach vicion algorihms for onlin vido is no rcommd. Th us of cos pr ass is mos valuabl if h asss ar fchd from diffrn sourc cachs, so h vicing cach could prfrably vic asss whos cos is lowr. If all h asss ar fchd from h sam origin srvr hn using a cos paramr pr ass may no b as valuabl. W do no us cos in our algorihms - w lav ha for furhr work. 2.2 Hirarchical Cach Algorihms Ths drmin whr o opimally, or nar opimally plac a givn ass in a r basd hirarchy of cachs. W lis som of h ky chniqus blow Simpl Tchniqus Lav Copy Down (LCD) [17] is a chniqu in which all h cachs in vry lvl of hirarchy ar rquird o rcord a numbr of rquss for h sam ass bfor making h dcision o sor ha ass in h local cach. Th mos common approach is o us h cach hirarchy numbr; for xampl in a hr layr hirarchy, h dg cach would no cach unil i ss h hird rqus for h sam ass. Mov Copy Down (MCD) [17] is similar o LCD, howvr if all cachs a a lvl hav a crain ass, hir immdia parn cach would rmov ha ass from is sor. This chniqu dos rquir som inr cach pr ass communicaion. Pracical sing shows sligh improvmn ovr LCD, bu no in all cass. Th filr algorihm oulind in [7] kps a characrisic im TC k pr cach in hirarchy lvl k as wll as an avrag of all asss 422

3 inr-arrival im T ij of h ih ass a h dg cach j. Th characrisic im is dfind as h avrag im an ass sps in h cach wihou bing rqusd bfor i is vicd. According o h algorihm, h ass is kp only in h hirarchy lvl k if: Th abov quaion applis o h hirarchy abov dg cach j. W find som problms wih his approach. If a highr lvl cach has mulipl cachs aachd o i a h lvl immdialy blow, hn h ass inr-arrival im usd a h highr lvl cach should b a funcion of all hos mulipl cachs inr-arrival ims a h dg. Furhr, according o h sam algorihm, an ass is addd o a cach s parn if ha ass is rmovd from i. This is o mak sur ha an ass always rmains in h hirarchy, from h laf cach o h op cach, bu a only on lvl. Howvr, i is no guarand ha h dg inr-arrival im T ij of a givn ass would b lowr han h characrisic im of h immdialy highr layr cach in ordr o saisfy h abov quaion. Th filr algorihm prformd significanly wors in a comparison wih h LCD and MCD algorihms [17]. W bliv h abov issus ar ky conribuors o ha lowr prformanc. Anohr issu wih all of h abov hirarchical algorihms is ha hy nd o collc informaion on vry ass sn by h cach; in h cas of LCD and MCD numbr of rquss for a givn ass and in h cas of h filr algorihm, h avrag inrarrival im; howvr unlik Window-LFU, his lis of asss dos no nd o b sord. Wih onlin vido cachs, h numbr of asss can bcom xcding larg, which can mak collcion of saisics for all asss xpnsiv from a sorag prspciv. If h saisics for all asss canno b kp in h mmory of a cach, hy nd o b ransfrrd o disk sorag. Frqun accss o disk sorag can rduc h hroughpu prformanc of a cach Globally Opimal Tchniqus A numbr of rsarchrs hav proposd chniqus o obain an opimal s of ass locaions in a s of conncd cachs; ky xampls ar [11][12]. Ths chniqus hav gnrally vry high compuaional rquirmns of h ordr of O(N 3 ), whr N is h ypical numbr of asss in h cach. In onlin vido cachs, ach ass is a small chunk of h oal vido and hr ar mulipl vido qualiy lvls dfind for ach vido. For a singl hour of vido wih 6 qualiy lvls and 2 scond chunks, ovr 10,000 chunks may b ndd. For a 10,000 ass vido library, his could amoun o ovr 100 million chunks! Typs of adapiv vido such as smooh-sraming or Appl s HLS may rquir diffrn packaging for h sam vido, which can furhr add o h numbr of asss. Algorihms nding mor han O(N) wih such a larg numbr of asss would ypically b infasibl in his nvironmn Grdy Tchniqus Ohr rsarchrs hav proposd local grdy algorihms o obain a nar opimal s of ass locaions [10][14]. In [14], h auhors propos ha for ach rqus sn upsram in a hirarchy for a givn ass; ach caching nod along h way would add h rqus ra for ha spcific ass and h oal rqus ra sn a ha nod. This combind s of informaion would b sn o h nod ha vnually srvs h rqus, which would mak a local dcision on wha locaions along h ass pah should sor h ass basd on h collcd informaion along h pah. Anohr s of rsarchrs hav proposd a similar algorihm in h conx of nrgy fficincy [10], which collcs informaion (1) abou h nrgy rquird for h ranspor of an ass from ach hop ha i ravrss in h simpls cas h nrgy is proporional o h hop coun. This informaion is usd a h rciving nod o driv h nrgy powr bnfi, which is dfind as h diffrnc bwn h ranspor coss for ha ass o bring i o h nod minus h sorag cos for ha ass dividd by h ass s rqus inr-arrival im. Asss ar sord and hn insrd and vicd basd on hir powr bnfi ranking. Ths chniqus ar gnrally much mor fasibl han h global opimal chniqus. Howvr hy rly on informaion abou h pah cos of a givn ass basd on whn h rqus was mad. If an ass was vicd from a parn nod afr h rqus was mad, h pah cos of ha nod in h child would bcom invalid. Sinc h ass vicion is basd on h avrag inrarrival im, hy may also rquir uning of h priod usd for calculaing h inr-arrival im. 3. A NEW CACHING ALGORITHM W now dfin a nw caching algorihm for hirarchical cachs. W basd i on h rquirmns for caching onlin vido as xplaind in arlir scions. This algorihm runs a ach cach in a givn hirarchy indpn of h algorihm in ohr cachs. Each cach simas h inr-arrival im of ach ass locally. Each cach also calculas is characrisic im, which w dfin as h avrag im an ass says in cach wihou bing rqusd bfor h ass is vicd. Each cach hn only sors asss whos inr-arrival im is smallr han h cach s characrisic im. Th vicion policy is h sam as LRU, i.., h las rcnly rqusd im is vicd firs. W dfin h algorihm furhr blow. 3.1 Nomnclaur Pr-ass variabls: T ijk Avrag inr-arrival im of ass i for cach j in hirarchy k. P ijk Prvious im ass i was rqusd from cach j in hirarchy k. Pr-cach variabls: TC jk Characrisic im of cach j in hirarchy k. TS Currn im. Paramrs for h cach hirarchy: w TC Wigh for h xponnial moving avrag of h characrisic im. w IA Wigh for h xponnial moving avrag of inrarrival ims. GS Gnl slop paramr on how quickly TC jk is incrasd ovr im. 3.2 Hirarchical Filring (HiFi) Algorihm Bfor h main algorihm is run, a fw variabls ar iniializd as follows: S all P ijk o h currn im TS. S all T ijk o a larg numbr, bu smallr han h numbr usd for iniial valu for h characrisic ims TC jk. This allows all asss o b cachd unil TC jk is updad o a ral valu. S all TC jk o a larg numbr, largr han h numbr for T ijk. 423

4 A h im of vry LRU ass vicion in a givn cach, w calcula h xponnial moving avrag (EWMA) of h characrisic im TC jk as follows, assuming ass i was vicd: Whnvr an ass is rqusd from any cach, whhr i is a laf cach or a highr layr cach, w calcula h EWMA of h inr-arrival im of ass i a ha cach using h xponnial moving avrag wigh w IA as follows: W hn s h prvious im P ijk o h currn im: A h im of vry rqus for a givn ass i; if h ass is no currnly in h cach, w chck if h ass inr-arrival im T ijk is lss han h characrisic im TC jk of h cach, and if ys, w cach ha ass; and prform an LRU vicion if hr is no spac for ha ass. If h abov s fails w obain h ass from h cach s parn and dlivr o h clin wihou vr soring h ass in h cach, which is ofn implmnd on non-volail sorag such as disks. This provids ky valu as i allows graly rducd disk inpu-oupu, which is ofn h bolnck for mos cachs. In cas h ass is availabl in h cach, w dlivr h ass from h cach. A pculiar cas was obsrvd wih his algorihm. Givn ha an ass is only sord in a cach if is inr-arrival im T ijk is lss han h characrisic im TC jk, his would imply ha during havy raffic, h TC jk for a givn cach would b lowr sinc h inr-arrival im for all asss is xpcd o b lowr during his im. In h cas whn his sam cach is srving raffic during low raffic, TC jk would rmain a his lowr lvl sinc TC jk is only updad by a LRU ass vicion vn. An ass vicion can only happn if h cach ris o sor a nw ass. During priods of low raffic h chck if h inr-arrival im of h ass is lowr han h characrisic im of h cach would fail mor ofn. In his cas h characrisic im TC jk of h cach may bcom suck a a low valu. In our schm h cach characrisic im TC jk of a givn cach is always gnly incrasing o avoid his. W upda TC jk a vry ass rqus as follows: W limi h oal numbr of asss whos inr-arrival im T ijk is bing rackd by h following: Whr S f drmins a snsiiviy facor of how much rror is allowd from h bs hi-ra achivabl from h algorihm. In driving h abov quaion, w assum ha h inr-arrival im of h sam ass is Poisson. This is a good assumpion as h inr-arrival im of rquss for whol asss is likly o b from diffrn usrs and hrfor should b clos o Poisson. A givn chunk in an ass is likly o b r-rqusd from diffrn usrs, which would mak h inr-arrival im of h sam chunk also Poisson assuming ha h im from h bginning of an ass o a givn chunk is approximaly drminisic. Thn h probabiliy of a singl inr-arrival im bing lss han T X is givn by h following; whr T A is h avrag inr-arrival im. (2) (3) (4) (5) (6) (7) If w limi racking of asss wih any singl inr-arrival im largr han S f ims TC jk, hn h probabiliy ha w would miss an ass whos avrag inr-arrival im is lss han or qual o TC jk is: This bcoms o h powr of -S f and using S f qual o 5 givs a probabiliy of 0.67% for a miss. W us 5 as h valu of S f for h rs of h papr. 3.3 Daa-Srucurs o Suppor HiFi W dfin wo liss for mainaining h inr-arrival ims. URL TRAK is a lis ha kps h EWMA of h inr-arrival im of asss as calculad in quaion (3). W dfin anohr lis URL OOL ; a on occurrnc lis which kps rack of asss whos rqus has only bn sn onc. W dfin an ass block pr ass which is shown in Figur 1; i may b accssd via a hash or r or som ohr combinaion daa srucur basd on h URL of h ass, as is ypical in oday s opraing cachs whr h cach is rquird o chck if a nw ass rqus is currnly cachd. Such a lookup may no b O(1) wih rspc o h numbr of asss N, howvr h incrmnal compuaion du o h HiFi algorihm is O(1). Each ass block conains a imsamp, whn h ass was las rqusd and also conains poinrs o hr addiional blocks: OOL, TRAK and Cach. Each of hs blocks conain wo poinrs so hs blocks can b par of a doubly linkd lis as wll as a poinr back o h main ass block. Th Cach block may conain dails of any ass currnly sord in h cach. Such dails would ypically b sord in opraing cachs oday and ar no dscribd hr; our proposal is o link such blocks of daa o h nw blocks, TRAK and OOL. P ijk OOL Poinr OOL TRAK Poinr TRAK Cach Poinr Figur 1: Ass Th valu of linking h Cach block o h ass block is o allow an accss daa srucur o poin o all daa for a givn ass, sinc running mulipl hashs or r srucurs can significanly add o h compu im pr ass. If a hash srucur is usd o accss h ass, mchanisms may b ndd o rsolv hash conflics; w do no dscrib hs hr sinc hy ar wll known and byond h scop of h papr. Figur 2 shows how h wo doubly linkd liss TRAK and OOL would b arrangd. Ths wo liss should nvr shar an ass. Each of hs wo liss would mainain poinrs o hir had and ail blocks. Boh of hs liss would b sord in h ordr of h im h las rqus was sn for ha spcific ass. Asss would b rmovd from ach of hs liss basd on h LRU policy as dscribd in h algorihms lar. Each block in h lis would b conncd o h ass block via a bi-dircional poinr. Th lis of Cach blocks, which is no shown in Figur 2, would hav asss which ar a subs of h TRAK lis. Blow ar algorihms ha show mhods o add nw asss using h TRAK, OOL and Cach liss. W do no dscrib how asss ar addd or dld in T ijk Cach (8) 424

5 h Cach lis as hs would b don in ypical opraing cachs oday. Figur 2: Ass wih TRAK and OOL Liss Tabl 1: Paramrs usd wih HiFi Daa srucurs URL i Th URL associad wih ass i. URL TRAK S f Ass TRAK Poinr o Had of TRAK Lis URL OOL TRAK_siz TRAK_limi OOL_siz OOL_limi Ass TRAK Ass TRAK URL Accss Daa Srucur Poinr o Tail of TRAK Lis Ass OOL Poinr o Had of OOL Lis Ass OOL Ass OOL Poinr o Tail of OOL Lis A doubly linkd lis mad up of TRAK blocks whr ach block also conncs o h ass block via bi-dircional poinrs. A consan ha dfins h largs inr-arrival im of a givn ass ha will b allowd o b sord in h URL TRAK lis as a funcion of TC jk. A doubly linkd lis mad up of OOL blocks whr ach block also conncs o h ass block via bi-dircional poinrs. Th currn siz of h URL TRAK lis in rms of numbr of asss, iniializd o 0. Th maximum siz of h URL TRAK lis. This allows h opraor o s a limi on h mmory usd for TRAK lis. Th currn siz of h URL OOL lis in rms of numbrs of asss, iniializd o 0. Th maximum siz of h URL OOL lis. This allows h opraor o s a limi on h mmory usd for OOL lis. In addiion o h dfiniions in Tabl 1, P ijk, TS, T ijk and TC jk which ar usd in h algorihms blow ar as dfind in scion 3.1. Whn a nw ass rqus is sn, is ass block is accssd via an accss daa srucur as dscribd arlir. If an ass block xiss, i is drmind if h ass is in h URL TRAK lis or h URL OOL lis or nihr basd on h blocks aachd o h main ass block. Algorihms A, B or C ar run basd on his rsul. Algorihm C is also run if no ass block is aachd for h ass. In hs algorihms, w do no dfin opraions on any doublylinkd liss as hs ar wll known. Brifly, Algorihm A updas h inr-arrival im of h incoming ass and sors i in h URL TRAK lis. Algorihm B rmovs h ass from h URL OOL lis, sinc h scond occurrnc of h ass has occurrd and adds i o h URL TRAK lis if is inr-arrival im ms h rquird cririon. Algorihm C adds h nw ass o URL OOL lis. Algorihm A: If (URL i is in URL TRAK lis) bgin P ijk =TS Upda T ijk for ass i as pr quaion (3) If ( T ijk > S f TC jk ) bgin Rmov ass URL i from URL TRAK Lis TRAK_siz-- For h ass rmovd from URL TRAK lis rmov ass block if hr is no Cach block conncd ls Mov ass i o had of URL TRAK lis Algorihm B: If (URL i is in URL OOL lis) bgin P ijk =TS Rmov URL i from URL OOL lis Rmov OOL block from ass block i OOL_siz-- If (TS-P ijk < S f TC jk ) bgin If (TRAK_siz TRAK_limi) bgin Rmov on ass from ail of URL TRAK lis TRAK_siz-- For h ass rmovd from URL TRAK lis rmov is ass block if no Cach block is conncd o i Add TRAK block o ass block of ass i wih T ijk = TS-P ijk Insr ass i o had of URL TRAK lis TRAK_siz++ ls Rmov ass block for ass i Algorihm C: if (ass no in URL TRAK or URL OOS liss ) bgin If no ass block allocad for i, alloca a nw on P ijk =TS If (OOL_siz OOL_limi) bgin Rmov on ass from h ail of URL OOS lis OOL_siz-- Rmov ass block for his ass Insr ass i o had of URL OOL lis OOL_siz++ Whnvr asss ar rmovd from ihr of h doubly linkd liss URL TRAK or URL OOL, h poinrs of h wo nighbours of h rmovd ass ar s o poin o ach ohr o kp h lis coninuous. If h ass o b rmovd is a h had or h ail of h lis, h had or h ail poinr is s o poin o h nighbour nx o h rmovd ass and is poinr owards h rmovd ass is s o NULL. Whnvr asss ar addd o ihr lis a h had, h nw had poinr poins o h nw ass and h nw 425

6 ass is conncd by bi-dircional poinrs o h ass prviously a h had of h lis. 4. Analyical Modl for Cachs wih Filring In his scion w driv h hi-ras achivabl wih h LRU and filr policis via analyical mans. W dfin h filr policy as h long rm bhaviour of h HiFi algorihm wihou h approximaions du o EWMAs, h daa srucurs or quaions (5) and (6) and wih saic populariy of asss. Also all asss ar assumd o b h sam siz; his is o allow analyical racabiliy of h soluion. W do h analysis o compar h hi-ras achivabl wih h filring policy wih h LRU policy and opimal hi-ras. Th analysis is for a wo layr cach hirarchy which assums on dg cach and on parn cach fding raffic o h dg cach. Mor complx opologis can drivd from h sam analysis, w us his simpl opology for as of undrsanding. W do no complly show h drivaion of h hi-ra for a LRU basd cach for ihr h dg cach or h parn cach, for dails on his plas rfr o [7] and [15], whr [15] shows h muli-ir vrsion of h analysis drivd in [7]. Th following ar dfiniions of variabls usd in h analysis. W modify h arlir nomnclaur for simpliciy, h cach locaion j,k is droppd as only wo cachs ar sudid. C N M T i T C p i T F0 T F1 f P R F1 i0 T0 i1 μ L0 μ F0 μ F1 Tabl 2: Paramrs for Analysis of LRU and filr policis Numbr of asss ha can b sord in h cach, w us h sam for boh h dg and parn cachs. Toal numbr of asss in h library. Th ass numbr whr h inr-arrival im of ha ass is largr han h characrisic im of h filring algorihm T F a h dg cach. Th avrag of inr-arrival im of ass i a h dg cach. Th characrisic im of h dg cach wih a LRU policy. Probabiliy of a rqus for ass i among all rquss a h dg cach. Th characrisic im of h dg cach wih a filr policy. Th characrisic im of h parn cach wih a filr policy. Probabiliy disribuion funcion of h populariy of ass rquss a h dg cach. Rplacmn ra raio a h parn cach wih h filr algorihm. Th rqus ra for ass i a h dg cach. Th oal rqus ra for all asss a h dg cach. Th rqus ra for ass i from h dg cach o is parn. Th hi-ra for all asss a dg cach wih LRU policy. Th hi-ra for all asss a dg cach wih filr policy. Th hi-ra for all asss a parn cach wih filr policy. 4.1 LRU basd cachs From [7] h following quaion is drivd o drmin h characrisic im T C : Whr P i (<T C ) is h probabiliy ha h inr-arrival im of h nx rqus for ass i is lss han T C and N is larg. If w assum (9) Poisson inr-arrival ims and ha h avrag inr-arrival im of ass i is T i, hn: (10) Th rqus ra i is calculad basd on h rqus ra for all asss and h fracion of i for ass i is as follows: (11) Using h quaions (9) (10), (11) and ha T i is 1/ i0, w solv for T C numrically. From [7], w no ha h rqus ra of ass i by h dg cach from is parn cach is: (12) Using h valu of T C obaind from h arlir quaions and using quaion (12), w obain h hi-ra a h dg cach as: (13) 4.2 Filring Policy basd Cachs To driv h hi-ra wih h filr policy a h dg cach, w dfin a characrisic im wih h filr policy as T F0. W also assum ha h Mh ass will hav an avrag inr-arrival im which is jus largr han h filr valu T F0 and ha asss ar rankd from 1 o N basd on hir populariy, wih 1 bing h mos popular. Using quaion (11) for i0, w obain h following: (14) From h abov and using h invrs of h populariy funcion, w obain M as follows: (15) To obain T F0, w us h sam rasoning as in quaion (9), xcp ha h asss which can b sord in h cach ar a subs of h oal s of asss as asss wih inr-arrival im largr han T F0 (Mh ass and highr) would b rjcd. W driv h following assuming M is larg: (16) W solv for T F0 numrically in a similar mannr as h LRU vrsion basd on h abov quaion and quaions (15), (10) and (11). Onc T F0 and M ar known w can obain h hi-ra a h dg cach as: (17) Th Mh ass and highr will pass righ hrough h dg cach. In a wo layr hirarchy, h rqus ras o h scond layr of h hirarchy ar givn by quaion (11) for h LRU cas. For h cas wih h filr policy, h rqus ras ar as blow basd a singl dg cach: (18) Ths ras ar hn usd in quaions similar o h dg cach lvl o drmin h hi-ra, howvr, sinc, a h 2 nd ir, h 426

7 probabiliy disribuion funcion of h populariy of ass i is no longr coninuously incrasing as i incrass, w chang quaion (16) wih h following o sa ha his quaion is valid only if h inr-arrival im of ass i o h parn cach is lss han T F1, whr i1 is basd on quaion (18): (19) W us quaions (19), (18), (10) and ha T i1, h inr-arrival im of ass i a h parn cach, is 1/ i1 o solv for T F1 numrically. T F1 should b usd in an quaion similar o quaion (17) o drmin h hi-ra, howvr, sinc h probabiliy disribuion funcion for h populariy of ass i is no longr coninuously incrasing wih rspc o i, w obain h following for h hi-ra a h parn cach: (20) Th rplacmn ra is dfind as h fracion of is downsram raffic rqusd by h cach from is parn ha acually is sord in is cach. Th rplacmn ra wih h LRU policy is simpl. I is on minus h hi-ra a ha cach. Th rplacmn ra wih h filr policy is h ra of raffic rqusd from h upsram cach whos inr-arrival im is lss han h filr valu sinc only ha raffic is sord in h cach, for xampl h rplacmn ra a h parn lvl wih h filr policy is as follows: (21) 4.3 Analyical Prformanc Comparison Using h analyical modl w simulad a wo ir hirarchy of cachs o valua how wll h filr algorihm would prform agains h LRU policy in ypical opraor condiions as wll as agains a policy which assums ha h mos popular C asss ar always in h cach, which is opimal for saic populariy disribuions. H i R a s 100.0% 90.0% 80.0% 70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% 50/ / / / /4000 Cach Sizs (1s Tir/2nd Tir) in Numbrs of Asss LRU - Edg Figur 3: Hi-ra prformanc using analysis Filr/Hifi - Edg Opimal - Edg LRU - 2nd Tir Filr/Hifi - 2nd Tir Opimal - 2nd Tir W assum a ass library and a populariy funcion as Zipf wih alpha qual o 0.8. A wo layr cach hirarchy is usd wih a singl dg cach and a parn cach. Edg cach sizs usd wr 500, 1000 and 2000 o simula ypical dg cach sorag capaciis. Th cach siz usd a h parn cach was always wo ims h siz a h dg cach. Two addiional combinaions wr usd o simula h hirarchical caching ofn implmnd in commrcial cachs whr a small cach using RAM or mmory is followd by a largr disk cach. For his w usd 50 and 100 asss a h RAM cach and 1000 asss a h disk cach. From Figur 3, a comparison of h filr policy wih h LRU policy indicas ha for vry small cach sizs such as ha availabl in ypical RAM basd cachs, hi-ra can mor han doubl from h LRU policy o h filr policy. Wih ypical dg cach sizs, for xampl an dg cach siz of 1000 or 10% of h oal library capaciy, hi-ra a h dg cach can incras by 30% as funcion of h LRU hi-ra and h combind hi-ra for h wo ir hirarchy can incras by 20%; also as a funcion of h LRU hi-ra. A comparison of h filr policy wih h opimal policy shows ha h filr policy is wihin 1-2% of h opimal policy for h cach sizs sudid. Running h sam analysis wih a Zipf populariy funcion wih an alpha valu of 0.6, w no ha h advanag of h filr policy ovr h LRU policy significanly improvs. W also valuad h rplacmn ra diffrnc bwn h filr and LRU policis as a raio, for cachs sizs of 5% o 40% of h library siz; i varid bwn in favour of h filr policy. 5. SIMULATION METHODOLOGY Simulaion of onlin vido caching prsns addiional challngs sinc ach vido is mad up of many small chunks. Th numbr of chunks, which would nd a discr vn in a simulaion, is prhaps 1000 or ims mor han a non-chunk basd simulaion, which maks a simulaion using a ral rac highly compu innsiv if hundrds of simulaions runs ar rquird o valua mulipl caching siuaions. In our simulaion runs, which w xplain lar, w ndd o hav ach run coninu for 35 days of simulaion im which would hav bn prohibiivly xpnsiv if ach chunk rquird a discr vn. W build a synhic simulaion nvironmn using saisics form ral racs. W mach h populariy curv of onlin vidos; h abandonmn ra onc a clin sars waching an onlin vido; h VQ ras and hir probabiliy of bing rqusd; h injcion ra of nw asss and h populariy dcay of asss o saisics obaind from ral racs. 5.1 Topology W simulad a wo layr caching hirarchy wihin a singl dg cach. Th cach is spli ino a RAM cach and 4 disk cachs, wih ach cach opraing is own vicion policy. Th slcion of a disk for a givn ass was basd on a hash of is URL. Many ral cachs opra wih his kind of archicur, for xampl ATS [9]. W simulad wo such cachs fding ino a highr layr cach; howvr w did no modl an addiional RAM cach a h highr layr cach as i will likly no achiv a significan hi-ra. Th siz of h highr layr cach was always wo ims h siz of h dg cach. 5.2 Modling Library Dynamics W modl mporal localiy in h sram by injcing nw asss on a rgular basis and dcaying hir populariy. As rpord in [2], saisics from ral racs show ha h voluion of populariy of an ass is govrnd by a dcaying procss. An ass i xprincs on h firs day of is lifcycl an iniial rqus ra, which dcays xponnially wih ra on h subsqun days. 427

8 (22) During an arbirary obsrvaion window W saring a im τ L and ing a τ H, h oal numbr of rfrncs for any obsrvd ass in W is givn by summing up h abov ovr W: (23) In a saic modl, ass populariy is ypically dscribd by h mpirical disribuion of ass rfrnc couns obsrvd ovr a givn and larg W. I has bn shown ha ass populariy for onlin can b approximad sufficinly accuraly wih a Zipf disribuion [8]. Givn an mpirical populariy disribuion (or is approximaion), w can xrac h numbr of rfrncs for any ass i and using powr sris xpansion w driv h following xprssion for h iniial numbr of rquss: (24) To simplify h modl, w nglc non-saionary ffcs such as asss ingsd bfor h bginning or a h of W Modling Ass Lifcycls W simula wo yps of asss, movis and TV shows. All asss ar of 60 minus lngh and cachs. Th cach a h scond ir was always s o hold wo ims h numbr of asss as h laf cachs. W injc asss for 750 TV shows vry day and asss for 1250 movis vry wk, which oals o 7000 asss pr wk wih a shows-o-movis raio of 4.2:1. W choos h xponnial populariy dcay ras for all movis uniformly disribud in h rang [0.05, 0.2] and for h TV shows uniformly disribud in h rang [0.3, 0.5], which sm rasonabl valus basd on h findings rpord in [2] and obsrvaions from our own daa ss Modling Onlin Vido W modl arly usr abandonmn, which can occur wih onlin vido by spliing ach ass ino fiv pars whr h usr can abandon waching h ass afr any of hs pars. W usd abandonmn ras of 55, 5, 5, 5 and 30 prcn afr ach on of h fiv pars basd on h saisics in [25]. W modld four VQ lvls for adapiv sraming vido a 4.5, 3, 1.5 and 0.75 Mbps. Th rlaiv prcnags of h clin rqusing ach of h abov VQ lvls was s o 70, 15, 10 and 5 prcn rspcivly basd on our own daa ss. Boh of hs wo ffcs oghr add significan variaion in h siz of asss rqusd by h clin HiFi Paramrs W sima h bs valus for h EWMA wighs w TC and w IA by considring h marginal ass in h cach, ha is h las popular ass xpcd o b in h cach. This ass would hav an inr-arrival im of approximaly TC jk. W wan o mak sur ha w hav an accura sima of is inr-arrival im a las by h im h ass s populariy has halvd. W assum A as h dcay ra of h marginal ass in days. Th dcay ra of h avrag ass is h avrag of h wo kinds of asss movis (avrag dcay ra 0.125) and TV shows (avrag dcay ra 0.4) which coms o 0.347, using h raio bwn h wo mniond arlir. Using h abov w driv h w IA as: (25) Whr h valu of TC jk is assumd o b in days. W us a valu which is 10 ims lowr for w TC as TC jk variaion is vry low. W hn did a snsiiviy analysis of boh of hs valus; varying w IA by a facor of 4 ihr way did no produc a chang in any of h hi-ras by mor han 1% and changing w TC by a facor of 10 ihr way did no produc a chang in hi-ras by mor han 0.1%. For sing h gnl slop paramr GS, w s i so ha h valu of h characrisic im TC jk would doubl in a 24 hour priod, if i is no rs by h las vicion im from h cach. 5.3 Ohr Caching Algorihms Simulad W compar h HiFi algorihm o h prformanc of h LRU, GDSF and LCD algorihms. W simula GDSF as i is on of mos popular algorihms usd in oday s opraing cachs ohr han LRU [9]. W also simulad h LCD algorihm, which prformd h bs amongs hirarchical algorihms [17]. 6. RESULTS AND DISCUSSION For h simulaion rsuls, w driv h by hi ra and h rplacmn ra, which is dfind as h prcnag of incoming raffic a a givn cach ha lads o a rplacmn in is cach. W also discuss cach hroughpu, which is h maximum raffic a givn cach can srv. 6.1 Simulaion Sup W buil a simulaion nvironmn according o h arlir scion and ran an iniial simulaion wih all h diffrn algorihms for 35 days wih an avrag rqus ra of 130,000 rquss pr day a ach laf cach. Using h VQ lvls, probabiliis and arly abandonmn ras mniond in scion 5.2.2, his corrsponds o 10.3 Gbps as h avrag cach hroughpu. W sar h simulaion wih an mpy library and coninuously incras h library siz ovr his priod by injcing nw asss as dscribd in scion 5.2. W obsrvd rlaivly sabl hi-ras afr 7 days, which indicas ha h ffciv library siz had approximaly bcom a saionary procss. This is rasonabl sinc a his poin in im h arlir injcd asss produc vry fw rquss as hir populariy dcays down o ngligibl lvls. Thus, w rpor all of h simulaion saisics bwn h 7h day and h 35h day of simulaions. Using h dcay ras from scion 5.2.1, and assuming ha TV asss dcay o ngligibl lvls in 7 days (using h 40% dcay ra, hy dcay o lss han 2% of hir iniial valu), w sima h numbr of aciv asss in h library rang from 6500 o bwn day 8 and day 35, wih an avrag of 9000 asss. Wih his ffciv siz, ass injcion ras as in scion corrspond o approximaly 10% nw asss vry day. 6.2 Rsuls Using a 50 ass RAM cach and ass disk cachs (sizs basd on highs VQ lvl only), w obaind h by hi-ras shown in Figur 4 for h dg cach. HiFi significanly ouprformd LRU a h RAM lvl by abou 80% o 200%. A h ovrall dg cach lvl HiFi improvd by hi-ras by abou 20-40% wih rspc o hir valus wih LRU. I is rmarkabl ha HiFi significanly ouprforms h LCD algorihm, vn hough LCD kps rack of all asss whras HiFi only racks a subs of asss. GDSF prformd h bs amongs h ohr algorihms for mos scnarios. W show by hi-ras wih diffrn cach sizs, boh a h RAM and ovrall dg cach lvls in Figur 5, using a Zipf alpha 428

9 valu of 0.8. By hi-ras d o b vry similar o hi-ras in rms of raios bwn h diffrn policis, bu slighly highr. 70% improvmn in h composi rplacmn in all h diffrn scnarios shown in Figurs 4 and % H i R a s 60% 50% 40% 30% 20% 10% LRU-RAM GDSF-RAM LCD-RAM Hifi-RAM LRU-Edg GDSF-Edg LCD-Edg Hifi-Edg R p l a c m n R a s 180% 160% 140% 120% 100% 80% 60% 40% 20% LRU-RAM LRU-Disk LRU-Comp Hifi-RAM Hifi-Disk Hifi-Comp 0% % Zipf Alpha Paramr Zipf Alpha Paramr Figur 4: By hi-ras wih diffrn Zipf alpha valus Th improvmn in by hi-ra bwn h LRU and HiFi policis was bwn 24% (1000 ass dg cach) o 4.5% (4000 ass dg cach). In h sam s of simulaions; h by hi-ra diffrnc bwn h LRU and HiFi policis for h combind cach hirarchy rangd bwn 20% (1000 asss) down o 2% (4000 asss). H i R a s 80.0% 70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% 50/ / / /4000 Cachs Sizs (RAM/Toal) - Numbrs of Asss Figur 5: By hi-ras wih diffrn cach sizs LRU-RAM GDSF-RAM LCD-RAM Hifi-RAM LRU-Edg GDSF-Edg LCD-Edg Hifi-Edg W rpor h rplacmn ras a h boh RAM and disk lvls in Figur 6, which uss h sam s of assumpions as in Figur 4. W no ha h rplacmn ra diffrnc bwn HiFi and LRU a h RAM lvl is bwn 35 and 24 ims and a h disk lvl bwn 7 and 8 ims. W calcula h composi rplacmn ra for h nir cach, including h RAM as follows: (26) Whr RR rprsns rplacmn ra and BHR, by hi-ra. W includ h rplacmn ra a h RAM lvl in h composi lvl sinc mos cachs o copy cach conns in h RAM on disk o mak sur h cach conns ar availabl in cas of a rsar. Figur 6 also shows h composi rplacmn ra which shows a diffrnc bwn HiFi and LRU policis a a 14 o 15 ims improvmn. W found a las a 10 ims Figur 6: Rplacmn ras wih diffrn Zipf alpha valus 6.3 Comparison o Opimal Hi-ras W simulad Blady s MIN (B-MIN) [3] algorihm for comparison agains opimal hi-ras. Howvr, B-MIN is no dfind for variabl sizs asss, so w ran h simulaion wihou VQ lvls, wih h sam s of assumpions as in Figur 4. W usd a oal of 2000 ass disk cach and a 50 ass RAM cach, h rsuls of which ar shown in Tabl 3 as a funcion of Zipf alpha valus. Tabl 3: Comparison o Blady s MIN RAM Edg Cach LRU HiFi B-MIN LRU HiFi B-MIN 0.6 4% 12% 20% 56.8% 64.8% 72.2% 0.7 6% 17% 26% 62.4% 69.3% 75.8% % 25% 33% 68.0% 73.8% 79.8% % 33% 41% 74.0% 78.6% 83.6% 6.4 Discussion Boh h improvd RAM hi-ra and h rducd rplacmn ra rduc disk inpu-oupu, which is ofn h bolnck in mos cachs. In ordr o obain a rough sima of h impac of hs facors on h hroughpu of h cach, w assum h following rlaiv hroughpu ras for a ypical cach. From our xprinc hs numbrs ar fairly rprsnaiv for a cach wih abou 20 mchanical disks. Ths numbrs ar likly o chang for diffrn cachs, for xampls cachs wih mor disks or cachs wih SSD disks will likly show a highr hroughpu for 100% disk accss. Scnario Tabl 4: Esimas for Cach Throughpu 100% RAM hi all asss ar assumd availabl in RAM and sn o clin 100% disk hi all asss ar fchd from local disk and sn o clin 100% miss disk wri all asss ar obaind from h parn cach and sn o h clin and all asss ar insrd ino h local disk cach as pr LRU policy 100% miss no disk wri all asss ar obaind from h parn cach bu all asss ar sn via RAM o clin wihou vr wriing o local disk as pr HiFi policy whn h ass fails h characrisic im chck Esimad Throughpu X 0.4X 0.25X 0.35X 429

10 W usd h abov numbrs and h hi-ras and rplacmn ras rpord in h prvious scion o sima h hroughpu diffrnc bwn a cach wih HiFi a h RAM and disk layrs and a cach wih LRU in h sam layrs. For Zipf valus of 0.7, 0.8, 0.9; a 50 ass RAM cach and a 1000 ass oal disk cach, w sima h improvmn in cach hroughpu du o HiFi o b 75%, 65% and 51% from a LRU basd cach rspcivly using linar inrpolaion for mixs of RAM hi prcnag, cach hi prcnag and miss prcnag. For h 4000 ass disk cach scnario wih a Zipf valu of 0.8, his numbr drops o 26%. Th major conribuor o h hroughpu improvmn is h improvd RAM hi-ra whn h hi-ra s o b high and rducion of disk wris, whn h hi-ra s o b low. W implmnd HiFi on som of our cachs wih mchanical drivs and wr abl o obsrv a subsanially highr hroughpu improvmn han h numbrs mniond abov in h sam s of scnarios. W no ha cach hroughpu has a dirc invrs rlaionship o h amoun of caching hardwar o b dployd. HiFi also improvd ovrall cach by hi-ra a h firs ir ovr LRU basd cachs. Our simulaions show his raio o b bwn 24% o 4.5% in various scnarios as dscribd in scion 6.2; which can sav on origin coss or highr ir cach hardwar coss as wll as nwork coss. Origin coss o b significanly highr han cach srvr coss. Th subsanial rducion in h rplacmn ra of 10 ims or mor can rduc SSD coss, if hy ar usd for sorag. SSDs ar ypically ihr SLC (Singl Lvl Cll) or MLC (Muli Lvl Cll), whr h SLC basd SSDs hav abou 10 ims h lifim [4] of MLC basd SSDs and ar approximaly wo or hr ims h cos. Th rducion in rplacmn ra may allow h us of MLC-basd SSDs insad of SLC for a similar lvl of lifim wri prformanc. In [6], h auhors show a hr o four ims rducion in disk failur ras du o a 3 ims rducion in usag of mchanical disks which also indicas a ponial rliabiliy improvmn in such disks wih rducd disk inpu-oupu. 7. CONCLUSIONS AND FUTURE WORK Many opraional cachs oday sill us h LRU policy dspi almos 20 yars of caching rsarch on improvd caching policis. Our rsuls indica ha HiFi can allow such cachs o opra nar h opimal hi-ra wihou h prformanc dgradaion ha coms wih policis ha hav radiionally bn ampd for his purpos. Rahr, wih HiFi, a vry significan hroughpu improvmn can b achivd, which lads o a similar rducion in cach hardwar coss. W in o horoughly s HiFi wih h various yps of workloads and condiions found in our opraor dploymns and also plan o sudy a cos-basd variaion of h algorihm. W also plan o s HiFi wih gnral Inrn raffic. 8. REFERENCES [1] Anirban Kan Shah and Mira Dhruv Maani. An O(1) algorihm for implmning h lfu cach vicion schm. Tchnical rpor, hp://dhruvbird.com/lfu.pdf [2] Ahula Balachandran, Vyas Skar, Adiya Aklla, and Srinivasan Sshan, "Analyzing h Ponial Bnfis of CDN Augmnaion Sragis for Inrn Vido Workloads," in Proc. IMC, Nw York, NY, USA, 2013, pp [3] Blady, Laszlo A. "A sudy of rplacmn algorihms for a virualsorag compur." 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