calable O-emad treamig of No-Liear edia Yaig Zhao erek Eager eartmet of Comuter ciece Uiversity of askatchewa askatoo, K 7N 5A9, Caada zhao,eager@cs.usask.ca ary K. Vero Comuter cieces eartmet Uiversity of Wiscosi-adiso adiso, WI 5376, UA vero@cs.wisc.edu Abstract A covetioal video file cotais a sigle temorally-ordered sequece of video frames. Cliets requestig o-demad streamig of such a file receive (all or itervals of) the same cotet. For oular files that receive may requests durig a file layback time, scalable streamig rotocols based o multicast or broadcast have bee devised. uch rotocols require server ad etwork badwidth that grow much slower tha liearly with the file request rate. This aer cosiders o-liear video cotet i which there are arallel sequeces of frames. Cliets dyamically select which brach of the video they wish to follow, sufficietly ahead of each brach oit so as to allow the video to be delivered without jitter. A examle might be choose-your-ow-edig movies. With traditioal scalable delivery architectures such as movie theaters or TV broadcastig, such ersoalizatio of the delivered video cotet is very difficult or imossible. It becomes feasible, i ricile at least, whe the video is streamed to idividual cliets over a etwork. This aer aalyzes the miimal server badwidth requiremets, ad rooses ad evaluates ractical scalable delivery rotocols, for o-demad streamig of oliear media. I. INTROUCTION A covetioal video file cotais a sigle temorallyordered sequece of video frames. Cliets that request the same file receive ecodigs of (all or itervals of) the same frames. We hyothesize here that geeralizig this structure to that of a tree or grah, so as to allow arallel sequeces of frames amog which cliets dyamically select durig layback, may eable ew streamig media alicatios, as well as erich existig oes. A examle is choose-your-owedig etertaimet videos, aalogous to the may chooseyour-ow-edig childre s books. For covetioal stored video, a umber of scalable streamig rotocols based o (IP or alicatio level) multicast or broadcast have bee develoed. uch rotocols require server ad etwork badwidth that grow much slower tha liearly with the file request rate. These iclude immediate service rotocols such as atchig 3], 7], 9] ad hierarchical stream mergig 5], as well as eriodic broadcast rotocols 1], 6], 8], 1] 1], 16]. I the immediate service rotocols, a ew stream is allocated for each icomig cliet request, ad This work was artially suorted by the Natural cieces ad Egieerig Research Coucil of Caada, ad by the Natioal ciece Foudatio uder grats ANI-11781 ad EIA-17857. To aear i Proc. IEEE Ifocom 4, Hog Kog, arch 4. streams servig closely saced requests for the same file are dyamically merged by havig cliets also liste to oe or more earlier streams to receive ad buffer data that they will eed to lay back i the future. I eriodic broadcast rotocols, the video file is segmeted, ad each segmet is reeatedly broadcast/multicast o oe of a umber of chaels (e.g., IP multicast grous) accordig to some rotocoldeedet trasmissio schedule. Ulike with the immediate service rotocols, cliets must wait to begi layback, with the legth of the waitig eriod deedet o the duratio of a trasmissio of the iitial segmet. For whole file layback requests, the best of the immediate service rotocols use server badwidth that grows logarithmically with the file request rate, while the best of the eriodic broadcast rotocols have startu delay that decreases exoetially with the (fixed) server badwidth allotted to the file. This aer first exlores the otetial badwidth savigs from usig scalable, multicast-based streamig techiques for o-demad delivery of o-liear stored video. As the diversity i the data each cliet receives icreases, the otetial beefits of multicast delivery ca be exected to dimiish. A basic questio is whether, or uder what coditios, the otetial beefits become egligible i this cotext. This questio is addressed through the develomet of tight lower bouds o the server badwidth required to suort a give file request rate ad cliet start-u delay, for o-liear media files with varyig ath diversity. Our results idicate that the otetial badwidth savigs ca be substatial, eve for videos with high ath diversity. calable streamig rotocols achieve badwidth reductios by trasmittig video file data to multile cliets. For the shared trasmissios to be ossible, at least some cliets receive data ahead of whe it is eeded for layback, bufferig it i memory or o disk util its layback oit. With oliear video, however, trasmittig data ahead of whe it is eeded is comlicated by ucertaity regardig which brach a cliet will follow at each brach oit. There is a tradeoff betwee receivig data that the cliet might ot eed, ad the server badwidth reductio arisig from receivig (eeded) data ahead of its layback oit, so as to be able to share the trasmissio with other cliets. We ivestigate various oits i this tradeoff usig tight lower bouds o the server bad-
width required for various classes of rotocols. ome of the rotocol classes cosidered make use of advace kowledge of which brach a cliet will likely follow at each brach oit. We cosider both the use of measured (over all cliets) brach choice frequecies, ad cliet-secific iformatio, as might result from re-declaratio of iteded cliet aths or from cliet classificatio. Our results show that fairly recise a riori iformatio regardig cliet ath selectio ca dramatically reduce server badwidth requiremets as well as the cliet data overhead of receivig data that is ever used. I the absece of such iformatio, strategies that restrict what data cliets will receive i advace of kowig whether or ot it will be eeded, based o how far ahead that data is i the video file rather tha more aroximate cliet ath redictios, ca greatly reduce the cliet data overhead at relatively small badwidth cost. Fially, usig isights derived from the bouds we desig ew immediate service ad eriodic broadcast rotocols for o-liear video, ad evaluate the badwidth savigs that they rovide. Withi each class of rotocols, variats are develoed that assume the extremes of either o a riori ath kowledge, or full kowledge. I geeral, as with our lower bouds, recise a riori iformatio regardig cliet ath selectio ca substatively reduce the server badwidth requiremets. The remaider of the aer is orgaized as follows. ectio II describes models for o-liear media. Tight lower bouds o the server badwidth required for a give file request rate ad cliet start-u delay, ad the corresodig cliet data overhead if o a riori cliet ath selectio iformatio is available, are derived i ectio III. ectio IV derives the server badwidth bouds ad associated cliet data overheads for various olicies that restrict the data that cliets receive ahead of whe it is eeded. ectio V resets ew stream mergig ad eriodic broadcast rotocols, ad comarative erformace results. Coclusios are give i ectio VI. II. NON-LINEAR EIA OEL A. No-Liear edia tructures The simlest iterestig structure for o-liear video is that of a height oe tree with root ode corresodig to a commo iitial ortio, ad child odes corresodig to multile ossible edig ortios. I a comlete ath layback of the video, the cliet lays the commo ortio lus oe of the edig ortios. If the desired variat of the edig ortio is chose sufficietly ahead of the ed of the commo iitial ortio (the brach oit), the comlete ath ca be layed without jitter. I the followig, excet whe stated otherwise, it is assumed that cliets make avigatio decisios soo eough to avoid jitter, but sufficietly close to the resective brach oit that the ga ca be eglected i our aalysis. A more geeral structure is a arbitrary tree, where each ode corresods to a ortio of the video, ad child odes corresod to variat subsequet ortios. A comlete ath layback would cosist of the commo root ortio, lus all other ortios o a ath u to ad icludig a leaf ode. This structure ca be further geeralized to a directed acyclic grah (i.e., aths ca coverge at shared ortios), or a geeral grah structure. I the latter case, the otio of a comlete ath layback may have o meaig; cliets simly start layback at some cliet-selected video ortio ad the grah liks determie the ossible subsequet ortios. The bouds i ectios III ad IV are develoed for tree structures, although the aalysis ca be geeralized. The immediate service rotocols develoed i ectio V.A are alicable to o-liear media havig a geeral grah structure, while our eriodic broadcast rotocols i ectio V.B are alicable to directed acyclic grahs i which the ath legths to ay video ortio with multile arets are idetical, ad to geeral tree structures. For clarity, however, we reset umerical results oly for balaced biary trees i which all video ortios have idetical layback time, ad assumig that each cliet request is for a comlete ath layback. We assume costat bit rate video. Geeralizatios for variable bit rate video ca be develoed usig similar aroaches as for liear media 13], 14], 18]. B. Cliet Brach electios A key issue cocers the relative frequecies with which cliets select amog alterative ortios of the video at brach oits. I the cotext of balaced biary tree structures, we have exlored several alterative oularity models. The model for which umerical results will be reseted assigs selectio robabilities to leaves accordig to a Zif distributio, as follows. First, the leaf that will be the most oular is chose radomly, ad assiged the corresodig robability. The, out of the remaiig leaves, a secod most oular is chose radomly, ad so o. Oce all of the leaves have bee give selectio robabilities, selectio robabilities for all iterior video ortios ca be comuted by workig u from the leaves. Other models that were cosidered iclude a model i which the leaves are assiged Zif-distributed selectio robabilities i order, with the leftmost leaf the most oular ad the rightmost the least oular, ad a model i which the selectio robabilities at each brach oit are Zif-distributed (secifically, for a brach oit with two braches, oe brach is selected with robability /3, ad the other with robability 1/3). Although these other models would aear to differ sigificatly from the chose model (i articular, they give more skewed selectio robabilities at the brach oits ear the root of the tree ad less skewed robabilities at those ear the leaves), they were foud to yield very similar results. C. A Examle Fig. 1 shows a samle o-liear video file structure. Each ortio of the video is deoted by a lie segmet, with brach oits deoted by solid black circles. As a tree structure with odes reresetig ortios of the video, the structure i Fig. 1 corresods to a balaced biary tree of height 3. I the figure each video ortio is labelled by its selectio robability, as comuted by choosig leaf selectio robabilities accordig to a Zif distributio, ad the workig u the tree. Also show
" " B # $.9.14 Fig. 1..5.56.41.46.37 1..1.44.18.6.61.74.18 Examle of a No-Liear edia tructure is the ath selected by a articular cliet, who made the most oular selectio at the first brach oit (followed i 56% of all cliet laybacks), ad who chose a comlete ath that is selected i 4.6% of all cliet laybacks.. erver Kowledge of Cliet Prefereces Of iterest are three cases: (1) o a riori kowledge is available of the likely ath through the video that a articular cliet will take, () oly the overall average selectio robabilities are kow, ad (3) more accurate cliet-secific ath redictio is ossible, as whe the revious behavior of cliets is measured, either idividually or i aggregate accordig to some cliet classificatio. I the secod case, the system might redict that the cliet will choose the most oular brach at each brach oit, i which case the cliet s choice is correctly redicted with robability equal to the (coditioal) selectio frequecy of the most oular brach. I the third case, we cosider i ectio IV.B a simle model of cliet-secific ath redictio accuracy i which sufficietly oular brach choices are always successfully redicted, ad the other, uoular brach choices are ever redicted. This aalytically tractable model has the key advatage, for biary tree structures, of coverig a sectrum from ath redictio i which oly choices of the most oular brach at each brach oit are successfully redicted (i.e., the same as if oly overall average selectio robabilities are emloyed), to fully accurate redictio i which all brach choices are successfully redicted, deedig o the quatificatio of sufficietly oular. Whe a icorrect redictio is made, it is assumed that the redictio is for each of the aths that could have bee redicted with robability roortioal to its relative oularity. III. POTENTIAL FOR CALABLE ELIVERY With uicast delivery, server ad etwork badwidth requiremets for o-demad streamig are liear i the cliet request rate. This sectio aalyzes the extet to which server badwidth requiremets might be reduced through use of multicast-based rotocols i the cotext of o-liear media, ad the associated cliet data overheads. ectio III.A defies TABLE I NOTATION FOR TREE-TRUCTURE NON-LINEAR EIA ymbol efiitio umber of ortios of the video file comlete ath layback time layback time of ortio (root umbered as ortio ) ortio relative start time ( ) robability the selected ath icludes ortio arameter of Zif distributio (oularity of th most oular item 1/ ) cliet request rate request rate for ortio ( )! average umber of cliet requests durig a layback time ( ) average umber of cliet requests for ortio durig time ( ) maximum cliet start-u delay required server badwidth lower boud, i uits of the layback data rate these erformace metrics ad outlies the aalysis aroach. I ectio III.B, a tight lower boud o the server badwidth requiremet is derived. ectio III.C derives the cliet data overhead required to achieve the server badwidth boud whe o a riori iformatio is available regardig cliet ath selectio. Classes of olicies that restrict the cliet data overhead are cosidered i ectio IV. A. etrics ad Aalysis Aroach The rimary erformace metric that is cosidered is the average server badwidth used for comlete ath laybacks of a sigle video file, for give cliet start-u delay ad request rate. Our aalysis ca be exteded to etwork badwidth i a similar fashio as for liear media 19]. Also of iterest is the average cliet data overhead, defied as the average amout of data a cliet receives from video ortios o differet aths tha that take by the cliet, ad therefore ot used, exressed i uits of the amout of video data o a comlete ath. Usig the otatio defied i Table I, our lower boud aalysis follows the same basic aroach as has bee used reviously for liear media ], 5], 6], 15]. For a liear media file, ad a arbitrary cliet request that arrives at time, the file data at each lay ositio # must be delivered o later tha time "%$'&($ #. If this data is multicast at time "%$)&($ #, the (at best) those cliets that request the file betwee time "*$+&,$ ad # ca receive the same " $&$ multicast. Assumig Poisso arrivals, the average time from # util the ext request for the file is -/.1. Therefore, the miimum frequecy of multicasts of the data at time offset # is -.43 &5$ -/.176, which yields a boud o required server badwidth, i uits of the layback data rate, of 859! ;:=<%>!?A@CB HJILK5I EGF?ONQP,R UT IWV%XZY This boud ca be geeralized to a broad class of o-poisso arrival rocesses, yieldig a similar result with differece bouded by a costat 5]. Bouds for o-liear media are derived below by alyig similar aalysis. (1)
Š Š B erver Badwidth 5 4 3 1 Portio Path No-Liear Liear 1 1 1 1 Fig.. Normalized Request Arrival Rate (N) erver Badwidth for No-Liear edia (balaced biary tree with height 3, = 1, = ) erver Badwidth 175 15 15 1 75 5 5 Portio Path No-Liear 1 3 4 5 6 7 8 9 1 Tree Height Fig. 3. Imact of Tree Height ( = 1, = 1, = ) B. iimum Required erver Badwidth erver badwidth is miimized whe a cliet listes to every multicast of data that it may eed i the future. Note that without a riori kowledge of cliet ath selectio, this requires that the cliet liste to ay multicast of data i the subtree below its curret lay oit, imlyig ossibly large cliet data overhead. With erfect a riori kowledge of cliet ath selectio, the cliet listes oly to all multicasts of data that it will actually use i the future. I either case, otig that the file data at a ositio # withi a video ortio \ is at (overall) lay ositio "^]_$ #, the above aalysis aroach yields the tight lower boud 8a`cb=`;d(e kl f `cgih=j? m io @ Bq HrILs ItK5I EGF? m NQP R IWV X Y io Tvu () B Fig. shows this boud as a fuctio of the ormalized request arrival rate w &, for immediate service ( = ) ad for a o-liear media file with a balaced biary tree structure of height 3 ad Zif-distributed leaf selectio robabilities as described i ectio II with Zif distributio arameter x = 1. (Alterative radom assigmets to leaves of the Zif selectio robabilities yield very similar results.) For comariso uroses, the figure also shows the boud for liear media from eq. 1, ad bouds for two aroaches i which delivery techiques for liear media are alied to o-liear media. I oe of these (ortio), each ortio of the o-liear media file is treated as a searate liear media file, yieldig a tight lower boud o required server badwidth of 8ryvz! > z NQP,R IWV%XZY?{m lo @tb H ILK5I EGF? m lo &~ & & ] T B Here, ad the terms for \*ƒ - admit the ossibility that with this aroach, a cliet selectio of video ortio \ & ] would be required to be made time rior to the ed I}V (3) of its aret ortio (or, alteratively, that there would be iterrutio i layback & ] U & ] of duratio ). For the results i the figure it is assumed that for all \. I the other aroach (ath), the cliet ath selectio is required to be kow a riori. Video data is relicated so that each comlete ath through the tree structure ca be stored as a searate file. For each cliet request, oe of these files is selected accordig to the ath selectio robabilities, ad delivered as if it were a ordiary liear media file. The corresodig tight lower boud o the required server badwidth is give by 8! y <? @ B ˆ HrICK5I? NQP R EGF ˆ IWV vx} (4) UT where Œ deotes the set of idices of the ortios of the video file that are leaves i the tree structure, ad where for otatioal coveiece it is assumed that each comlete ath has the same layback time. The key observatios from Fig. are that: (1) multicastbased delivery techiques for o-liear media have the otetial to yield large reductios i badwidth requiremets (ote that with uicast, the required server badwidth is w ), ad () techiques that exloit the articular o-liear structure, rather tha treatig each ortio or ath as a searate liear media file, have the greatest otetial. The otetial badwidth reductios from multicast-based delivery are deedet o the o-liear media structure. Fig. 3 shows the imact of icreasig the height of a balaced biary tree structure, for fixed ormalized request rate. As the height icreases, the umber of ortios of the video file icreases exoetially, as does the umber of ossible aths that cliets may select from. Furthermore, relative to the total legth of a ath the legth of each video ortio decreases; i.e., brach oits become more closely saced. Not surrisigly, the otetial beefits of multicast-based delivery decrease. (imilarly, these beefits also decrease whe the brachig factor is icreased at each brach oit, with fixed height, owig to the resultig icrease i the umber of aths.) However, eve with a height of 1 ad more tha
m T I m m a thousad ossible aths, multicast-based delivery still has the otetial for a order-of-magitude reductio i server badwidth, assumig immediate service ad the request rate cosidered i the figure. These otetial badwidth savigs are exlaied largely by the otetial for shared delivery of the video ortios with the highest selectio robabilities (i.e., those alog oular aths or ear the root). C. aximum Cliet ata Overhead Without a riori kowledge that would rule out some ath choices, achievig the lower boud of eq. requires that a cliet liste to ay multicast of data from a video ortio that (at the time of the multicast) could still be o the cliet s evetual ath. ice data is beig multicast at miimum frequecy, it is guarateed that the same data is ot multicast multile times durig the time that a cliet ca obtai it. Thus, o average, the amout of data received from each video ortio ot o the cliet s evetual ath is give by the rate at which data from that ortio is multicast, times the legth of the eriod over which the cliet ca obtai such multicasts. The latter quatity for a cliet that follows the ath to a leaf video ortio \ ad for a video ortio Ž that is ot o this ath (i.e., is ot \ or a acestor of \ ), is equal to the sum of the start-u delay & ad the layback duratios of all video ortios o the chose ath that are also o the ath to Ž. This yields a average cliet data overhead, i uits of the amout of video data o a comlete ath, of ˆ Š Qi HrI ; Q % q š NQP T%u i B IWV šœ ša where ž 3\^6 deotes the set of idices of those ortios that are ot ortio \ or a acestor of ortio \, ad žÿ3\% =Ž6 deotes the set of idices of those ortios that are acestors of both \ ad Ž. Fig. 4 shows the average cliet data overhead icurred to achieve the lower boud of eq. for balaced biary tree structures of various heights, immediate service, ad o a riori kowledge of cliet ath choices. Note that, for a give height tree, as the request rate icreases the average cliet data overhead iitially icreases ad the levels off sice the lower boud server badwidth for ortio Ž has fiite asymtote for all Ž ƒ-. imilarly, for fixed arrival rate, as the height icreases the average cliet data overhead also icreases. Fially, the data overhead whe cliets soo o all ortios that could still be o their evetual ath ca be sigificat, articularly whe the tree height is greater tha four ad the ormalized request rate is greater tha 1. IV. RETRICTE NOOP-AHEA Owig to cliet recetio rate ad/or buffer sace limitatios, the cliet data overheads show i Fig. 4 may be ifeasible. This sectio cosiders aroaches i which cliets soo less aggressively o multicasts from video ortios ahead of their curret lay oit, thus reducig this overhead. oo-ahead ca be restricted i at least two basic ways. First, as cosidered i ectio IV.A, restrictios may be Cliet ata Overhead 1 8 6 4 Height=1 Height=8 Height=6 Height=4 Height= 1 1 1 1 Fig. 4. N Cliet ata Overhead for Urestricted oo-ahead ( = 1, =, o a riori kowledge of cliet ath selectio) based o distace from the curret lay oit. ecod as cosidered i ectio IV.B, restrictios ca be based o (a) overall ath selectio robabilities, or (b) cliet-secific ath redictio, accordig to the ast behavior of that cliet, cliet classificatio, ad/or advace selectio by the cliet. A. istace-based Restricted oo-ahead A simle aroach that restricts soo-ahead based o distace is to oly soo o multicasts from the curret video ortio (but ahead of the curret lay oit), ad from all ortios followig the ext brach oit. 1 Thus, with this aroach, cliets soo o multicasts from each video ortio \ durig layback of that ortio, ad, if ot the iitial, root ortio (i.e., \ ), durig the layback of \ s aret i the tree structure. A tight lower boud o the required server badwidth for ay techique utilizig this aroach is give by 8 kl ;:? @CBG HrICKªI @ B EGF lo «<; i ILK5I EGF?ONQPŸR IWV%XWI NQP I}V lo «Bq v l± š (5) BG B where ²_3\^6 deotes the idex of the immediate acestor (aret) of \. Achievig this boud would icur a average cliet data overhead of io(«š <G Qi NQP IWV ;³4 Ql Bq v ± I}V š ša B where µ53 \ 6 deotes the set of idices of the sibligs of \ i the tree structure. Corresodig results ca be derived for aroaches i which cliets soo o trasmissios from future video ortios u to brach oits ahead, for some fixed ƒ -. 1 For clarity of resetatio, we assume here ad for the subsequet restricted soo-ahead aroaches, that rior to begiig layback, i the case of 5¹, cliets oly liste to multicasts from the iitial, root ortio of the video. The same aalysis aroach ca be emloyed with alterative assumtios.
T T T T B. Cliet Path Predictio Aroaches With skewed brach selectio robabilities, it may be ossible to substatially reduce the cliet data overhead, with oly a small cost i icreased server badwidth, by sooig o multicast trasmissios from oly the most oular ortio of the video followig the ext brach oit. The corresodig tight lower boud is give by 8! yvzyg:? @tb;?on!p R HrICK5I EGF I º @ B I ;º KªIEGF @tb IWV X I Gº I BG NQP½¼ I}V¾( º N!P <; Ql ICK5I EGF Bq» l± B IWV š where ad deote the set of idices of those ortios of the video file that are the most oular, or are ot the most oular, video ortios amog their sibligs, resectively (excludig the root ortio, which has o sibligs). Achievig this boud would icur a average cliet data overhead of º Š <; Ql NQP ½À Ql IWV À Ql B v l± šœ ša BGÁ l± where  3\^6 deotes the idex of the most oular siblig of video ortio \. Rather tha just sooig o trasmissios from the most oular video ortio after the ext brach oit, cliets could soo o trasmissios from all video ortios o the most oular ath from the curret ositio to a leaf. The corresodig tight lower boud is give by 8½Ã b à à h=ä Å!?ONQP R? @tbg B; HrICKªI EGF I º @ B I Gº KªIEGF @tb IWV IWV X I NQP ;º I N!P½¼ IWV¾Ë º qæç i EGF ItK5I GÈ É%Ê l± B B IWV š where ÌÍ3 \ 6 deotes the set of idices of acestors o the ath back towards the root from \ (ot icludig \ itself), u to ad icludig the first ortio that is ot the most oular amog its sibligs. (If there is o such ortio o this ath, the set icludes the idices of all acestors o the ath back to ad icludig the root.) Achievig this boud would icur a average cliet data overhead of º Š ¼ qæ_ Qi ¾ NQP GÎ <; i ÈrÏ ÉvÊ ± B Ï B I}V š š (6) (7) where Ð 3 ²_3 \ 6»6 deotes the set of idices of video ortios o the most oular ath dow to a leaf from (but ot icludig) the aret of ortio \. Cosider ow the case i which more accurate clietsecific ath redictio is ossible, ad cliets soo o multicasts from all video ortios o their redicted (rather tha the overall most oular) ath from the curret ositio to a leaf. Aalysis of this aroach requires a model of ath redictio accuracy. Here we use a very simle model i which brach choices with selectio frequecy (coditioal o reachig the resective brach oit) at least equal to a arameter Ñ are always successfully redicted, ad less oular brach choices are ever redicted. The corresodig tight lower boud is give by 8 à j giò!? @ BG?WNQP R HJItKªI EGF BG I Ó I ;Ó @tb @ B KªIEGF I}V X I N!P GÓ I NQPª¼ IWV¾Ë Ó ;ÔÕ Qi Q EGFItKªI ;È ÉqÖ i± B B IWV š where ad deote the set of idicies of those ortios of the video file whose coditioal selectio frequecy is at least Ñ, or less tha Ñ, resectively, ad ØÙ3\^6 deotes the set of idicies of acestors o the ath back towards the root from \ (ot icludig \ itself), u to ad icludig the first ortio that is a member of the set. (If there is o such ortio o this ath, the set icludes the idices of all acestors o the ath back to ad icludig the root.) Achievig this boud would icur a average cliet data overhead of Ó Š ¼ ÔÕ i ¾ 9 ˆ4 ³4 Qi i Ú Š 9 Û ˆ4 ³( i Š ;Î <; Ql 9 8 y >^:! where Œ53µ53\^6Ü6 deotes the set of idices of leaf video ortios i the collectio of subtrees rooted at sibligs of \ for which the ath from that siblig icludes oly video ortios i the set, Ð 3ݲ_3\^6cvÞÝ6 deotes the set of idices of video ortios o the ath dow to leaf ortio Þ begiig from (but ot icludig) the aret of \, ßáàqâvãÜä å5æ ]iç deotes the badwidth used for multicasts of video ortio Ž, as give by the term for video ortio Ž o the right-had side of eq. 8, ad where we have assumed that a icorrect ath redictio is for each of the aths that could have bee redicted with robability roortioal to its relative oularity. C. Policy Comarisos Figs. 5 ad 6 grah the badwidth exressios give above as fuctios of the request rate (for the same biary tree structure assumed for Fig. ), ad the tree height (for fixed request rate), resectively. Also show is the server badwidth for the aroach (exttwo) i which cliets soo o multicasts (8)
erver Badwidth 5 4 3 1 Portio Next Nexttwo Lower Boud erver Badwidth 5 4 3 1 Portio Poext Poath Pred (f=.35) Lower Boud 1 1 1 1 1 1 1 1 N N (a) istace-based Policies (b) Predictio-based Policies Fig. 5. Performace with Restricted oo-ahead (balaced biary tree with height 3, = 1, = ) erver Badwidth 175 15 15 1 75 5 5 Portio Next Nexttwo Lower Boud 1 3 4 5 6 7 8 9 1 Tree Height (a) istace-based Policies erver Badwidth 175 15 15 1 75 5 5 Portio Poext Poath Pred (f=.35) Lower Boud 1 3 4 5 6 7 8 9 1 Tree Height (b) Predictio-based Policies Fig. 6. Imact of Tree Height o Restricted oo-ahead Performace ( = 1, = 1, = ) from the curret video ortio lus from all ortios followig the ext ad ext two brach oits, which is derived similarly to eq. 5. For comariso uroses, the figures also show the server badwidth for urestricted sooig (i.e., the lower boud of eq. ), ad for the aroach i which each ortio is treated as a searate liear video file (ortio). Corresodig results for the cliet overhead are give i Figs. 7 ad 8. Cosider first the results for ortio, ext, exttwo, ad urestricted sooig. With ortio, cliets oly liste to multicasts of data from the video ortio curretly beig layed. ooig of multicasts of data from beyod the ext brach oit (ext) yields a large reductio i server badwidth. ooig farther ahead, as i exttwo, yields dimiishig returs. As see by the results i Fig. 6(a), for trees of low to moderate height exttwo has miimal required server badwidth fairly close to the lower boud of eq.. The results i Figs. 5(a), 6(a), 7, ad 8 show that the ext ad exttwo aroaches ca ofte achieve large reductios i average cliet data overhead comared to the urestricted sooig aroach, at fairly modest cost i server badwidth. The oext, oath, ad red (f=.35) aroaches use a riori iformatio regardig cliet ath selectio i a attemt to achieve a better tradeoff betwee server badwidth ad cliet overhead. Although oext ad oath achieve low cliet overhead, as see i Figs. 7 ad 8, they achieve oorer server badwidth scalability tha ext ad exttwo. These results show that very aroximate cliet ath redictio, such as occurs with oext ad oath at brach oits at which the brach selectio robabilities are ot highly skewed, is ot as effective i reducig server badwidth as is sooig o all multicasts of data that could be eeded soo, as i ext. I cotrast, the more accurate red (f=.35) aroach achieves lower cliet data overhead tha ext ad comarable server badwidth scalig. Fially, ote that the aroaches i which cliets soo o multicasts from all video ortios o a ath from the curret ositio to a leaf (oath ad red) become relatively more attractive with resect to their server badwidth usage, ad relatively less attractive with resect to cliet data overhead, for high tree heights. Hybrid aroaches may erform eve somewhat better uder some coditios. For examle, cosider a brach oit at which oe choice is highly oular ad the other is much less oular. Cliets could soo o multicasts from both of these video ortios (as i ext), while also redictig a
Cliet ata Overhead 1.6 1..8.4 Urestricted oo-ahead Nexttwo Next Poath Poext Pred (f=.35) 1 1 1 1 Fig. 7. N Cliet Overhead with Restricted oo-ahead (balaced biary tree with height 3, = 1, = ) Cliet ata Overhead 1.6 1..8.4 Urestricted oo-ahead Nexttwo Next Poath Poext Pred (f=.35) 1 3 4 5 6 7 8 9 1 Tree Height Fig. 8. Imact of Tree Height o Overhead ( = 1, = 1, = ) erver Badwidth 6 5 4 3 1 Portio Poath Pred (73% i set F) Next Urestricted oo-ahead Cliet ata Overhead 1.6 1..8.4 Urestricted oo-ahead Next Poath Pred (73% i set F).1 1 1.1 1 1 Parameter of Zif istributio Parameter of Zif istributio (a) erver Badwidth (b) Cliet Overhead Fig. 9. esitivity to kewess i electio Probabilities (balaced biary tree with height 3, = 1, = ) ath that icludes the highly oular choice ad sooig o multicasts from subsequet video ortios (as i oath or red). Prelimiary ivestigatios of a hybrid of the ext ad red aroaches cofirm this ituitio. Fig. 9 shows the sesitivity of the above results to skewess i the leaf selectio robabilities, secifically to the Zif arameter x. (Curves for exttwo ad oext have bee omitted but have similar form.) For red, the arameter Ñ has bee varied so that the ercetage of video ortios i the set is costat, equal to that with Ñ 4è é ê ad x -. Thus, for red (as well as for oath), the umber of relatively oular video ortios whose selectio is successfully redicted remais costat as x varies. Note that there is relatively little variatio i the required server badwidth ad cliet data overhead for each aroach for xaë - (i.e., for o skew to moderately high skew). As x icreases beyod oe, the server badwidth ad cliet data overhead for each aroach decrease substatially. A key coclusio is that the simle ext aroach, ad the red aroach with correct ath redictios for at least 75% of the video ortios, achieve a attractive trade-off betwee required server badwidth ad cliet data overhead, over a wide rage of x values. V. CALABLE ELIVERY PROTOCOL A. Hierarchical tream ergig Hierarchical stream mergig (H) rotocols 5], as alied to liear media, start a ew trasmissio of the media file for each cliet request. I the simlest tye of H, each cliet also listes to the closest active earlier stream, so that its ow stream ca termiate after trasmittig the data that was missed i the earlier stream. At that oit, the cliets associated with the two streams are said to be merged ito a sigle grou, which ca the go o to merge with other grous. Extedig H to o-liear media requires a more dyamic otio of cliet grou, sice cliets that merge while listeig to oe video ortio may take differet aths at the ext brach oit, thus slittig the grou. Also, a more comlex olicy may be required for determiig what stream a cliet listes to, i the case where the closest earlier stream is beyod the ext brach oit. It would seem that, i this case, the cliet should liste to the closest earlier stream curretly deliverig data from the ath that the cliet will select, should such a stream exist ad should the brach choice be kow or accurately redicted.
E1 B1 Chael 1 E1 Chael E1 B1 E B E E3 B3 E Chael 3a B E3 E4 Fig. 1. E4 E5 E6 E7 OPB-KP egmet Partitioig for a Examle edia tructure ( label is for start of media, Bi labels are for brach oits, Ei labels are for segmet ed oits, dashed lies idicate segmet boudaries, ì = 3, í =, î = 1) E3 Chael 3b B3 Fig. 11. OPB-KP Chaels for tructure of Fig. 1 (shaded areas are listeig eriods of examle cliet, ì = 3, í =, î = 1) E5 E6 E7 The results from ectio IV suggest that usig overall ath selectio robabilities to guide which earlier stream a cliet listes to whe the closest earlier stream has ast the ext brach oit may ot be the best strategy. This ituitio is cofirmed by simulatio results showig that listeig to the closest earlier stream (o or ast the same video ortio, regardless of which brach it may be o if beyod a brach oit) yields slightly better erformace tha listeig to the closest stream o the most oular brach 17]. ectio V.C resets simulatio results for both this H-Ukow Path (H-UP) rotocol i which cliets liste to the closest earlier stream, ad for H-Kow Path (H-KP) i which it is assumed that recise cliet-secific ath redictio is ossible, ad thus cliets ca liste to the closest earlier stream deliverig data from the ath they will select. Note that with H-KP, cliets belogig to the same grou may be listeig to differet earlier streams. With both rotocols, a grou may slit as the cliets withi a grou reach a brach oit, i which case the server will eed to start additioal stream(s) so that there is oe stream er ath followed. These characteristics also comlicate mergig behavior. I the simulatios from which results are reseted here, it is assumed that whe a cliet or grou of cliets merges with a earlier grou, all cliets i the earlier grou restart listeig to earlier stream(s), as i H for liear media. Other otios are ivestigated i 17]. B. Otimized Periodic Broadcast The eriodic broadcast rotocols that we develo here for o-liear media are based o the otimized eriodic broadcast (OPB) rotocols described i 1]. I these rotocols, as alied to liear media, the media file is artitioed ito ï segmets, with each segmet beig reeatedly multicast o a searate chael at rate ð. Cliets are assumed able to simultaeously liste to a maximum of  chaels. The segmet size rogressio is comuted such that each segmet is received just i time for layback if cliets begi listeig to the  chaels deliverig the first  segmets immediately, begi listeig to the chael for segmet ( ñƒùâ ) immediately after fully receivig segmet ÕòOÂ, ad begi layback after recetio of the first segmet is comlete. For the case i which cliet ath selectio is kow a riori, we roose a variat of OPB called OBP-Kow Path (OPB-KP). Each comlete ath through the o-liear media file is artitioed usig the same segmet size rogressio as i OBP for liear files. hared ortios of aths share the corresodig segmets. (We assume here that if the file has a directed acyclic grah structure, the the ath legths to ay video ortio with multile arets are idetical.) If a segmet crosses a brach oit, the data from each media ortio after the brach oit is delivered o a searate sub-chael, each at rate ð. Thus, for such a segmet, the server will reeatedly first trasmit the data from before the brach oit (at rate ð ), ad the trasmit the data from after the brach oit (at total rate ð times the umber of ortios after the brach oit). Each cliet listes to the chaels ad sub-chaels aroriate to its ath. Fig. 11 shows the chaels used i the OPB-KP rotocol for the examle o-liear video structure show i Fig. 1, assumig each ath is artitioed ito three segmets (ï = 3), cliets liste to two chaels cocurretly ( = ), ad segmets are trasmitted at the layback data rate (ð = 1). Also show are the eriods durig which a examle cliet listes to the trasmissios o each chael, assumig the cliet request arrives at the oit idicated ad that the cliet takes the ath show i Fig. 1. As show by the results i ectio V.C, if it is assumed that the server ca detect if there are ay listeers o a chael (or sub-chael), ad sto trasmittig o the chael if ot, this scheme is efficiet. For the case i which cliet ath selectio decisios are kow oly whe they are made at the resective brach oits, our key isight is that eriodic broadcast is still feasible as log as ay segmet that a cliet begis to dowload rior to a brach oit, ad that icludes data from after the brach oit, icludes the resective data from all of the braches.
Fig. 1. E8 E6 E4 E9 E E1 E3 E5 E1 E7 E11 E1 E13 E14 E15 OPB-UP egmet Partitioig for a Examle edia tructure ( label is for start of media, Ei labels are for segmet ed oits, dashed lies idicate segmet boudaries, ì = 6, í =, î = 1) E1 Chael 1 E1 E/3 Chael E/3 E4/5 Chael 3 E4/5 E6/7 Chael 4 E6 E8/9 Chael 5a E7 E1/11 Chael 5b E8/9 E1/E13 Chael 6a E1/11 E14/15 Chael 6b Fig. 13. OPB-UP Chaels for tructure of Fig. 1 (shaded areas are listeig eriods of examle cliet, stried areas idicate multilexed trasmissios, ì = 6, í =, î = 1) ecifically, suose that betwee whe a cliet begis to liste to the trasmissio of a articular segmet ad the begiig of layback of that segmet, video layback does ot cross a brach oit. If segmet itself also does ot cross a brach oit, the it must be art of the same video ortio that was beig layed back durig its recetio. If, o the other had, segmet does cross a brach oit, the it must iclude some of the video ortio rior to the brach oit (as determied by the segmet startig ositio), lus a fractio of each video ortio after the brach oit (as determied by the segmet edig ositio). Note that the layback duratio of such a segmet will be less tha what its size i bytes (ad corresodig trasmissio time) would suggest, sice the cliet will layback oly the data o its chose ath. uose ow that betwee whe a cliet begis to liste to the trasmissio of a segmet ad the begiig of layback of that segmet, video layback does cross a brach oit. I this case, the etire segmet multilexes data from multile aths, as the segmet begis after the brach oit ad it is ukow which brach a cliet will take. Fig. 13 shows the chaels used i this OBP-Ukow Path (OPB-UP) rotocol for the examle o-liear video structure show i Fig. 1, assumig each ath is artitioed ito six segmets (ï = 6), cliets liste to two chaels cocurretly (Â = ), ad segmets are trasmitted at the layback data rate (ð = 1). Also show are the eriods durig which a examle cliet listes to the trasmissios o each chael, assumig the cliet request arrives at the oit idicated i the figure ad that the cliet takes the ath show i Fig. 1. Feasible segmet sizes for OPB-UP ca be comuted usig the algorithm outlied i Fig. 14. Although this algorithm is desiged for balaced biary trees, it ca be exteded for more geeral tyes of media structures. Here Þó deotes the layback duratio of segmet, ôçó deotes the time whe a cliet begis recetio of the segmet, measured relative to the start of the video file layback, õ/ó deotes the latest time by which a cliet ca ed recetio of the segmet, measured relative to the start of video layback (also equal to the layback oit corresodig to the begiig of the segmet), ö ó deotes the segmet trasmissio time whe the segmet is of maximal legth, ad ó deotes the layback oit corresodig to the ed of the segmet i the case i which the segmet does ot ecouter a brach oit. The outer loo attemts to fid the start-u delay (trasmissio time of the first segmet) such that the cumulative legth of ï segmets (where ï is give as a iut) matches the legth of a comlete ath. The algorithm makes the simlifyig restrictio that o segmet ca have a multilexig level of more tha two (i.e., iclude data from more tha two aths), ad the assumtio that the first segmet does ot cross ay brach oits. It further assumes that brach oits are ever sufficietly close together that a zero legth is comuted for a segmet (as would occur i case. whe the brach oit ß is at õ/ó ), although it could be exteded to hadle this case by simly delayig begiig recetio of the segmet util after the ext brach choice has bee made. uch delays could be more geerally beeficial, as well, but the algorithm i Fig. 14 simly assumes that a cliet begis recetio of a ew segmet (if ay remai) immediately after recetio of a revious segmet comletes. The desig of otimal eriodic broadcast rotocols for various tyes of oliear media structures is left for future work. C. Performace Comarisos Figs. 15, 16, ad 17 show the server badwidth used by the H ad OPB rotocols for o-liear media streamig, together with the aalytic lower boud from eq.. H results are from simulatio. The results for the OPB variats are obtaied uder the assumtio that trasmissio o a chael is stoed wheever o cliet is listeig to that chael. (The robability that o cliet is listeig to a chael ca be easily comuted uder the assumtio of Poisso request arrivals, which are also assumed i the simulatio of H.) For H-KP ad OPB-KP, ath redictio is assumed to be erfect. For H, imerfect ath redictio would yield results itermediate betwee the results for H-UP ad H-KP. For OPB-KP, a error i ath redictio would be more difficult to recover from. All data is received rior to
Fuctio øjù;úcûýüû üýýcþçÿ ú 1. For (ü ; ü ; ü ++). ü^ÿcú! 3. "*ý$#%'& û)( *(+, vü.-/(ÿ 1' ú 34 4. If ( 516 87:9 ; < = ) 5. Retur *&?>>(@ $ 6. Ed For 7. Retur AJù;ü 7 ($ Ed Fuctio Procedure "*ý$#%'& û)( *(+, vü.-/(ÿ ' ú 8. 7 B ;ú 9. For (C E ; CFG ; C ++) 1. & 9 HI, CFG ; & 9 J th latest of K& 5 7 5 cúlonpqrct, CVU WGN 3 11. ( 9 59YX 6 7 5 ; Z 9 ( 9 & 9 1. Case 1: o brach oit i ÿ:& 9 ( 9 13. \ 9 Z 9 úi]( 9 14. Case 1.1: o brach oit i ^ ( 9 )\ 9 15. 7:9 GZ 9 ú 16. Case 1.: first brach oit i ^ ( 9 1\ 9 is at _ ad o brach oit i ÿ` azÿz 9 útÿ _b( 9 ) ' E/ 17. trasmit iterleaved data after brach oit 18. 7:9 _Hc( 9 Zÿ:Z 9 útÿ_bc( 9 1 ' E 19. Case 1.3: first brach oit i ^ ( 9 1\ 9 is at _, ad first brach oit i ÿ` azÿz 9 útÿ _b( 9 ) ' E/ is at _d=. segmet eds at brach oit _d= 1. 7:9 _d=bc( 9. Case : oe brach oit i ÿ& 9 ( 9 3. trasmit iterleaved data 4. \ 9 Z 9 ú EIe( 9 5. Case.1: o brach oit i ^ ( 9 )\ 9 6. 7:9 GZ 9 ú E 7. Case.: first brach oit i ^ ( 9 1\ 9 is at _ 8. segmet eds at brach oit 9. 7:9 _Hc( 9 3. Ed For Ed Procedure Fig. 14. Algorithm for OPB-UP egmet izes (balaced biary tree) its layback time. A cliet whose ath is misredicted will have listeed to trasmissios of the wrog data from after the misredicted brach oit. Recovery would require either iterrutio i layback (so as to allow time for the cliet to receive the data that it would have received by this oit, had the brach choice bee correctly redicted), or use of a uicast stream that would deliver data sequetially from the brach oit at rate at least equal to the layback data rate. The key observatios from these figures are: (1) stoig trasmissio o a chael whe there are o cliets listeig allows eriodic broadcast erformace to be cometitive eve uder light load, () recise ath redictio yields a large imrovemet i erformace, (3) OPB-KP yields erformace essetially as close to the lower boud from eq. as could be exected, give that the former assumes that each cliet ca oly receive data at each oit i time at a total aggregate rate of twice the streamig rate (ðfœâ ), whereas the latter laces o such restrictio (see 5], 1] regardig the imact erver Badwidth 5 4 3 1 H-UP OPB-UP H-KP OPB-KP Lower Boud 1 1 1 1 Fig. 15. N Performace of calable elivery Protocols (balaced biary tree with height 3, = 1, =.1 for OPB ad lower boud, î =.5, í = 8) erver Badwidth 175 15 15 1 75 5 5 1 3 4 5 6 7 8 Fig. 16. H-UP OPB-UP H-KP OPB-KP Lower Boud Tree Height Performace with Varyig Height ( = 1, = 1, =.1 for OPB ad lower boud, î =.5, í = 8) of cliet receive rate limitatios), ad (4) the recise relative erformace of the H ad OPB variats deeds o request arrival rate ad the cliet start-u delay used i OPB (ote that H rovides immediate service, although variats that use a batchig start-u delay have also bee roosed 4]). The results for H-UP ad H-KP suggest that it may be fruitful to ivestigate H variats i which cliets may soo o multile earlier streams (e.g., oe for each ossible choice at the ext brach oit, similar to ext), or i which cliet-secific ath redictio is emloyed (as i red).. Prototye Imlemetatio A rudimetary imlemetatio of scalable o-liear media streamig has bee added to the WOR rototye streamig system 1]. The WOR system cosists of server ad cliet comoets, built usig the oe source Aache roxy server code as a base. These iterose betwee Widows edia layers ad servers, ad relace the ormal uicast delivery with multicast delivery usig hierarchical stream mergig. Our imlemetatio of o-liear media streamig stores
erver Badwidth 5 4 3 1 H-UP OPB-UP H-KP OPB-KP Lower Boud.1.1.1 Fig. 17. Cliet tart-u elay (d) Imact of OPB tart-u elay (balaced biary tree with height 3, = 1, = 1, î =.5, í = 8) each ortio of the o-liear structure as a searate file. odificatio of header fields ad soofig of requests by the WOR cliet comoet allow this structure to be ivisible to the cliet layer, to which it aears that oly a sigle video file is beig layed (trasitios betwee the video ortios are seamless). yamic cliet ath selectio is curretly suorted through a web age iterface. The reset imlemetatio uses built-i kowledge of the media file structure; o-goig work cocers descritio of o-liear media structures i meta files. Our imlemetatio has demostrated that o-liear media streamig ca be imlemeted relatively easily, eve i the cotext of commercial media streamig systems. VI. CONCLUION This aer has cosidered o-liear video cotet i which cliets ca tailor their video stream accordig to idividual refereces, withi the costraits of a redefied tree or grah structure. Tight lower bouds o server badwidth were develoed that show the otetial for badwidth reductio usig multicast delivery i the cotext of o-liear media, as well as illumiate the advatages/disadvatages of various aroaches to cliet soo-ahead ad the beefits of a riori ath kowledge. The key isights from the bouds aalysis are (1) correct cliet ath redictios for more tha 75% of the video ortios greatly reduces the required server badwidth with very modest cliet data overhead, ad () i the absece of fairly recise a riori iformatio about cliet ath selectios, a simle olicy i which cliets oly liste to trasmissios from their curret video ortio ad those immediately followig the ext brach oit, achieves better server badwidth scalability tha usig overall ath selectio robabilities to determie which trasmissios to liste to. New stream mergig ad eriodic broadcast rotocols were devised, i art usig isight from our bouds aalysis, ad show to achieve much of the otetial badwidth savigs. The ew eriodic broadcast rotocols were foud to be cometitive with the ew stream mergig rotocols at all request rates, assumig that i the former rotocols the server trasmits o a chael oly whe at least oe cliet is listeig. 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