Control of Perceived Quality of Service in Multimedia Retrieval Services: Prediction-based mechanism vs. compensation buffers

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1 1 Control of Prcvd Qualty of Srvc n ultmda Rtrval Srvcs: Prdcton-basd mchansm vs. compnsaton buffrs Aurlo La Cort, Alfo Lombardo, Srgo Palazzo, Govann Schmbra Isttuto d Informatca Tlcomuncazon, Unvrsty of Catana V.l A. Dora Catana - ITALY Abstract In multmda systms nd-to-nd dlay jttr has a grat mpact on th contnuty of nformaton playback. Thrfor t s ncssary to ntroduc approprat mchansms to compnsat for dlay varatons, so that th ntramda and ntrmda tmporal rlatonshps can b prsrvd. In ths papr, two mthods for compnsaton of th ntwork dlay jttr n a dstrbutd multmda rtrval srvc ar compard: th frst s basd on prdcton of th ntwork dlay jttr suffrd by ach nformaton unt and rtrval tm modfcaton at th sourc st; th scond s basd on a compnsaton buffr at th dstnaton st. Comparson s mad by assumng a mastr/slav rlatonshp btwn th monomda strams composng th multmda data flow. Kywords: multmda communcatons, ntramda and ntrmda synchronzaton, jttr, skw

2 1. Introducton In tradtonal tlcommuncaton srvcs, usr nds dtrmn dffrnt prformanc rqurmnts n trms of dlay and packt loss accordng to th mda supportd. Audo srvcs, for xampl, can tolrat packt loss and modrat dlay wth vry lmtd jttr, whras data srvcs tolrat dlay but rqur strngnt packt loss paramtrs. Wth th advnt of multmda srvcs th prformanc rqurmnts usrs hav to b provdd wth ar bcomng mor and mor constranng [1-4]. In a multmda rtrval srvc, for xampl, th charactr strams concrnng flm subttls hav dlay rqurmnts smlar to thos of vdo or audo. Ths s du to th fact that th man charactrstcs of multmda srvcs ar rlatd to synchronzaton. A multmda stram s, n fact, charactrzd by multpl monomda strams rlatd to ach othr by mans of tm rlatonshps whch must b prsrvd. Du to th varous dlays th monomda strams may undrgo durng transmsson n a hgh-spd ntgratd ntwork, approprat mchansms must b ntroducd so as to mt both th rqurmnts of ach monomda stram (ntramda synchronzaton) and thos rlatd to how th monomda strams ar ntgratd to form th multmda stram (ntrmda synchronzaton). In ordr to quantfy ths synchronzaton rqurmnts and to mplmnt th rlatd control mchansms, som Qualty of Srvc (QoS) paramtrs hav bn dfnd [4-6]. Ths QoS paramtrs ar bascally lnkd to th dlay jttr th nformaton unts of ach monomda stram undrgo and th skw occurrng n th multmda stram, that s th dffrnc btwn th nstantanous dlays of nformaton unts blongng to two dffrnt monomda strams. As masurmnts of human prcpton of th abov paramtrs [6] hav shown that monomda strams may appar to b "n synch" f th jttr and skw ar lmtd to approprat valus, th QoS paramtrs prcvabl at th usr ntrfac, hrn rfrrd to as Prcvd Qualty of Srvc (P_QoS) paramtrs [7], can b xprssd as rstrctons on th statstcs of th valus assumd by th jttr and skw. In ltratur svral mchansms dalng wth th problm of lmtng dlay jttr and/or skw n multmda rtrval srvcs hav bn prsntd [5-6][8-4]. any of ths mchansms can b classfd nto two catgors: th frst on comprss mchansms basd on th us of buffrs at th dstnaton st, th scond on modfcaton of rtrval tms at th sourc st so as to compnsat for dlay jttr. Th applcaton of buffrng tchnqus rqurs th bounds of th dlay jttr ntroducd by th ntwork to b known a pror or stmatd at th dstnaton st [11-13]. Ths tchnqus ar xtrmly smpl to mplmnt but th buffr ndd to guarant th synchronzaton rqurmnts may b so bg that t causs unaccptabl dlays. Th scond knd of tchnqu uss mchansms whch rshap th probablty dnsty functon (pdf) of th dlay jttr at th dstnaton st [14-18] by varyng th nformaton unt rtrval tms at th sourc st. In ths papr w compar th us of ths two tchnqus; n partcular, as far as th lattr tchnqu s concrnd, an xtnson of th on prsntd n [17] s usd. Comparson btwn th abov two tchnqus s mad by assumng a mastr/slav rprsntaton of th componnt monomda strams [8]. Th papr s organzd as follows: Scton dfns th synchronzaton problm, ntroducng th ntra/ntrmda synchronzaton condtons to b appld to ach monomda stram n trms of Prcvd Qualty of Srvc paramtrs. Scton 3 ntroducs th proposd prdctonbasd dlay jttr compnsaton mchansm. Scton 4 shows how th P_QoS rqurmnts ar mappd on th paramtrs of th ntra/ntrmda synchronzaton mchansms. Scton 5 prsnts a cas study whch hghlghts th lmts of th applcablty and ffctvnss of th two synchronzaton mchansms by varyng statstcal proprts of th ntwork dlay and th rqurd P_QoS paramtrs. Fnally, Scton 6 summarzs th papr.

3 3. Dfnton of th problm End-to-nd dlay jttr has a grat mpact on th contnuty of playback of nformaton of ach monomda stram and on th concurrnt playback of svral monomda strams. A systm supportng multmda rtrval srvcs has to b quppd wth functons whch wll guarant ntra/ntrmda synchronzaton rqurmnts by lmtng varatons n th dlay jttr. To dfn th systm nvronmnt n whch ths functons ar to b locatd, lt us consdr th gnral data locaton modl shown n Fg. 1. In ths modl svral sourcs us a broadband ntgratd ntwork to snd pr-rcordd multmda data strams to a dstnaton nod. Th sourcs can b thr locatd n a sngl st or dstrbutd ovr th ntwork. A multmda stram s thrfor a combnaton of N monomda strams whch ar rtrvd by dffrnt sourcs and transportd autonomously, for xampl through sparat vrtual channls. Blow w assum that th tchnology usd to transport nformaton s th Asynchronous Transfr od (AT), whch, n th long trm, s th most capabl of supportng multmda srvcs. Each mda stram, as shown n Fg., s sn as bng mad up of an ordrd squnc of Informaton Unts (IUs) [10], contanng a st of packts rlatng to th sam mda. Th nd-to-nd dlay btwn th sndr and rcvr of th monomda strams conssts of collcton dlay, whch s th tm ndd at th sourc st to collct and prpar IUs for transmsson, ntwork dlay and dlvry dlay, whch s th tm ndd at th dstnaton st to procss and prpar IUs for playback [0]. In th followng w only consdr ntwork dlay. Howvr, th sam ln of rasonng can b usd to nclud th othr two knds of dlay n solvng th synchronzaton problm. Sourc #1 Sourc #... Sourc #N channl #1 mda #1 channl # mda #... Dstnaton channl #N mda #N ntgratd ntwork Fg. 1: Data locaton modl for a multmda rtrval srvc IU 1 (n-1) IU 1 (n) IU 1 (n+1) channl #1 tm IU (n-1) IU (n) IU (n+1) channl # tm IU (n-1) N IU (n) N IU (n+1) N channl #N Fg. : Informaton Unts (IUs) tm

4 4 Th IUs from th -th mda ar rtrvd and prpard for transmsson at th sourc st at th tm t_tx (n); thy ar subjct n transmsson to a varabl dlay and at th tm t_rx (n) ar dlvrd to th dstnaton st, whr thy ar procssd for playback to th usr. W assum that clock tcks at th sourc st and at th dstnaton st hav th sam advancmnt [1-13]. Th tm rlatonshps btwn IUs blongng to th sam monomda ar altrd on account of th ntwork dlay jttr (hncforward smply calld jttr), dfnd as j (n) =t_rx (n) - t_tx (n) - d (1) whr d s th avrag ntwork dlay suffrd by th -th mda. As j (n) s a random procss, th tmporal rlatonshps btwn th IUs of th -th mda ar not mantand at th dstnaton st. Th tm rlatonshps btwn IUs blongng to dffrnt mda ar altrd on account of th dffrnt startng tms for th sourcs, st, th dffrnt avrag dlays and th jttrs th IUs undrgo. or spcfcally, w dfn th skw s,k (n) at th nstant n btwn th n-th IUs of th mda "" and "k" as th dsplacmnt n tm btwn th IUs blongng to "" and "k": s,k (n) = d d k + st st k + j (n) j k (n) () As th frst 4 trms of th abov rlaton ar constant and can asly b compnsatd for at th dstnaton st by mans of a buffr, wthout loss of gnralty, w assum that d d k + st st k = 0 Th skw s,k (n) s thrfor: s,k (n) = j (n) j k (n) (3) Agan, as s,k (n) s a random procss, th tmporal rlatonshps btwn th IUs blongng to mda and mda k ar not mantand at th dstnaton st. A synchronzaton mchansm has to mantan th jttr and skw varatons boundd wthn sutabl valus [6]. To achv ths goal t has to act on all th monomda strams makng up th multmda stram. In partcular, n a multmda sourc thr s on monomda stram whch s compltly ndpndnt of th othrs, and th othrs ar dpndnt only on th frst. W wll ndcat th frst as th mastr and th othrs as slavs [8][5]. Th playback of th mastr can b spard from dscontnuts. Whras th mastr plays back at ts natural rat, th slav strams can b subjctd to skps and pauss, n ordr to rman synchronzd wth th mastr [8]. Th Prcvd Qualty of Srvc th multmda systm has to provd th usr wth can thrfor b dfnd n trms of th probablty that th jttr suffrd by th mastr stram and th skw occurng btwn ach slav stram and th mastr stram wll xcd crtan maxmum admssbl valus. Lt us dfn th rsdual jttr j_r (n) and th rsdual skw s_r,k (n) as th jttr and th skw that occur at th dstnaton st aftr applyng th synchronzaton mchansm. Th P_QoS th multmda systm has to provd th usr wth can b thrfor spcfd as: p j_ r( n) > J,max ε for th mastr (4a) { } { _ ( ) max} p s rs, n > SS, ε S for th slavs (4b) whr th symbol p {}. s usd to ndcat probablty, th ndxs "" and "S" ar usd to ndcat mastr and slavs, and J,max and S S,max ar th maxmum admssbl rsdual jttr and rsdual skw valus rspctvly. Thrfor a synchronzaton mchansm has to rshap th pdf s of thr th jttr of th mastr and th skw of th slavs wth rspct to th mastr n such a way that th abov P_QoS rqurmnts ar mt for ach mda. Lt us not that f w assum that IUs ar dscardd whn th rsdual jttr or th rsdual skw xcds th maxmum admssbl valu, th P_QoS can b spcfd quvalntly as:

5 5 p(loss) ε for th mastr (4a') p(loss) εs for th slavs (4b'). In ordr to provd usrs wth th P_QoS thy rqur hrnaftr w wll us two dffrnt jttr compnsaton tchnqus. Th frst compnsats for jttr at th sourc st through prdcton and rtrval tm varaton; th scond uss a compnsaton buffr at th dstnaton st [13]. Hncforward, th sz of ths buffr, rfrrd to as b, whr = and =S ndcat th buffrs for th mastr and slav strams rspctvly, wll b dfnd as th maxmum IU jttr varaton t can compnsat for. As rgards th frst tchnqu, n th followng scton w ntroduc an mprovmnt of th tchnqu prsntd n [17] and [18]. Subsquntly w analyz th ffctvnss of th two dffrnt tchnqus vrsus th statstcal proprts of th jttr and th dffrnt P_QoS rqurmnts. 3. Sourc st jttr compnsaton by jttr prdcton Th jttr pdf can b rshapd by varyng th nformaton unt rtrval tms at th sourc st. To do so, th rtrval tms ar modfd n such a way as to compnsat for th jttr valus prdctd at th sourc st. If w us j ( n) to ndcat th jttr valu of IU (n) prdctd at th sourc st and stablsh that th tm nstant at whch IU (n) s rtrvd and prpard for transmsson at th sourc st, t_tx (n), b rplacd by [t_tx (n) - j ( n) ], th rsdual jttr, j_ r ( n), s th jttr prdcton rror, that s: j_ r( n) = ( n) = j( n) j ( n ) (5) At th sourc st th prdctd jttr valu can b calculatd by an optmal prdctor [6], that s, on whch s abl to mnmz th prdcton rror varanc. To achv ths, th prdctor uss th valus of th jttr th prvous IUs undrwnt and th dstnaton st thrfor has to notfy th sourc st of th arrval tm, t_rx (n), of ach of th IUs t has rcvd. Th nformaton unts that th dstnaton snds back to th sourc for ths purpos ar calld Fdback Informaton Unts (FIUs). or spcfcally, whn th FIU (n) arrvs at th sourc st, th jttr that was suffrd by th IU (n) s calculatd from rlaton (1) takng nto account th varaton that has bn mad on th rtrval tm for IU (n), that s: j (n) = t_rx (n) - [t_tx (n) - j ( n) ]- d (6) On account of th propagaton tm for th IUs and corrspondng FIUs, whn th jttr for IU (n+1) has to b prdctd at th sourc st th jttr valus for th IUs mmdatly prcdng t may not b avalabl. Th prdctor to b usd has to b abl, thrfor, to mak a prdcton mor than on stp ahad. If, for xampl, whn IU (n+1) has to b mttd FIUs up to th (n-l)-th hav bn rcvd, t wll b ncssary to mak a prdcton (L+1) jttr sampls n advanc. Obvously, th lowr th valu of L th mor rlabl th prdcton wll b [6]. Th bst prdcton s obtand whn L=0,.. whn FIU (n) arrvs back at th sourc st bfor IU (n+1) s rtrvd. In ths cas a lnar prdctor can b usd [6]. To achv a crtan prdcton ffcncy t may b ncssary to lmt th valu of L. Assumng th procssng tms at th dstnaton and sourc sts to b nglgbl, onc th statstcal faturs of th ntwork dlay hav bn fxd, ths condton wll hav an mpact on th synchronzaton granularty [10]. It mposs a constrant, n fact, on th mnmum sz of th IU and thus on th mnmum tm ntrval btwn th rtrval tms of two conscutv IUs. It should b notd, howvr, that n any cas an FIU rcvd lat at th sourc st s usd to updat th hstory of th jttr valus and s thn usd n subsqunt prdctons. In th lght of what has bn sad so far, for ach mda th stps of th prdcton-basd jttr compnsaton algorthm w propos ar thrfor th followng:

6 6 at th dstnaton st, for ach IU rcvd, th arrval tm s mbddd n an FIU and fd back to th rlvant sourc; at ach sourc st, th prdctd jttr valu s calculatd on th bass of th jttr valus avalabl and th rtrval tm of th nxt IU s calculatd n such a way as to compnsat for th prdctd jttr valu. Whnvr an FIU arrvs th prdctd jttr valu and th rtrval tm ar rcalculatd. If th jttr s a wd-sns statonary random procss, th ordr of prdcton s suffcntly hgh and an optmal prdctor s usd, th jttr prdcton rror, ( n), and thrfor th rsdual jttr, can b rgardd as wht nos [6]; that s, t s practcally uncorrlatd, has a Gaussan pdf and th jttr prdcton rror varanc, σ,, ndcats achvd jttr pdf rshapng. 4. P_QoS control As w saw n Scton, th P_QoS rqurmnts ar spcfd by paramtrs dfnd as: P_QoS = [J,max, ε ] for th mastr P_QoS S = [S S,max, ε S ] for ach slav To mt th P_QoS rqurmnts, thrfor, any jttr compnsaton mchansm has to tak two stps: n th frst t has to ft th mastr rqurmnts dfnd by rlaton (4a) or (4a ); n th scond t has to mt th slav rqurmnts dfnd by rlaton (4b) or (4b ). In ths scton w dscuss how to st th valu of th paramtrs of th synchronzaton tchnqus w ar dalng wth, that s th compnsaton buffr sz to b usd and th jttr prdcton rror varanc to b achvd. W consdr th P_QoS rqurmnts spcfd n (4), but th sam ln of rasonng can b followd startng from (4'). In addton, as far as th prdcton-basd mchansm s concrnd, w wll not consdr dffrnt typs of prdctors snc t s byond th scop of ths papr; w wll only assum us of an optmal prdctor, that s, on whch s abl to mnmz th prdcton rror varanc. Fnally, as th ffctvnss of th two jttr compnsaton mchansms dpnds on th jttr statstcal proprts, w hncforward assum that th jttr has thr a bll-shapd pdf that can b approxmatd wth a Gaussan pdf, or a unform pdf n th ntrval [-Δ, Δ ]. In any cas, th rasonng followd blow can asly b xtndd to othr typs of jttr pdf. Obvously t s not ncssary to apply any jttr compnsaton mchansm to th mastr stram whn th jttr j (n) s such that rlaton (4a), calculatd wth j_r (n)=j (n), holds. In both th jttr pdfs consdrd, ths s lnkd to th jttr varanc σ. In fact, whn th pdf of th jttr suffrd by th mastr s unform n th ntrval [-Δ, Δ ], for th followng rlaton to hold ( J,max) p{ j( n) > J,max} = Δ 1 ε (7) Δ J,max σ (8) 3 1 ε ( ) must b tru, as th jttr varanc σ = Δ [6] 3 If, on th othr hand, th jttr pdf s Gaussan, no synchronzaton mchansm nd b appld whn J,max p[ j( n) > J,max] = 1 Φ ε (7 ) σ x 1 y whr Φ() x = dy s th rror functon [7]. To solv th nqualty n (7') on th bass of π 0 th jttr varanc, an approxmatd xprsson of ths rror functon has to b usd. W us Gtnk s

7 7 approxmaton [8], accordng to whch th nqualty Φ( x) 1 ε can b rplacd by x ε ε n whch th trm of th scond ordr s nglctd. Th nqualty n (7') can thrfor b rwrttn as: J σ <.,max (8 ) ln( ε ) So, whn th jttr varanc s such that rlaton (8) or (8') dos not hold, t s ncssary to compnsat jttr suffrd by th mastr stram. Th sam can b sad for th slav stram. In fact, accordng to th dfnton of skw gvn n Scton, th rsdual skw s th dffrnc btwn th rsdual jttr of th mastr and th slav. Assumng that th jttrs th dffrnt mda undrgo ar statstcally ndpndnt of ach othr, th rsdual skw pdf s gvn by th convoluton btwn th rsdual jttr pdf's of th mastr and th slav. So, to guarant th P_QOS S rqurmnts,.. rlaton (4b), th followng rlaton must hold + SS,max + p[ ss, ( n) SS,max ] = fj_ r () τ fj r ( x ) d dx _ + τ τ > 1 ε S S (9) SS,max If rlaton (9), calculatd wth j_r S (n)=j S (n), dos not hold, t wll b ncssary to apply a mchansm to compnsat for th jttr th slav stram undrgos. 4.1 Intramda synchronzaton of th mastr Lt us suppos that th condtons dfnd by rlaton (8) or (8 ) do not occur. In ths cas t s ncssary to ntroduc a compnsaton buffr and/or rshap th jttr pdf by jttr prdcton n such a way that th rsdual jttr satsfs rlaton (4a). Lt us not that th rsdual jttr suffrd by th mastr s: j_ r( n) = ( n) = j( n) j( n) (10) whn only th prdcton-basd mchansm s usd, 0 f j( n) 05. b j_ r ( n) = j( n) 05. b f j( n) > 05. b (11) j( n) b f j( n) < 05. b whn only th compnsaton buffr-basd mchansm s usd, and fnally 0 f ( n) 05. b j_ r ( n) = ( n) 05. b f ( n) > 05. b (1) ( n) b f ( n) < 05. b whr ( n) = j( n) j( n), whn th prdcton-basd mchansm followd by th compnsaton buffr s usd. Blow w dscuss how to st th compnsaton buffr sz to b usd and/or th jttr prdcton rror varanc to b achvd n ordr to mt th P_QoS rqurmnts. Jttr Compnsaton by mans of a Buffr

8 8 Fg. 3 s a schmatc rprsntaton of th ffct of th compnsaton buffr on th jttr pdf n th two cass consdrd - unform pdf and Gaussan pdf. If th jttr pdf s unform, th rsdual jttr pdf for th mastr, j_r (n), s gvn by: b f x = 0 Δ f j_ r () x = 1 f 0 < x ( Δ 05. b ) Δ whr b s th sz of th compnsaton buffr nsrtd nto th mastr stram and, obvously, > 05. b. Thrfor, for th followng rlaton to hold: Δ 05. b { _ ( ),max } 1 j_ r ( ) p j r n > J = f x dx ε b 05. b [ ( ) J,max] 3 1 ε σ (13) must b tru. If, on th othr hand, th jttr pdf of th mastr s Gaussan, th rsdual jttr pdf s gvn by: So, to obtan f () x b Φ f x = 0 σ = ( x + 05 b ) 1 - σ f x 0 π σ j_ r. J p[ _ j r( n) > J,max] = 1 Φ,max b agan usng Gtnk's approxmaton [8], smpl calculatons yld σ ε f j ( x ) ( x) f j _ r (a) Δ Μ Δ Μ Δ -0.5 b 0.5 b Μ +0.5 b Δ Μ 0.5 b compnsaton f j ( x ) ( x) buffr f j _ r (b) -0.5 b 0.5 b Fg. 3: jttr pdf - f j ( x ) - and rsdual jttr pdf - ( ) f j _ r x - aftr buffr compnsatng for all th jttr valus of th IUs contand n th ntrval [-0.5 b, 0.5 b ], whn th jttr pdf s unform (a) and Gaussan (b).

9 9 f j ( x ) f j _ r ( x) Δ Μ Δ Μ prdcton- Δ Μ Δ Μ -basd ( ) jttr compnsaton mchansm f j _ r f j x ( x) Fg. 4: jttr pdf - f j ( x ) - and rsdual jttr pdf - ( ) x - aftr applcaton of th prdctonbasd jttr compnsaton mchansm. f j _ r ln( ε ) b σ J,max (13') As can b obsrvd from rlatons (13) and (13'), th compnsaton buffr sz ndd for th P_QoS rqurmnts to b mt s smallr n th cas of a unform jttr pdf than n th cas of a Gaussan jttr pdf, provdd that ε s lss than Jttr Compnsaton Usng th Prdcton-basd chansm As w sad abov, f th jttr s a wd-sns statonary procss, an optmal prdctor s usd and th ordr of prdcton s suffcntly hgh, th jttr prdcton rror (n) can b rgardd as wht nos, that s, th rsdual jttr of th mastr s practcally uncorrlatd and has a bll-shapd pdf whch can b approxmatd by a Gaussan pdf dspt th ntal shap (as n Fg. 4). So, n th cas of both jttr wth a unform pdf and jttr wth a Gaussan pdf, th rsdual jttr pdf s gvn by: σ, - x, 1 f j _ r ( x ) = π σ whr σ, s th jttr prdcton rror varanc. To satsfy rlaton (4a), th followng must hold: J,max p[ _ j r() n > J,max] = 1 Φ ε (14) σ, Th problm of guarantng a crtan P_QoS for mastr ntramda synchronzaton can b rplacd by th problm of rshapng th jttr pdf of th mastr n such a way that th jttr prdcton rror varanc, σ,, s such as to satsfy rlaton (14). Agan usng th Gtnk s approxmaton of th rror functon, from (14) w obtan that th prdcton rror varanc to b achvd has to b: J,max σ, (15) ln( ε )

10 10 Jttr Compnsaton Usng th Prdcton-basd chansm and th Buffr Us of th compnsaton buffr alon may lad to xcssvly long buffrs and unaccptabl nd-to-nd dlays. On th othr hand, th ffctvnss of th prdcton tchnqu dpnds on both th jttr corrlaton dgr [6] and th ntwork dlay bcaus, as w sad, th lattr dtrmns how far n advanc prdcton nds to b mad (.. th valu of L). Both factors ar dcsv for th valu of th jttr prdcton rror varanc, σ,, that th prdcton-basd mchansm can rach. For ths rason t may b ncssary to combn th two tchnqus by ntroducng a compnsaton buffr aftr th prdcton-basd jttr compnsaton mchansm. In ths cas th rsdual jttr pdf s of th knd shown n Fg. 5. It s xprssd by: b Φ f x = 0 σ, f j_ r () x = ( x b ) 1 - σ, f x 0 π σ, To mt th P_QoS rqurmnt for th mastr ntramda synchronzaton,.. to mt rlaton (4a), th followng must hold: J,max b p[ _ j r( n) > J,max] = 1 Φ ε σ Agan usng th Gtnk s approxmaton, w obtan that th jttr prdcton rror varanc σ, and th sz of th compnsaton buffr b now hav to satsfy th rlaton: σ, ( J,max b) (16) ln( ε ) So th valu of b n (16), that s, th sz of th buffr that has to b nsrtd on th mastr stram, has to b chosn n such a way that th prdcton-basd mchansm s abl to supply a valu for σ, whch wll satsfy rlaton (16). Of cours, th largr th compnsaton buffr th gratr th admssbl valu for σ,, and thrfor th lss pdf rshapng th prdcton-basd mchansm has to do, and vc vrsa. It s worth rmarkng that n som cass th prdcton-basd mchansm dos not rduc th, f j ( x) (a) f ( x) compnsaton buffr f j r _ ( x) f j ( x) prdcton- -basd tchnqu -0.5 b (b) 0.5 b (c) - ΔΜ Δ Μ (a) Fg. 5: jttr pdf - f j ( x ) - (a), jttr prdcton rror pdf - ( ) ( x ) - aftr th compnsaton buffr (c). f j r _ f x - (b), rsdual jttr pdf -

11 11 compnsaton buffr sz, so t s countrproductv. Ths happns whn th jttr prdcton rror varanc s gratr than th jttr varanc or whn, wth boundd jttr, th ffct of prdcton s an ncras n th bounds of th jttr whch s not compnsatd by an adquat rducton n th jttr prdcton rror varanc. Ths occurrncs dpnd on th lvl of corrlaton of th jttr, on ts pdf and, f th lattr s boundd, on th valus of th P_QoS rqurmnts. In fact, wth rfrnc to th two jttr pdf's consdrd, th prdcton-basd mchansm s countrproductv whn: ( 1 ε ) σ, σ f th jttr pdf s unform (17) ln ε ( ) σ σ f th jttr pdf s Gaussan (17'), 4. Intrmda synchronzaton btwn mastr and slavs Aftr mtng th P_QoS rqurmnts for mastr ntramda synchronzaton, th jttr compnsaton mchansms hav to act n such a way as to nsur th P_QoS rqurmnts concrnng th skw btwn th mastr and th slavs. As n th cas of ntramda synchronzaton for th mastr, ths s achvd by rshapng th slav jttr pdf ntroducng a compnsaton buffr and/or usng th prdcton-basd jttr compnsaton mchansm so that rlaton (4b) s mt. Th am of ths scton s to dntfy, for ach slav, th jttr prdcton rror varanc σ S, and/or th sz b S of th compnsaton buffr to b ntroducd n ordr to mt rlaton (4b). Tabl 1 summarzs th pdf of th rsdual jttr aftr applcaton to both th mastr or th slav of th compnsaton buffr alon, th prdcton-basd jttr compnsaton mchansm alon, or both tchnqus, n th two jttr pdf cass hypothszd. As mntond prvously, accordng to th dfnton of skw gvn n Scton and assumng that th jttrs th dffrnt mda undrgo ar statstcally ndpndnt of ach othr, th rsdual skw pdf of th slav wth rspct to th mastr s gvn by: + fs_ r ( x) = fj r ( ) fj r( ) d S, _ τ _ x + τ τ (18) S To guarant th P_QOS S rqurmnts,.. for rlaton (4b) to hold, rlaton (9) must hold. Snc th jttr pdf rshapng and/or th compnsaton buffr rlatd to th mastr hav alrady bn dtrmnd n such a way that th P_QoS rqurmnts ar mt, th ntgral n rlaton (9) can b solvd numrcally, thus dtrmnng th valus of th jttr prdcton rror varanc, σ S,, and/or th sz, b S, of th compnsaton buffr to b appld to th slav stram so as to nsur that th P_QoS S rqurmnts ar mt. If th rsdual jttr pdf of th mastr and slav ar both Gaussan, as for nstanc whn th prdcton-basd mchansm alon s usd for both th mastr and th slav, t s possbl to obtan an approxmat analytcal xprsson of th ntgral n (9). In fact, from (9) w hav [7]: SS,max P[ ss, ( n) SS,max] = Φ > 1 ε S (19) σ, + σ S, from whch w obtan th prdcton rror varanc of th slav jttr as a functon of both th prdcton rror varanc of th mastr jttr and th maxmum valu of skw dfnd n (4b), that s:

12 S S,max σs, < σ, ln( εs) (0) So, to mt th P_QoS rqurmnts for ntrmda synchronzaton, n th cas bng xamnd t s ncssary to rshap th slav jttr pdf n such a way that th prdcton rror varanc mts rlaton (0). 5. A cas study In ordr to gan a clarr undrstandng of how to apply th two synchronzaton mchansms so as to guarant th P_QoS rqurmnts, and show up th applcaton lmts of th two mchansms, w wll now dscuss a cas study. W wll rfr to a gnrc multmda rtrval srvc comprsng a mastr and a slav stram and, as n th prvous sctons, w wll consdr two knds of jttr pdf - unform and Gaussan. W assum that th jttr autocorrlaton squnc for both strams has an xponntal trnd, that s m R ( m)= σ α, =S,, wth 0 < α < 1 An xponntal autocorrlaton squnc was usd to mak th long-trm prdcton rror varanc, σ,, ndpndnt of th prdcton ordr whn a lnar prdctor s usd. In ths cas t s [6]: ( 1 ) σ = σ α =,S (1), compnsaton buffr prdcton- -basd mchansm prdcton-basd mchansm + compnsaton buffr f j_ r b Δ ( x) = 1 Δ and s th mnmum jttr prdcton rror varanc valu that th prdcton-basd mchansm can rach. In (1) th valu of α can b st so as to rprsnt varous lvls of jttr corrlaton (.g. α =0.9 for a hghly corrlatd jttr, α =0.75 for a jttr wth mdum corrlaton and α =0.5 for a jttr wth low corrlaton). Frst of all lt us dal wth th problm of ntramda synchronzaton of th mastr stram. In th cas of unform jttr pdf, from rlatons (15) and (1) t s sn that th prdctonunform jttr pdf Gaussan jttr pdf f x = 0 ( Δ 05. b ) f 0 < x f j_ r () x f j _ r ( ) x = f 1 π σ () x b Φ f x = 0 σ = ( x + 05 b ) 1 - σ f x 0 π σ j_ r., x - σ, b Φ f x = 0 σ, = ( x b ) 1 - σ, f x 0 π σ, Tabl 1: rsdual jttr pdf aftr applcaton of th compnsaton buffr, th prdcton-basd jttr compnsaton mchansm or both (=,S).

13 13 basd mchansm would n no cas b abl to guarant th mastr synchronzaton rqurmnts on ts own,.. t would nvr b abl to supply a jttr prdcton rror varanc valu such as to mt rlaton (4a), whn: J α < 1.,max () σ ln( ε ) If, on th othr hand, J α 1.,max (3) σ ln( ε) th prdcton-basd mchansm alon may b abl to guarant th mastr synchronzaton rqurmnts as long as th prdctor can supply a jttr prdcton rror varanc that mts rlaton (15). Stll n th cas of unformly dstrbutd jttr, from rlatons (17) and (1) t can b sn that th compnsaton buffr alon must b usd to mt th P_QoS paramtrs whn: ( 1 ε ) α 1. (4) ln( ε ) From Tabl, whch gvs som α valus for varous ε accordng to rlaton (4), t can b obsrvd that t s always ncssary to us th compnsaton buffr alon, unlss th jttr s hghly corrlatd or hgh ε valus ar admttd. ε =10-1 α 0.54 ε =10 - α ε =10-3 α ε =10-4 α ε =10-5 α ε =10-6 α 0.96 ε =10-7 α Tabl : α valus for whch t s convnnt to us th compnsaton buffr alon whn th jttr pdf s unform. Agan n th cas of unform jttr pdf, whn ( 1 ) ε < < 1. J,max α ln( ε ) σ ln( ε) t s usful to us a combnaton of th two tchnqus to guarant th ntramda synchronzaton rqurmnts for th mastr. If, on th othr hand, th jttr pdf s approxmatd wth a Gaussan pdf, from rlatons (17') and (1) w dduc that th prdcton-basd jttr compnsaton mchansm always has a postv ffct. Th prdcton rror varanc s, n fact, always lowr than th jttr varanc [6]. By way of xampl, lt us consdr a mastr stram whch undrgos a jttr wth a Gaussan pdf and a varanc of σ =100 ms. If w chos to us th buffr-basd jttr compnsaton mchansm alon to obtan J,max =30 ms and ε =10-3, ε =10-4 or ε =10-5, from rlaton (13') w would obtan th followng compnsaton buffr sz valus: ε =10-3 ε =10-4 ε =10-5 b 3.4 ms b 14. ms b 3.6 ms It s pontd out that th compnsaton buffr sz obvously dos not dpnd on th lvl of jttr

14 14 corrlaton. If, on th othr hand, th prdcton-basd mchansm alon s usd to obtan th sam valus for J,max and ε, from rlaton (15) th rsdual jttr varanc,.. th jttr prdcton rror varanc, must b: σ, ε =10-3 ε =10-4 ε = ms σ, 65.5 ms σ, 51.5 ms From rlaton () t can b dducd that by mans of an optmal prdctor t s possbl to obtan ths dsrd valus for σ,, n th thr cass consdrd f α =0.9 or α =0.75. If, on th othr hand, α =0.5 and ε =10-4 or ε =10-5, th prdcton rror varanc cannot b lowr than th valus ndcatd abov so t s ncssary to us a compnsaton buffr as wll. Rlaton (16) provds th rlaton btwn th sz of th compnsaton buffr and th jttr prdcton rror varanc ndd to guarant th P_QoS rqurmnts. For xampl, f α =0.5 and w choos a sngl σ, valu and varyng ε valu, possbl chocs would b thos gvn n th followng. σ, ε =10-4 ε = ms b =4.6 ms b =13 ms σ, 85 ms b =8.4 ms b =17 ms σ, 90 ms b =10.4 ms b =19.4 ms σ, 95 ms b =1. ms b =1.4 ms σ, 99 ms b =13.8 ms b =3. ms Smlar consdratons ar vald f w consdr a unform jttr pdf. If, for nstanc, th jttr varanc s σ, δ =700 ms and w want to obtan J,max =60 ms, from rlatons (13), (15) and (16) w obtan th jttr prdcton rror varanc and compnsaton buffr sz valus gvn n Tabl 3. In th tabl null b valus man that th ncssary rshapng of th jttr pdf can only b achvd by th prdcton-basd jttr compnsaton mchansm. Th rows n whch only b appars ndcat th valu b ndd to guarant P_QoS rqurmnts wth th compnsaton buffr alon. Clls markd wth "--", on th othr hand, ndcat cass n whch th prdcton-basd mchansm cannot b usd. By usng th compnsaton buffr alon t rsults from (13), n fact, that b = 4 ms f ε =10-1, b = 58 ms f ε =10 -, and b 60 ms f ε Th jttr prdcton rror varanc that th prdctor s abl to supply dpnds not only on th dgr of jttr corrlaton but also on how far n advanc th prdcton has to b mad,.. on th valu of L [6]. In gnral, onc th statstcal proprts of th jttr hav bn fxd, f a crtan jttr prdcton rror varanc valu s to b obtand t s ncssary to lmt th valu of L [6]. If th prdcton s to b mad at most L sampls ahad, th FIU (n) has to arrv bfor IU (n+l) s rtrvd. In ths cas, assumng for th sak of smplcty that th ntwork dlay btwn th sourc and th dstnaton sts s th sam as that btwn th dstnaton and sourc,.. that th ntwork dlay a gnrc IU undrgos s th sam as that suffrd by th corrspondng FIU, th followng must hold: L = 1 T ( IU n+ ) = t _ tx ( n+ L ) t _ tx ( n ) d + ( n ) + j( n) + j( n+ L) (5)

15 15 α =0.9 α =0.75 α =0.5 σ, σ, σ, ε = 10-1 ε = 10 - ε = b =0 σ, b =0 σ, b =0 σ, 540 b = b =18. σ, 756 b = b =0 σ, 864 b = σ, 1647 b = σ, 403 b = σ, σ, b 4 b 58 b b =0 σ, 115 b = b =0 σ, 14 b = σ, b = σ, 178 b = σ, 457 b = b 4 b 58 b 60 σ, 05 b = σ, 95 b = σ, 430 b = b 4 b 58 b 60 Tabl 3: Jttr prdcton rror varanc and compnsaton buffr sz ncssary to guarant th P_QoS rqurmnts wth varous corrlaton lvls whn th jttr pfd s unform ( σ =700 ms and J,max =60 ms). Ths condton thrfor affcts th valu of th ntrarrval tm at th sourc st for IUs, and thus th sz of th IUs. If w consdr that th mastr stram s a contnuous mda [6],.. that TIU ( n) = cons tant = T IU, rlaton (5) s quvalnt to: d n j n j n L T + ( ) ( ) ( ) IU (6) L Obvously, th hghr th valu of L th hghr th prdcton rror varanc that th prdctonbasd mchansm s capabl of supplyng. For xampl, n th cas of jttr wth a Gaussan pdf, a varanc of σ =100 ms and an avrag dgr of corrlaton (α =0.75), f rlaton (6) s satsfd wth L=1, from rlaton () t s possbl to obtan a jttr prdcton rror varanc valu of σ, =45 ms ; f, on th othr hand, rlaton (6) holds for L=, by mans of an 8th-ordr prdctor [6] w would gt σ, =63 ms. In th frst cas th prdcton-basd mchansm alon can guarant P_QoS =[J,max =30, ε =10-5 ], whras n th scond cas t s ncssary to ntroduc a compnsaton buffr such that b = 8 ms. W wll now analyz ntrmda synchronzaton btwn th mastr and th slav. As w saw n th prvous scton, guarantng ntrmda synchronzaton rqurmnts mans rshapng

16 16 th jttr pdf for th slav, takng nto account what has bn don to th mastr. In othr words, havng fxd th valus of P_QoS S =[J S,max, ε S ], th synchronzaton mchansms, th prdctonbasd mchansm and/or th compnsaton buffr-basd on hav to prform rshapng n such a way that rlaton (9) s satsfd. For ths rshapng th consdratons mad for th mastr stram stll hold,.. ntrmda synchronzaton s nsurd by th ntramda synchronzaton of th slav stram. It should, howvr, b pontd out that th sam P_QoS paramtrs can b obtand by choosng dffrnt combnatons of jttr prdcton rror varanc and compnsaton buffr sz valus for th mastr stram, corrspondngly, th sam P_QoS S paramtrs can b obtand by choosng dffrnt combnatons of jttr prdcton rror varanc and compnsaton buffr sz valus for th slav stram, th valus of whch dpnd on what was don to th mastr stram. As w hav dfnd th compnsaton buffr sz as th maxmum IU jttr varaton t can compnsat for, t s obvous that, for a gvn b, =S,, th sz of that buffr n clls s gratr th hghr th avrag bt rat of th sourc s. So, n makng th choc t s ncssary to consdr that f, for xampl th avrag bt rat of th slav s much gratr than th avrag bt rat of th mastr, th choc of a smallr compnsaton buffr on th slav has th advantag of brakng down th sz of th buffr for th monomda stram wth th gratst load. 6. Conclusons In ths papr w hav dscussd two dffrnt tchnqus for jttr compnsaton amng at guarantng ntra/ntrmda synchronzaton rqurmnts n a dstrbutd multmda rtrval srvc: th frst s basd on prdcton of th jttr suffrd by ach nformaton unt and th scond on a compnsaton buffr at th dstnaton st. A comparson btwn th two tchnqus has bn mad, n a scnaro n whch monomda strams ar rprsntd by on mastr stram and on or mor slav strams. orovr, th us of th two tchnqus combnd has bn studd. AT d Δ (n) ε ε S FIU FIU (n) Φ(x) IU IU (n) b j (n) j_r (n) j ( n) J,max Lst of acronyms and symbols Asynchronous Transfr od avrag ntwork dlay of th -th mda maxmum dlay jttr provdd by th ntwork (= mastr, =S slav) whn th jttr pdf s unform prdcton rror of ntwork dlay jttr suffrd by th n-th IU of th -th mda maxmum admssbl probablty that jttr wll xcd J,max maxmum admssbl probablty that skw wll xcd S S,max Fdback Informaton Unt n-th FIU of th -th mda rror functon ndx of th gnrc -th mda. = mans mastr stram, =S mans slav stram Informaton Unt n-th IU of th -th mda sz of th compnsaton buffr (= mastr, =S slav) ntwork dlay jttr of th n-th IU of th -th mda rsdual jttr of th n-th IU of th -th mda th prdctd ntwork dlay jttr valu of th n-th IU of th -th mda maxmum admssbl ntwork dlay jttr for mastr

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