Packet Dispersion and the Quality of Voice over IP Applications in IP networks

Transcription

1 acet Dsperson and the Qualty of Voce over I Applcatons n I networs Ham Zlatorlov, Hanoch Levy School of Computer Scence Tel Avv Unversty Tel Avv, Israel Abstract- Next Generaton Networs (NGN and the mgraton towards I networs s lely to mae the I technology the man vehcle for carryng voce and vdeo calls on modern networs acet dsperson s a mechansm by whch the pacets of a certan sesson are dspersed over multple paths, n contrast to the tradtonal approach by whch they follow a sngle path most of the tme In ths wor we examne the qualty of Voce over I (VoI applcatons and the effects of pacet dsperson on t We focus on the effect of the networ loss on the applcatons, where we propose to use Notceable Loss Rate ( as a measure correlated wth the voce qualty We analyze the for varous pacet dsperson strateges over paths experencng memory-less (Bernoull or bursty (Glbert model losses, and compare them to each other Our analyss reveals, that n many stuatons, n partcular for most cases where losses are bursty, the use of pacet dsperson reduces the and thus mproves sesson qualty The results suggest that the use of pacet dsperson can be qute benefcal for these applcatons Keywords -- Stochastc processes; pacet dsperson; notceable loss rate; voce over I qualty; bursty losses I INTRODUCTION Next Generaton Networs and today s mgraton towards I based networs s lely to mae these networs the man nfrastructure for carryng Voce and Vdeo applcatons A maor ssue that needs to be solved to mae ths mgraton successful s that of the requred qualty of the applcatons over the best effort I networ acet dsperson n I networs s a mechansm n whch applcaton pacets are dspersed between parallel paths leadng from the source to the destnaton, based on a predefned dsperson strategy acet dsperson can be mplemented by the source applcaton (eg by usng source routng or other technques or by nodes n the networ (eg mult-homng devces or Content Delvery Networ companes, such as Aama, that use edge archtecture to acheve load-balancng and mproved networ utlzaton In ths study we examne the qualty of real tme stream-orented applcatons, n partcular VoI, n lght of pacet dsperson The am of ths study s to examne whether pacet dsperson Ths wor was partally supported by Israel Scence Foundaton grant 35/03 Snce we focus our dscusson on I networs, we wll use the term acet Dsperson nstead of the general term Traffc Dsperson can be used as a machnery to mprove QoS of VoI applcatons under nown networ statstcal characterstcs and to examne the effect of dsperson conducted n multhomng archtectures on VoI qualty Traffc dsperson technques are used n many technologes, for a varety of reasons In CDMA rado networs, traffc dsperson (also called frequency-hoppng s used for securty reasons and n order to statstcally multplex noses In [6][3] traffc dsperson n I networs s suggested to reduce traffc burstness and therefore acheve hgher resource utlzaton Another dea, proposed n [], suggests usng traffc dsperson as a better method to Forward Error Correcton (FEC technque for voce over I (VoI applcatons Traffc dsperson s mplemented de-facto n I networs for load balancng purposes Several factors affect the qualty of VoI applcatons One can dvde them nto two classes, the underlyng networ behavor and the technology bult-n mechansms, such as codec type, acet Loss Concealment (LC mechansms and Forward Error Correcton (FEC Our focus s on the networ behavor, whch s usually measured n three measures: acet loss, delay and tter (delay varance Clearly, as these measures grow, qualty degrades However, the acceptable delay, for b-drectonal real-tme streamng applcatons, s usually lmted by values of mll-seconds For ths reason, both delay and tter can be roughly translated, physcally and mathematcally, nto a loss measure, snce late pacets arrvng at the destnaton are not useable and can be counted as lost We therefore wll concentrate n ths study on the pacet loss experenced by a sesson, regardless of the cause of the loss (whether a real networ loss or a dropped pacet due to late arrval erceptual studes of applcatons such as I phones have shown that user dssatsfacton rses dramatcally n presence of bursty losses Average pacet loss rate property, as shown n many studes, s not enough to capture the effect of networ behavor on VoI applcatons For better qualty evaluaton one should also tae nto account loss burstness and recency effects Tang these together wth the technology bult-n mechansms can lead to a good estmaton of VoI applcaton qualty, as suggested n the E-model [7][] One ntrnsc property shown n these studes s that bursty losses degrade voce qualty Due to these propertes we conclude that n many stuatons the pacet Loss-Rate measure should be replaced by the Notceable-Loss-Rate ( measure [4] as the basc ngredent n computng the perceved qualty of

2 VoI applcatons The metrcs counts losses of close pacets and gnores losses of dstant pacets Based on [] we value the as a metrcs well correlated wth perceved voce qualty (the lower the the better the qualty Therefore, n ths wor we focus on the experenced by VoI sessons The analyss n ths wor s based on assumng that the losses experenced n the networ are ether memory-less (Bernoull or bursty (followng the Glbert loss model, Though the Bernoull loss model s a specal case of the Glbert model, we start the analyss wth the Bernoull model, as to smplfy the exposton Our analyss provdes the mathematcal machnery needed for computng the experenced by the sessons n these systems Despte the fact that the dmenson of problem addressed s very large (exponental state space the results are formulated n expressons whose computatonal complexty s very small (lnear Thus, usng our analyss, one can easly compute the of a gven networ scenaro Examnng several common data-drven pacet dsperson strateges usng the Bernoull loss model, we demonstrate that pacet dsperson reduces the n many practcal cases An examnaton of the under bursty losses leads to the concluson that n many cases pacets dsperson can hghly reduce, though n some other cases, dependng on path characterstcs, there are opposte results The formulae derved as well as the cases examned n the paper can be used n the process of networ desgn and traffc engneerng where dsperson s appled Though the results show that pacet dsperson s benefcal n many cases for VoI, one should be aware of the fact that pacet dsperson may have some sde effects and may cause other networ problems (eg out of order pacets, whch may harm other applcatons 3 Thus, technologes mplementng pacet dsperson should tae nto consderaton the specfc applcaton requrements, networ condtons over the routes and the dsperson strateges for overall enhanced networ performance It s worthwhle to menton that traffc dsperson can also be used for QoS dfferentaton and enhanced networ utlzaton purposes over asymmetrc paths The structure of ths wor s as follows: In Secton II we dscuss the modelng consderatons of ths wor, present the underlyng assumptons of our model, and ntroduce the Notceable Loss Rate model adopted from [4] We then turn nto mathematcal analyss of pacet dsperson strateges under the Bernoull loss model (Secton III and under the Glbert model (secton IV For both loss models, we frst analyze the experenced by a sesson traversng a sngle path (no-dsperson, as s typcally the case n tradtonal networs We then turn to analyze the as experenced n mult-path envronment, and examne two typcal pacet dsperson schedulng polces: The memory-less random pacet schedulng, n whch the paths taen for the pacets of a stream are chosen usng a memory-less probablstc 3 In [] t clamed that gven the loss rate, the performance of TC applcatons mproves when losses tend to appear n bursts Meanng that the same effect of reducng burstness that s benefcal for VoI s bad for TC mechansm (selecton from a predefned set of paths, and The perodc pacet schedulng n whch the paths taen for a pacet stream are selected accordng to some perodc order; a common specal case of the latter schedulng s the Round- Robn schedulng Havng analyzed these systems we then compare them to each other and brng numercal results to support our fndngs II MODELING ASSUMTIONS, MODEL AND NOTATIONS A Voce qualty, the factors affectng t and ts evaluaton Tradtonally, voce perceved qualty s measured by the Mean Opnon Score (MOS or by mechancal technques such as ESQ [0] and SQM [9] Another non-ntrusve montorng technque for VoI, ncorporatng the effects of tme varyng pacets loss and recency, based on the E- model [7] s suggested n [] There are many factors affectng voce qualty n VoI applcatons In general, one can dvde these factors nto applcaton factors (eg codec type, tter buffer mplementaton, etc and networ performance factors: delay, tter and loss The technques suggested n [] propose that gven the codec type and other applcaton parameters, loss (I e and delay (I d mparments are the man factors affectng voce qualty From these mparments one can compute the gross score, called R value, whch can be mapped to MOS The delay mparment causes relatvely small affect as long as t s bounded wthn certan constrants (usually up to 50ms Roughly speang, ths factor can be used to translate networ delay nto networ loss by countng all the pacets whose delay exceeds a certan threshold as lost pacets Ths results wth networ loss beng the maor networ performance parameter affectng voce qualty The average pacet loss rate metrcs alone s not enough to determne voce qualty The other factors, mentoned n [], are the recency effect (the relatve locaton of the lost frames, eg losses occurrng at the end of the sesson sgnfcantly degrades perceved qualty n comparson to losses occurrng at the sesson begnnng and the loss burstness (a pacet s consdered to be n a burst f less than g mn pacets have arrved snce the prevous pacet was lost Loss burstness, havng the greater mpact, can reduce MOS n more than one grade (out of fve as shown n [] erceptual studes, such as those referenced n [5], also support the fact that bursty losses may dramatcally reduce perceptual qualty, especally for audo Common VoI manpulaton technques also ncrease the mportance of bursty losses Frst, n modern codecs nternal acet Loss Concealment (LC, see [8] algorthms are used to reduce the effect of pacet loss on perceved qualty When a loss occurs the decoder derves the data of the lost frame from prevous frames to conceal losses A smple example of a LC mechansm would be to use the last (properly arrved pacet to replace a lost pacet Some codec concealment mechansms may be effectve for a sngle lost pacet, but not for consecutve losses or bursts of losses Second, Forward Error Correcton (FEC, see [0] mechansms are also used to compensate for lost pacets by appendng the nformaton of

3 prevous voce frames to pacet payload Clearly, for ths technque sequental losses decrease FEC effcency and reduce voce qualty We thus conclude that the loss rate and loss burstness are the maor networ performance factors affectng voce qualty and we focus on ther performance Next we defne and dscuss the Notceable Loss Rate ( as a measure for loss burstness that s well correlated wth voce perceved qualty B Notceable Loss Rate ( The I erformance Metrcs (ppm worng group n the IETF has proposed a set of metrcs for pacet loss [4] Ths ncludes loss constrant dstance (e the threshold for dstance between two losses and the Notceable Loss Rate ( metrcs, whch s the percentage of lost pacets wth loss dstance smaller than the loss constrant dstance 4 In VoI applcatons the loss constrant dstance s usually related to the convergence tme of the decoder Clearly, the perceved voce qualty decreases wth the A Defnton of The Loss Dstance s defned (as n [4] as the dfference n sequence numbers between two successvely lost pacets The loss event of a pacet s defned to be a notceable ( loss event (and s denoted as NL, f the loss dstance between the lost pacet and the prevously lost pacet s no greater than, where, a postve nteger, s the loss constrant In order to measure how notceable a loss mght be for qualty purposes, the loss dstance may be selected to be equal to g mn (the parameter used n [], typcally g 6 mn, determnng whether a pacet belongs to a burst Alternatvely, small values of can be used when FEC or LC mechansms are enabled Below we wll defne the Notceable Loss Rate ( as the fracton of all pacets, whch are notceable loss pacets Ths defnton agrees wth, but slghtly devates from, the metrcs Type--one-Way-Loss-Dstance-Stream defned n [4] Where necessary we wll assocate the parameter wth the noton of notceable loss rate, readng ( - notceable loss rate, or The loss ndcator functon for a certan flow reflects the loss event of pacet t: f pacet t s lost l ( t ( 0 Otherwse The event that pacet n sesson s a notceable loss wth loss constrant, s denoted by ndcator functon NL ( : l( and t [ -, -] where l( t NL ( ( 0 otherwse The notceable loss rate for sesson wth loss constrant, and for a sequence of K pacets, s then gven by: K ( K NL ( s (3 K s Next we propose an alternatve defnton to that gven n Eq ( for the notceable loss event ( NL ( : l( and t [ +, + ] where l( t NL ( (4 0 otherwse roposton : For any sequence of loss events, the number of notceable loss events under the defntons ( and (4 are dentcal to each other The proposton s proven by countng, under both defntons, the number of losses that are not notceable and subtract them from the total number of losses In the analyss we analyze the system under the assumpton of steady state Thus, for a sesson of M pacets we have: lm NL ( (5 M ( ( M M That s, the equals the steady state probablty that a pacet s a notceable loss In order to conduct a meanngful comparson n scenaros where multple sessons are nvolved, we wll evaluate the average taen over the N sessons, denoted ( N, N C Independent Multple-aths over pacet swtched networs The constructon of parallel paths can be acheved by usng parallel paths n MLS networs, usng Source Routng, constructng statc parallel routes n the I networ or any other way, as dscussed n [] and [] 5 Moreover parallel paths exst de-facto n today s networs va the mult-homng connectvty approach, where load-balancng devces dsperse traffc to parallel routes We wll assume that the losses on the dfferent paths are ndependent of each other Ths s lely to occur f the paths are fully dsont or f at least the nosy, n terms of loss and delay, components of the dfferent paths are dsont Theoretcally speang, ths assumpton can hold n a multhomng envronment n the Internet as well acets n the Internet usually cross only a few managed networs on the way to destnaton Hence, t mght be enough for the frst doman to dsperse the pacets between two dfferent managed networs to acheve the effect of dsperson over ndependent parallel paths 4 Note that the Consecutve Loss Factor (CLF, mentoned n [5], s a specal case of the metrcs 5 The constructon of ndependent parallel paths mght be problematc n the Internet, but feasble n managed networs

4 The destnaton endpont, n VoI applcatons, must be able to receve and synchronze pacets arrvng from parallel paths and manage the tter-buffer optmally n order to reduce delay to mnmum and handle out-of-order pacets (whch may be very common f the paths are not of equal delay In our model we assume that parallel paths have small delay dfferences n comparson to the allowed bufferng delay Ths assumpton can hold for many networ scenaros In applcatons where large bufferng s allowed, such as one-way vdeo or voce streamng, the gap n delay may be unmportant and compensated for by ncreased tter-buffer For nteractve applcatons that demand quc response (eg phone-call only small bufferng s allowed, up to few tenths of mllseconds, and choosng elgble set of paths s crucal D Modelng ath Loss Losses at the applcaton level are caused both by the I networ losses and by networ delays In ths study, we model the applcaton loss, regardless the source of the loss (networ loss or networ delay 6 Internet loss models have been studed n many studes, such as [3][4] Here we are focusng on modelng the losses experenced by VoI applcatons For ths matter we loo at these applcatons as constant pacet rate applcatons We assume that tme s dvded nto tme slots 7 At each tme slce t, a pacet s sent by the applcaton For clarty, n the analyss we refer to the pacet sent at tme slce t as pacet t Thus the loss model, expresses the loss experenced by the applcaton We also assume that the traffc tself does not affect the loss model over the paths We wll focus on a Bernoull loss model to model memory-less losses (Secton III and the Glbert loss model to model bursty losses (Secton IV The Glbert loss model s used n many studes to model the bursty loss behavor n the Internet Ths bursty loss behavor has been shown to arse from the drop-tal queung dscplnes mplemented n many Internet routers E Dsperson strateges acet dsperson can be mplemented through a varety of strateges, of whch we focus the followng: Determnstc schedulng dsperson a erodc dsperson sesson pacets are dspersed n a perodc schedule manner over the routes repeatedly For example, f the schedule s (,,,, then n every cycle 3 pacets n a row are sent over path p, and then the followng two pacets are sent over path p, where ths schedule repeats cyclcally b Determnstc round robn dsperson a specal case of perodc dsperson where pacets are sent n a round robn fashon (cyclc schedule over the paths Random pacet dsperson for each pacet of the sesson, the dspersng devce pcs randomly one of the paths leadng to the destnaton and sends the pacet over t The tradtonal delvery of pacets over a sngle path s referred to as a no-dsperson strategy We wll assume that the pacet dsperson strateges are executed n sesson context 8 III ERFORMANCE ANALYSIS UNDER BERNOULLI LOSS MODEL The am of ths secton s to evaluate the effect that pacet dsperson has on applcaton performance, where the networ paths experence Bernoull (memory-less losses, that s, each pacet t shpped over path, has the probablty of L to be lost To ths end we evaluate the for sessons traversng a sngle or multple paths, for a varety of pacet dsperson strateges We wll consder stuatons, whch possbly consst of N streams, denoted s LsN, and possbly are routed over parallel paths, denoted p L p A The under No-Dsperson From the defnton of notceable loss n Eq (4, the probablty for pacet to be counted as a notceable loss s gven by: r[ NL ( ] (6 r[ l( ] r[ l(, l( + 0,, l( + 0] As we do the analyss under the Bernoull (memory-less loss model: r[ NL ( x] r[ NL ( + t x] t, x {0,} Thus, under steady state we may defne lmt NL lm NL ( and Eq (5 translates to: ( NL as the r[ ], (7 NL whch s the probablty for an arbtrary pacet n the sesson to be counted as notceable loss Below we assume that each sesson s drected over a sngle path (no-dsperson strategy Based on (7, the, when the system s under steady state, experenced by sesson s sent over p s: r[ NL ] L L ( L (8 Now, assumng that each sesson taes a sngle path, the ( expected networ for the N sessons,, s then smply calculated by averagng the N sessons B The Under erodc acet Dsperson In perodc dsperson, pacets of sesson s are dspersed over the paths accordng to a fxed polcy Consder a perodc 6 Roughly, we may say the pacets delayed beyond 50ms are consdered lost 7 Usually n duraton of 0 to 30 mllseconds n VoI applcatons 8 Ths assumpton s not mandatory snce random dsperson or perodc dsperson of all pacets, regardless of the applcaton, wll lead n many cases to the same results

5 dsperson polcy Q, wth perod length K The polcy s defned by Q ( ( Q( { } and ( K, meanng that pacet n the perod wll always be sent on p Q( perodcally Thus, the path taen for pacet t, wthout loss of generalty, s p Q(( t mod K + The for sesson s, startng at an arbtrary locaton of the perod s then: K L K ( L + + Q(( mod K, (9 where L s the loss probablty over the path p taen by the sesson For smplcty of presentaton consder perodc dsperson where the perod length s a whole multple of ( + Gven the perodc dsperson selected, let c, ( c, and assume c, s an nteger denote the fracton of pacets belongng to sesson s that are sent on path p, The experenced by sesson s s: c,, ( c L ( ( L (0 Note that the experenced by s s not affected by sesson s Therefore, the expected average for N sessons over routes s then gven by: N c ( c, L ( ( L, N ( Under lmted resources (eg the total capacty of paths equals or approxmately equals to the requred sessons payload, perodc dsperson can be used for QoS purposes by spreadng the sessons n a way that as many sessons as possble wll meet ther QoS requrements Fndng the optmal perodc dsperson assgnment s a problem left for further study C The Under Random Dsperson In random dsperson the decson regardng over whch path to send pacet t of sesson s, s done n a random fashon Let ρ ( ρ denote the probablty that,, pacets of s are sent on path sesson s s then gven by: p The experenced by Under the random dsperson strategy we assume that the path selecton of one sesson s ndependent of that of another sesson Under ths settng the loss experenced by the t th pacet of s s ndependent of the loss experenced by the t th pacet of s Further, the loss of the (t+ st pacet s ndependent of the loss of the t th pacet The average over all sessons s then: where N N ( L ( ( L L ρ L, (3 The Under Random Dsperson wth Lmted Resources Consder random dsperson where the system resources are lmted That s, the combned paths capacty equals, or approxmately equals, to the sessons payload Thus, the of sesson s s dependent on the of sesson s through the sharng of the resources Consder the case of N sessons and paths havng together the capacty to carry exactly N sessons For smplcty assume that <N The source endpont can choose N one of possble dsperson combnatons for assgnng sessons over the paths The formulaton s smlar to that gven n Eq ( where: ρ, and, equals to the N number of sessons wthn the capacty of path p The observed by each sesson depends only on the loss probabltes of the paths t travels over, and s smlar to the case of random dsperson Note that the of sesson s depends on the of sesson s But ths dependency s taen nto account n the calculaton of ρ, Once ρ, s set, ths model s completely smlar to the observed n the random dsperson model wthout any path capacty lmtatons To demonstrate how the transmsson probabltes can be set, consder two sessons s and s, and two parallel paths p and p, each wth the capacty of one sesson There are two possble combnatons for sendng the pacets: Send s over p and s over p, and Send s over p and s over p To meet the obectve of sendng a fracton ρ, pacets of s over p and ρ, over p (wth complement probabltes for s, the frst dsperson combnaton should be assgned probablty of ρ, ρ ρ, L ρ, L ( D Comparson of Dsperson Strateges under Bernoull loss model Clearly, f there are no capacty lmtatons t would always be better to send all the traffc over the best path usng the nodsperson strategy The comparson of strateges under the

6 Bernoull loss model s thus sgnfcant under lmted path resources and provdes nsght to the queston of whch dsperson strategy to mplemented by load-balancng devces for VoI sessons For the sae of presentaton, we wll present the tradeoffs between the strateges under the scenaro of two sessons that need to be delvered over two parallel paths wth lmted resources (for smplcty consder capacty of sngle sesson on ( each path We wll compare the average,, observed by the sessons Equal Qualty paths Corollary : For equal loss rate over the paths, L L L L N, all dsperson strateges provde the same Ths mples that under the Bernoull loss model, dspersng pacets over paths wth smlar random loss probabltes has no affect on the VoI qualty From the practcal pont of vew, under no capacty lmtatons, the use of pacet dsperson n a mult-path envronment s undesrable due to the possble effects of delay varaton, pacet out-of-order events, etc Random and erodc Dsperson vs No-Dsperson The form of the expresson of of a sngle sesson, under random dsperson s dentcal to that of under nodsperson, where the loss parameter L s replaced by the average loss experenced by sesson s, L Ths means that random dsperson n practce averages out the loss over all paths For meanngful comparson one should compare the average (averaged over multple sessons Fgure dfference between random dsperson and no- dsperson for Fgure dfference between perodc round robn dsperson and nodsperson for The dfference n average (for the two sesson system two path system between random dsperson and nodsperson, for, s presented n Fgure Random dsperson s superor, n ths scenaro, to no-dsperson f one of the paths experences low loss rate whle the other experences very hgh loss rate and can sgnfcantly reduce the (n up to 3% However, f the paths experence very hgh loss rate (non-dentcal the no-dsperson strategy becomes superor The reason s that dspersng the sesson ncreases the probablty for losses over the better path to be counted as notceable Comparng the perodc round robn dsperson and nodsperson brngs to smlar results as presented n Fgure Under the same condtons (two sessons to be sent over two paths wth lmted resources we present the followng queston: Under what values of, determnstc round robn pacet dsperson s superor to no-dsperson By comparng ( under no-dsperson (calculated as the averaged over the sessons (9 to (, we may compute the values of for whch determnstc round robn dsperson s superor to no-dsperson Ths result, as functon of the path loss rates, s gven by: log( L / L < log( L / L log( L / L > log( L / L for for L L L L (4 In Fgure 3 the regon above the plane represents the values of for whch no-dsperson s superor and the regon below the plane represents superorty of round-robn dsperson Note that for most practcal stuatons, that s, f loss probabltes on both paths are lower than 5%, perodc dsperson s superor for all practcal ranges of 3 Further, perodc dsperson s superor also for loss probablty between 5% and 0%, for any < 8 The Fgure also demonstrates (as mentoned n Corollary that for equal paths the s equal

7 Fgure 3 Comparson of round robn pacet dsperson and nodsperson: Above plane no-dsperson s superor; below plane dsperson s superor For two paths the gan of perodc and random dsperson over no-dsperson decreases once becomes larger (eg 0 However, for such values of the gan may agan ncrease f the number of paths ncreases Fgures of these results are provded n [4] We thus conclude that both perodc and random dsperson can reduce the average n many scenaros and thus mprove qualty n comparson to the tradtonal nodsperson 3 The Superorty of Random Dsperson over erodc Dsperson Corollary : Random dsperson results n lower than perodc dsperson (where the perod length s a multple of + acheved under smlar condtons Gven a perodc dsperson one can always produce a random dsperson that results n lower Consder random dsperson and perodc dsperson where c, ρ, Ths means that the random dsperson sends on average the same fracton of pacets belongng to sesson s over path p By comparng ( to (3, random dsperson results n lower snce: ( L c, < c, L (5 where L L Note that (5 holds snce the arthmetc weghed average s always greater than the geometrc weghted average when c (see [9], Fgure 4 demonstrates the reducton of by random dsperson n comparson to perodc dsperson, when two sessons are sent over two paths and The gan grows when the dfference n loss rates between the paths ncreases Fgure 4 dfference between random dsperson and perodc dsperson for IV BURSTY LOSSES THE UNDER THE GILBERT LOSS MODEL The am of ths secton s to evaluate the effect that pacet dsperson has on VoI performance To ths end we evaluate the for sessons traversng a sngle or multple paths that are subect to bursty losses, for a varety of pacet dsperson strateges Intutvely speang, pacet dsperson can reduce and thus mprove voce qualty, especally over paths sufferng bursty losses, snce dsperson s expected to spread the losses We wll use the Glbert loss model to model the bursty losses over the paths We wll consder a general stuaton n whch N streams, denoted s Ls N, are possbly routed over parallel paths, denoted p L p A The Glbert loss Model A Two States Marov Chan The loss probablty as expressed n the Bernoull model, s a basc parameter that affects the performance of VoI applcatons However, t s nsuffcent n capturng loss burstness whch s hghly mportant for these applcatons The Glbert model allows one to express hstory-dependent losses and thus to capture loss burstness Ths model has been used n many studes to characterze bursty loss n the Internet [3][][5] The model uses a two-state Marov chan to represent the pacet losses We consder a dscrete tme model where the tme unt corresponds to pacet transmsson for path p Let S ( t denote the state of the path at tme t We assume that t 0, L,, where B stands for Bad and G stands Good The states of the path, S ( t are governed by a Marov chan depcted n Fgure 5: Fgure 5 The Glbert channel loss model

8 When the path s n state G(B t s subect to Bernoull loss at rate ( 9 Consderng path p we have: G B r[ pacet t s lost over p S ( t G], G r[ pacet t s lost over p S ( t B] (6 B Clearly G < B To put ths n matrx notaton let state represent G and state represent B, and let Α be the state transton matrx for path p, that s Α ( m, n r[ S ( t n S ( t m] Then we have: α α Α Let π denote the steady β β state probablty vector, of path p Let B be a vector representng the loss probablty G condtoned on the path state, that s B Also let B 0 l and B l B Note that the Bernoull loss model can be represented by specal cases of ths model, such as B The Under Varous Dsperson Strateges We start our analyss by frst studyng the as observed over a sngle path Let L (t be a random varable denotng the event of loss or success at tme t on path p Let l (t be the actual event occurrng at t on p, l ( t {0,, φ} where denotes loss, 0 denotes success and φ denotes ether loss or success (a don t care 0 Let E ( t, n ( L ( t, L, L ( t + n For a partcular event sequence ( l ( t, L, l ( t + n we want to compute r[ E ( t, n ( l ( t, L, l ( t + n ], whch s done n the next theorem Theorem : Let ( l ( t, L, l ( t + n be an arbtrary success/loss sequence where l ( {0,, φ} t t + n Assume that the state probabltes at t- are gven by π ( t Then: 9 In many studes, such as [], the values G 0 and B are used, whch leads to modelng bursts of consecutve losses 0 The actual event of cause s ether 0 or The φ event s modeled for cases where we do not care for the actual outcome of (t l G B r[ E ( t, n ( l ( t, L, l ( t + n ] n l ( t + (7 T π ( t Α l 0 Α B f l ( t + ' ' where l ( t 0 Α + Α B f l ( t + '0', Α f l ( t + ' φ' α α, G 0 B 0, B Ι B, and where β β 0 Α B T π ( t denotes the transpose of the state probablty vector at tme t- For lac of space we omt the proof, whch can be found n [4] l ( Note that Α denotes the matrx of probabltes where: l ( Α ( m, n r[ L ( l ( S ( n S ( m] th That s, the ( m, n entry s the probablty for the Marov chan to transt from S ( to S ( and for pacet to be a loss/success/don t care, based on the value of l ( Remar : One should note the low complexty for computng (Eq (7 Despte the fact that the number of possble sequences s exponental n n, the specal form of Eq (7 allows one to compute the probablty of E ( t, n n lnear tme n n The under the no-dsperson Based on (6 and assumng that the state probablty at t- T s gven by π ( t, we may now compute the notceable loss rate for sesson s delvered over path p (based on the defnton n (4: r[ NL ( t ] r[ l ( t ] r[ l ( t, l ( t+ 0, L, l ( t+ 0] π Α Α ( T T 0 ( t B - π ( t l (8 When the system s under steady state we substtute π ( t, by π lm π( t The notceable loss rate, t gven by: T T r[ ] π -π NL B Α from whch the average over N sessons, follows ( 0 ( Α, s then l,(9 (, readly The Under erodc acet Dsperson The analyss of the under perodc dsperson polcy s based on calculatng the of a sesson vstng paths accordng to the specfc perodc dsperson polcy To

9 calculate ths properly, the states n the Marov chan on each of the paths must be accounted for One should note that a straghtforward analyss of the path system may requre usng a dmensonal state space, wth computatonal complexty exponental n However, our analyss shows that the problem s decomposable and thus the computatonal complexty s only lnear n The overall computatonal complexty s only: O ( K, where K s the determnstc perod lenght Full analyss of the under perodc dsperson polcy can be found n [4] For the sae of presentaton, we demonstrate the methodology descrbed n [4], on the specal case of roundrobn dsperson We assume a smple round robn dsperson polcy conducted over two paths p and p, n whch the odd pacets are sent over p and the even pacets are sent over p Wrtng the probabltes mplctly, gven the ntal state probablty vectors on the paths, π ( t and π ( t, we have: r[ NL ( t ] r[sesson starts at p] r[ l( t ] / r[ E( t, + (, ( φ,0 r[ E ( t, + (( φ,0 + r[sesson starts at p ] r[ l ( t ] / r[ E ( t, + (, ( φ,0 r[ E( t, + (( φ,0 / /, φ] (0, φ] / where φ stands for a don t care and ( φ,0 stands for a sequence of / don t cares and pacet arrvals The for the system, assumng steady state and even, s then: T π B T + π B T π Α T π Α 0 / ( T 0 Α Α l π ( Α Α / ( T 0 / Α Α ( l π Α Α l 0 / l ( Note that the events E( and E ( n Eq (0, reflect the behavor of the paths p and p respectvely and are ndependent of each other (due to the ndependence of the path behavor Ths leads to the product form n Eq ( The dervaton for odd s smlar 3 The Under Random acet Dsperson In our analyss we assume that the loss models over the paths are ndependent, meanng that the state ( (t on path p s ndependent of the state ( S (t on path p S, at tme t A sesson dspersed over the paths usng the random dsperson strategy, experences losses as f t was delvered over a sngle path wth the underlyng loss model that s the combnaton of loss models over the paths The loss model experenced by the sesson, s characterzed by a Marov chan, and a matchng set of loss probabltes on each state The calculaton of the s then very smlar to that of the no-dsperson calculaton, Eq (9 For the lac of space we omt the full analyss, whch can be found n [4] The computaton complexty of ths analyss s exponental n the number of paths, that s: O ( C Comparson of the Dsperson Strateges Under the Glbert loss model In ths secton we compare the experenced by sessons sent usng varous dsperson strateges over paths experencng bursty losses (followng the Glbert loss model Snce the loss model s affected by four parameters, t s dffcult to present a thorough comparson For smplcty we wll compare paths wth equal characterstcs and wll assume that n all paths G 0 A numercal comparson of paths wth dfferent characterstcs leads to smlar conclusons For a better understandng of the results we present n Fgures 6- plots comparng ratos between the strateges gven In the plots we present the Marov chan parameters n term of T G and T B, whch are the average duraton tme for the chan to be n states G and B, respectvely ( T G / α, T B / β The tme duraton n our model s actually measured n the number of pacets sent n each state (e TG 00 means that 00 pacets are sent on average n state G for pacetzaton perods of 30ms n codecs ths would mean 3 seconds In a thorough examnaton we conducted [4], the cases we examned demonstrate that under a vast range of networ condtons, pacet dsperson, both va random and perodc dsperson, can hghly reduce the n comparson to the tradtonal no-dsperson strategy Only n a very small set of parameter ranges the no-dsperson strategy s superor to dsperson A sample of those cases s gven n Fgures 6-9; n these fgures all the ratos are smaller than, mplyng full superorty of dsperson Smlarly to the results under the Bernoull loss model, Random dsperson s n many cases superor to perodc dsperson, as can be seen n Fgures 0- Fgure 6 rato between random and no-dsperson for T g000 and T b00

10 Fgure 7 rato between random and no-dsperson for T g000 and Fgure rato between random and round robn dsperson for T G000, Remar : In the comparsons we can see that the largest dfferences between the strateges are when 0 The reason for that s that we compare the strateges usng two paths only Clearly, f more paths are used, dsperson wll have greater mpact on qualty even for hgher values of Fgure 8 rato between round robn and no-dsperson for T G000, T B00 Fgure 9 rato between round robn and no-dsperson for T G000, Fgure 0 rato between random and round robn dsperson for T G000 and T B0 V DISCUSSION AND CONCLUSIONS We addressed the factors affectng voce qualty of VoI and focused on pacet loss We proposed the notceable loss rate ( as a metrcs well correlated wth voce qualty for VoI applcatons We studed the effect of pacet dsperson strateges, as performed de-facto by load balancng (multhomng devces or can be mplemented usng other mechansms, on the We conducted ths analyss under the assumpton of Bernoull losses and the Glbert loss model, over the networ paths We showed that under the Bernoull loss model, n many cases the dscussed pacet dsperson strateges could reduce and thus mprove voce qualty We showed that for dentcal paths all dsperson strateges and no-dsperson are equally good and thus pacet dsperson s not recommended We also showed that random dsperson s superor to perodc dsperson (under several assumptons and as such preferred for VoI applcatons We provded mathematcal analyss of the for sessons travelng over paths experencng bursty loss model (Glbert model We provded low complexty expressons for the computaton of the under the dsperson strateges We demonstrated, usng numercal examples, that the effectveness of the varous pacet dsperson strateges strongly depends on the model parameters, and that n many envronments both perodc dsperson and random dsperson can hghly reduce n comparson to the tradtonal routng, where a sngle path s used We observed that as the number of paths used for dsperson grows, the mpact of pacet dsperson ncreases and therefore s recommended n many scenaros The superorty of pacet dsperson mples that ths strategy can mprove VoI applcaton qualty, regardless of how dsperson s realzed, whether by a mult-homng devce located n the networ or by a dedcated dspersng element

11 ntended to mprove qualty Due to ths mprovement t mght be worthwhle to place dspersng devces n the networ Such devces should be located on the path between the sender and the recever and may tae automatc dsperson decsons based on current networ condtons or base on a-pror nowledge gathered by networ management elements REFERENCES [] D G Apostolopoulos Relable vdeo communcaton over lossy pacet networs usng multple state encodng and path dversty In roceedng Vsual Communcaton and Image rocessng, pages , Jan 00 [] E Altman, K Avrachenov, C Baraat, TC n resence of Bursty Losses, roceedngs of ACM SIGMETRICS, Santa Clara, Calforna, June 000 [3] Y Br and N Bloch, Improvng networ performance wth prortzed dspersal [4] J-C Bolot, End-to-end pacet delay and loss behavor n the Internet, In roceedngs of ACM SIGCOMM 93 Conference on Communcatons Archtectures, rotocols and Applcatons, pages 89{98, San Francsco, CA, USA,September 993 [5] Hung Ngo, S Varadaraan and J Srvastava, Error-Spreadng: Reducng Bursty Error n Contnuous Meda streamng, n roceedngs of IEEE Multmeda Systems '99 (ICMCS, vol 999: [6] F Ishza, Study on reducton of total bandwdth requrement by traffc dsperson, roceedngs of Internatonal Conference on ATM and Hgh Speed Internet 00, pp85-89, Seoul, Korea, 00 [7] ITU-T, The E-model, a computatonal model for use n transmsson plannng, recommendaton G07 [8] ITU-T, A hgh qualty low complexty algorthm for pacet loss concealment wth G7, recommendaton G7 Appendx I (999 [9] ITU-T, Obectve qualty assessment of telephone band speech codecs (SQM, recommendaton 86 [0] ITU-T, erceprual Evaluaton of Speech Qualty (ESQ, Recommendaton 86 [] W Jang and H Schulzrnne, Modelng of acet Loss and Delay and Ther Effect on Real-Tme Multmeda Servce Qualty, NOSSDAV 000 aper #7 [] W Jang and H Schulzrnne Comparson and Optmzaton of acet Loss Repar Methods on VoI erceved Qualty under Bursty Loss, NOSSDAV 00 [3] W Jang, H Schulzrnne, erceved Qualty of acet Audo under Bursty Losses, In procedngs of IEEE INFOCOM 00, June 00 [4] R Koodl, R Ravanth One-Way Loss attern Sample Metrcs, etf, draft-etf-ppm-loss-pattern-05txt, 999 [5] Y J Lang, E-G Stenbach and B Grod, Mult-Stream Voce Over I Usng acet ath Dversty, roceedngs IEEE Fourth Worshop on Multmeda Sgnal rocessng, pp , Cannes, France, Oct 00 [6] Y J Lang, E-G Stenbach and B Grod, Real-tme Voce Communcaton over the Internet Usng acet ath Dversty, ACM Multmeda '0, Ottawa, Canada, Oct 00 [7] V Marovs, Smulaton and Analyss of Loss n I networs, Thess, Unversty Sts Cyrl and Methodus, Macedona, October 000 [8] Y Nebat and M Sd, Resequencng Consderatons n arallel Downloads, In roceedngs of IEEE INFOCOM 00, June 00 [9] F Q, J Q Me, D Xa, S Xu, New proofs of weghted power mean nequaltes and monotoncty for generalzed weghted mean values, Mathematcal Inequaltes and Applcatons 3 (000, no3, RGMIA Research Report Collecton (999, no, Artcle 0, 99--0; (999, no4, Artcle 6, [0] J Rosenberg, L Qu, H Schulzrnne, Integratng acet FEC nto Adaptve Voce layout Buffer Algorthms on the Internet, INFOCOM 000 [] D Thaler, C Hopps, Multpath Issues n Uncast and Multcast Next- Hop selecton, RFC99, Novemver 000 [] TIA, Telecommuncatons I Telephony Equpment Voce Qualty Recommendatons for I Telephony N-4689 ( TIA/EIA/TSB6 TIA Engneerng Commttee TR-4 [3] S-J Yang, Traffc Dsperson For Bursty Traffc On Heterogeneous Networs, Master Thess Report, 998, UT Austn [4] HZlatorlov, acet Dsperson and the Qualty of Voce over I Applcatons n I networs, Master thess, School of Computer Scence, Tel-Avv Unversty, May 003