Adptive VoIP Smoothing of Preto Trffic Bsed on Optiml E-Model Qulity Shyh-Fng Hung 1, Eric Hsio-Kung Wu 2, nd Po-Chi Chng 3 1 Deprtment of Electricl Engineering, Ntionl Centrl University, Tiwn hsf@vplb.ee.ncu.edu.tw 2 Deprtment of Computer Science & Informtion Engineering, Ntionl Centrl University, Tiwn hsio@csie.ncu.edu.tw 3 Deprtment of Communiction Engineering, Ntionl Centrl University, Tiwn pcchng@ce.ncu.edu.tw Abstrct. Perceived voice qulity is key metric for VoIP pplictions. It is minly ffected by IP network impirments such s dely, jitter nd pcket loss. Adptive smoothing lgorithms re cpble of djusting dynmiclly the smoothing size by introducing vrible dely bsed on the network dely nd loss prmeters to rchive the best voice qulity. This work formultes n online loss model which incorportes buffer sizes nd introduces n efficient nd fesible perceived qulity method for buffer optimiztion. Distinct from the other optiml smoothers, the proposed optiml smoother suitble for most of codecs crries the lowest complexity. Since the dptive smoothing scheme introduces vrible plybck delys, the buffer re-synchroniztion between the cpture nd the plybck becomes essentil. This work lso presents buffer resynchroniztion lgorithm to prevent uncceptble increse in the buffer overflow. Simultion experiments vlidte tht the proposed dptive smoother rchives significnt improvement in the voice qulity. 1 Introduction The rpid progress of the development of IP-bse network hs enbled numerous pplictions tht deliver not only trditionl dt but lso multimedi informtion in rel time. The next genertion network, like n ALL-IP network, is future trend to integrte ll heterogeneous wired nd wireless networks nd provide semless worldwide mobility. In n All-IP network, one revolution of the new genertion Internet pplictions will relize VoIP services tht people cn tlk freely round through the mobile-phones, the desktops nd VoIP telephones t ny time nd plce. Unfortuntely, the IP-bsed networks do not gurntee the vilble bndwidth nd ssure the constnt dely jitters (i.e., the dely vrince) for rel time pplictions. In other words, individul trnsmission delys for given flow of pckets in network my be continuing to chnge cused by vrying trffic lod nd differing routing pths due to congestions, so tht the pcket network delys for continuous series of intervls (i.e. tlkspursts) t the receiver my not be the sme (i.e. constnt) s the sender. In ddition, pcket dely my introduce by the signl hnd-out or the difference of bndwidth trnsporttion in wireless/fixed networks. Y.-S. Ho nd H.J. Kim (Eds.): PCM 2005, Prt II, LNCS 3768, pp. 747 758, 2005. Springer-Verlg Berlin Heidelberg 2005
748 S.-F. Hung, E.H.-K. Wu, nd P.-C. Chng For dely sensitive pplictions, dominting portion of pcket losses might be likely due to dely constrint. A lte pcket tht rrives fter dely threshold determined by plybck time is treted s lost pcket. A tight dely threshold not only degrdes the qulity of plybck but lso reduces the effective bndwidth becuse lrge frction of delivered pckets re dropped. In fct, dely nd loss re normlly not independent of ech other. In order to reduce the loss impct, number of pplictions utilize n dptive smoothing technique in which buffers re dopted to reduce the qulity dmge cused by loss pckets. However, lrge buffer will introduce excessive end-to-end dely nd deteriorte the multimedi qulity in interctive reltime pplictions. Therefore, trdeoff is required between incresed pcket loss nd buffer dely to chieve stisfctory results for plyout buffer lgorithms. In the pst, the works on the degrdtion of the voice qulity consider the effect of pcket loss, but not tht of pcket dely. Within literture on predicting delys, the use of neurl network models to lern trffic behviors [1] requires reltively high complexity or long lerning period. Therefore, we consider the smoothers [2]-[8] which employ sttisticl network prmeters relted with the voice chrcteristic, i.e. loss, dely nd tlk-spurt tht hve significnt influence to the voice qulity. They detect dely spike in trffic nd quickly clculte the required buffer size to keep the qulity s good s possible. The E-model is computtionl model, stndrdized by ITU-T in G.107, G.109 nd G.113 which uses the vrious trnsmission prmeters to predict the subjective qulity of pcketized voice. Unfortuntely, the E-model is complex to nlyze in the optimiztion process. An lterntive study is to pply simplified E-model, first proposed by R. Cole nd J. Rosenbluth [9], bsed upon observed trnsport mesurements in the VoIP gtewys nd the trnsport pths. Authors indicted the simplified E- model method requires more pttern cses for trces to enhnce the vlidtion. Atzori nd Lobin [10], nd L. Sun nd E. Ifechor [11] proposed to utilize simplified E- model tht considers the loss nd dely together to set dijitter time, which is the optiml plyout dely derived by dynmic progrmming-bsed solution. However, the usbility nd the ccurcy of simplified E-model will be limited by non-typicl trffic ptterns. For perceptul-bsed buffer optimiztion schemes for VoIP, voice qulity is evluted s key metric since it represents user s perceived QoS. However, it requires n efficient nd ccurte objective wy to optimize perceived voice qulity. To consider the well-defined dely nd loss impirments of the E-model, we employ complete E-model for the qulity optimiztion to obtin optiml perceived voice qulity. In pcket switching network, without resynchroniztion scheme, plybck clock with minor frequency error will eventully cuse buffer overflow or n underflow t the receiving end. The overflow pckets re usully discrded due to the finite buffer size nd the rel-time requirement. This discontinuity cused by discrded pckets might crete n unplesnt effect to the plybck qulity becuse the lost pckets could be the importnt prt of the signls. This effect is more serious for udio signls thn video signls becuse humn ers re more sensitive to the continuity of sounds thn humn eyes.
Adptive VoIP Smoothing of Preto Trffic Bsed on Optiml E-Model Qulity 749 The contributions of this pper re three-fold: (i) A new method optimizing voice qulity for VoIP is esily pplied to codecs which were well-defined in the ITU-T E- model. (ii) Different from the other optiml smoothers, our optiml smoother hs the lowest complexity with O ( n). (iii) A fesible scheme is introduced to solve the buffer re-synchroniztion problem. 2 Relted Work The performnces of the proposed plyout pproch re compred with the other pproch. In prticulr, for non-dynmic progrmming-bsed solutions, i.e. the liner filter, Spike Detection (SD) lgorithm [2]-[11] ws referred by most people. A dely spike is defined s sudden nd significnt increse of network dely in short period often less thn one round-trip. This lgorithm djusts the smoothing size, i.e. plybck dely, t the beginning of ech tlk-spurt. The results of this lgorithm re therefore compred to the results obtined herein. The SD Algorithm in [2] estimtes the plyout time p i of the first pcket in tlk- v for pcket i s spurt from the men network dely d i nd the vrince i p i = ti + di + γ vi (1) where t i represents the time t which pcket i is generted t the sending host nd γ is constnt fctor used to set the plyout time to be fr enough beyond the dely estimte such tht only smll frction of the rriving pckets could be lost due to lte rrivl. The vlue of γ = 4 is used in simultions [3]. The estimtes re recomputed ech time pcket rrives, but only pplied when new tlk-spurt is initited. The men network dely d i nd vrince v i re clculted bsed on liner recursive filter chrcterized by the fctors α nd β. If ni > d If ni d i-1 i-1 di = βd vi = βvi di = αd vi = αvi i 1 1 i 1 1 + (1 β)n + (1 β)d + (1 α)n + (1 α)d i 1 i i i 1 n n i i (SPIKE_MODE) Where n i is the totl dely introduced by the network nd typicl vlues of α nd β re 0.998002 nd 0.75 [3], respectively. The decision to select α or β is bsed on the current dely condition. The condition n i > d i 1 represents network congestion (SPIKE_MODE) nd the weight β is used to emphsize the current network dely. On the other hnd, n i d i 1 represents network trffic is stble, nd α is used to emphsize the long-term verge. In estimting the dely nd vrince, the SD Algorithm uses only two vlues α nd β tht re simple but my not be dequte, prticulrly when the trffic is (2)
750 S.-F. Hung, E.H.-K. Wu, nd P.-C. Chng unstble. For exmple, n under-estimted problem is when network becomes spiked, but the dely n i is just below the d i 1, the SD Algorithm will judge the network to be stble nd will not enter the SIPKE_MODE. 3 Adptive Smoother with Optiml Dely-Loss Trde off The proposed optiml smoother is derived using the E-model to trde off the dely nd loss. This method involves, first, building the trffic dely model nd the loss model. Second, the dely nd loss impirments of the E-model re clculted ccording to the dely nd the loss models. Third, the E-model rnk R is mximized nd thus the dely nd loss optimized solution is obtined. In this study, voice pckets re ssumed to be generted t constnt pcket rte. Current voice codecs used in stndrd VOIP (H.323 or SIP) systems, e.g., G.711, G.723.1 nd G.729, generlly fit this ssumption lthough the pcket size my be different when the voice is inctive. 3.1 E-Model Description In the E-model, rting fctor R represents voice qulity nd considers relevnt trnsmission prmeters for the considered connection. It is defined in [12] s: R = Ro Is Id Ie _eff + A Ro denotes the bsic signl-to-noise rtio, which is derived from the sum of different noise sources which contin circuit noise nd room noise, send nd receive loudness rtings. Is denotes the sum of ll impirments ssocited with the voice signl, which is derived from the incorrect loudness level, non-optimum sidetone nd quntizing distortion. Id represents the impirments due to dely of voice signls, tht is the sum of Tlker Echo dely (Idte), Listener Echo dely (Idle) nd end-to-end dely (Idd). Ie _ eff denotes the equipment impirments, depending on the low bit rte codecs (Ie, Bpl) nd pcket loss (Ppl) levels. Finlly, the dvntge fctor A is no reltion to ll other trnsmission prmeters. The use of fctor A in specific ppliction is left to the designer s decision. 3.2 The Dely nd Loss Models in E-Model For perceived buffer design, it is criticl to understnd the dely distribution modeling s it is directly relted to buffer loss. The multimedi chrcteristics of pcket trnsmission dely over Internet cn be suggested by sttisticl models which follow Preto distribution for Internet pckets (for n UDP trffic) hs been shown to consistent with Preto distribution [13][14]. In order to derive n online loss model, the pcket end-to-end dely is ssumed s Preto distribution with prmeter nd k t the receiving end for multimedi trffic. The CDF of the dely distribution F ( t ) cn lso be represented by [13][15] (3)
Adptive VoIP Smoothing of Preto Trffic Bsed on Optiml E-Model Qulity 751 where F( t ) k = 1, t for t k k = min xi nd i = 1 = n xi n log i k 1 (4) nd the PDF of the dely distribution f (t ) is df( t ) k f ( t ) = =, for t k (5) dt +1 t In rel-time ppliction, pcket loss tht is solely cused by extr dely cn be derived from the dely model f (t ). Figure 1 plots the dely function f (t ), which shows tht when the pcket dely exceeds the smoothing time; the delyed pcket is regrded s lost pcket. The loss function l(tb ) cn be derived from Fig. 1 s ( t ) l b = k f ( t )dt = t + 1 b t = t b From Eqs. (5) nd (6), we obtin the dely nd loss functions tht will be used in dely nd loss impirments of the E-model. k t b (6) f (t) Smoothing time t b Loss t b Dely t 3.3 Optimiztion on E-Model Fig. 1. The reltion of smoothing dely nd loss The dely nd loss fctors over trnsmission hve greter impcts to the voice qulity thn the environments or equipments. To simplify the optimiztion complexity, we mke ssumptions in communiction connection s the following: (i). The circuit noise, room noise nd terminte signls will not chnge. ( Ro nd Is re fixed). (ii). An echo dely in the Sender/Receiver will not chnge. (Idte nd Idle re fixed). (iii). A codec will not chnge (Ie is fixed). In [12], R is rewritten s Eq. (7) ( Ro Is Idte Idle + A) Idd Ie _ eff R = (7)
752 S.-F. Hung, E.H.-K. Wu, nd P.-C. Chng where Idd is pproximted by 1 1 6 6 6 ( ) = 25 1+ 6 X Idd X 3 1+ + 2, 3 T ln 100 X =, ln when T > 100 ms nd Idd =0 when T 100, ( 2) (8) nd Ie _ eff = Ie + 95 ( Ie) Ppl Ppl + Bpl Fctors Ie nd Bpl re defined in [16] nd T is one-wy bsolute dely for echofree connections. Due to the three ssumptions bove, the optimiztion process cn be concentrted on the prmeters of Idd nd Ie_eff. Eq. (7) is derived to yield Eq. (10) 1 R = Cons tn t 25 95 3 1 6 X 6 ( X ) 1+ 6 3 1+ + 2 ( Ie) Ppl Ppl + Bpl 6, when t > 100 ms k According to Eq. (6), the loss probbility of smoothing time t is Ppl =, so t the solutions for t re difficult to get directly from Eq. (10) since it contins the complex polynomil nd exponentil function. Therefore, some reserches employ dynmic progrmming tools tht need lrge of computing procedures, like MATLAB, to clculte n optiml solution. Owing to simplify lrge quntity of computtions nd solve the best smoothing time t, we consider the following three conditions. (i). In Eq. (8), when the smoothing time t 100 ms, Idd is zero (no dely impirment). It implies smoother should set the minimum smoothing dely to 100 ms to prevent the most pcket loss. (ii). The mximum end-to-end dely of 250 ms is cceptble for most user pplictions to prevent serious voice qulity destruction. (iii). For common low bit rte codec, like G.723.1 nd G.729, the frme rte is fixed. Bsed on fixed frme rte of vrious codec i, denodes s fr i, we cn nlyze some cses, t1 = ( 100 + fri )ms, t2 = ( 100 + fri 2)ms,, tn = ( 100 + fri n)ms, nd t n should less thn the mximum cceptble dely 250 ms to clculte the correspondence, R 1, R 2,, R n, by the numericl nlysis in Eq. (10) nd n error is less thn 0.001. Here we cn find mximum R m { R 1, R 2, L, R n } by computing the n = times to obtin the op- 250 100 fr i timl smoothing buffer size. The optiml smoothing buffer size will be clculted s 100 + m fr i ms to keep the optiml voice qulity. (9) (10)
Adptive VoIP Smoothing of Preto Trffic Bsed on Optiml E-Model Qulity 753 4 Buffer Re-synchroniztion A necessry condition tht smoother cn work correctly is the synchroniztion between the cpture nd the plybck. This section proposes buffer re-synchroniztion mchine (BRM) to help synchroniztion nd the clock drift nlysis of resynchroniztion to vlidte the effectiveness. 4.1 Buffer Re-synchroniztion Mchine This work proposes synchroniztion scheme tht segments udio signls by detecting silences. The mismtch between the cpture nd the plybck clocks is solved by skipping silences t the receiving end. The durtion of the silent period my be shortened negligibly degrding the qulity of plybck. An ctive pcket contins voicecompressed dt, wheres silent pcket does not. Skipping some silent pckets will not significntly degrde the qulity of the voice, but cn efficiently prevent the buffer from overflowing. Notbly, k (could be djusted) continuous silent pckets could be utilized to seprte different tlkspurts. S Buffer<b Init A Smooth Buffer>=b A Skip A or Number of S <= k Ply Number of S > k S Fig. 2. Buffer Re-synchroniztion Mchine Figure 2 depicts the buffer re-synchroniztion lgorithm. Init-stte, Smooth-stte, Ply-stte nd Skip-stte re used to represent the voice conference initiling, the buffer smoothing, the buffer plying out, nd the silent pckets skipping, respectively, nd A nd S represents n ctive pcket nd silent pcket, respectively. In the Init-stte the buffer wits for the first rriving pckets to initilize voice conference. If Init-stte receives n S, it stys in Init-stte; otherwise when n A is received, the Smooth-stte is ctivted to smooth the pckets. In the Smooth-stte, the smoothing time b is computed by pplying the optiml dptive smoother lgorithm dynmiclly. When the buffer smoothing time is over b, the Ply-stte is ctivted; otherwise it stys in Smooth-stte for smoothing. In the Ply-Stte the pcket is
754 S.-F. Hung, E.H.-K. Wu, nd P.-C. Chng fetched from the buffer nd plyed out. In fetching process, when it encounters three consecutive S pckets, implying tht the tlk-spurt cn be ended, the buffer resynchroniztion procedure then switches to the Skip-stte. In the Skip-stte, if A is fetched from buffer, it mens the new tlk-spurt hs begun, nd then it skips remined silent pckets in the buffer, nd switches to the Smooth-stte to smooth the next tlkspurt. Otherwise, if S is fetched from buffer, it implies current tlk-spurt is not ended nd will be decoded to ply out t the sme stte. With the bove four-stte mchine, the smoother cn smooth the pckets t the beginning of the tlkspurt to void buffer underflow in the Smooth-stte nd skip the silent pckets t the end of the tlkspurt to prevent the overflow in the Skip-stte. 4.2 Effectiveness of Re-synchroniztion To demonstrte the effectiveness of re-synchroniztion mchine for buffer overflow, we nlyze the clock inconsistence constrint s the following. C s nd C r represent the sender clock (frme/sec) nd the receiver clock, respectively, nd M nd M s denote the men ctive pckets nd men silent pckets in tlkspurt, respectively. The buffer overflow cused by the clock inconsistence (difference) will occur when C s is lrge thn C r condition. Cs Cr, the difference vlue by subtrcting the receiver clock from the sender clock, represents the positive clock drift between the sender nd the receiver. Therefore, ( Cs Cr ) (( M + M s ) frme _time) represents the men extr buffer size cused by the positive clock drift for men tlkspurt time. In order to distinguish the consecutive tlkspurts, t lese k silent pckets re utilized. Therefore, the smoother hs M s k silent pckets to be skipped nd resynchronizes with the following tlkspurt. When the re-synchroniztion mchine stisfies ( C C ) (( M + M ) frme _ time) ( M k) s r s s, (12) the buffer overflow cuse by the positive clock drift will not occur. 5 Simultion 5.1 Simultion Configurtion A set of simultion experiments re performed to evlute the effectiveness of the proposed dptive smoothing scheme. The OPNET simultion tools re dopted to trce the voice trffic trnsported between two different LANs for VoIP environment. Ninety personl computers with G.729 trffics re deployed in ech LAN. The durtion nd frequency of the connection time of the personl computers follow Poisson distributions. A six-hour simultion ws run to probe the bckbone network dely ptterns, which were used to trce the dptive smoothers nd compre the effects of the originl with the dpted voice qulity.
Adptive VoIP Smoothing of Preto Trffic Bsed on Optiml E-Model Qulity 755 PC PC PC Router T1 Router PC PC PC Fig. 3. The simultion environment of VoIP Tble 1. Simultion prmeters Attribute Vlue Numbers of PC in one LAN 90 PCs Codec G.729 Bckbone T1 (1.544 Mps) LAN 100 Mbps Propgtion dely Constnt Router buffer Infinite Pcket size 50 bytes 0.016 600 0.012 dely (ms) 400 Vrince 0.008 200 0.004 0 0 0 1000 2000 3000 4000 Pcket Number () The dely of trffic 0 10 20 30 40 Tlk Spurt (b) The vrince of trffic Fig. 4. VoIP trffic pttern
756 S.-F. Hung, E.H.-K. Wu, nd P.-C. Chng Figure 3 shows the typicl network topology in which T1 (1.544 Mbps) bckbone connects two LANs, nd 100 Mbps lines re connected within ech LAN. The propgtion dely of ll links is ssumed to be constnt vlue nd will be ignored (the derivtive vlue will be zero) in the optimiztion process. The buffer size of the bottlenecked router is ssumed to be infinite since the pcket loss in router buffer is not considered in the performnce comprison of dptive smoothers. The network endto-end dely for the G.729 trffic with dt frme size (10 bytes) nd RTP/UDP/IP heders (40 bytes) is mesured for six hours by employing the OPNET simultion network. Tble 1 summrizes the simultion prmeters. Figure 4() nd 4(b) plot the end-to-end trffic dely ptterns nd the corresponding dely vrinces for VoIP trffic observed t given receiver. The results vlidte tht individul trnsmission delys for given G.729 flow of pckets in network re continuing to chnge cused by vrying trffic lod; therefore, the rrivl pcket rtes for continuous series of intervls (i.e. tlkspursts) t the receiver re not constnt ny more s the sender. 5.2 Voice Qulity in Smoothers The test sequence is smpled t 8 khz, 23.44 seconds long, nd includes English nd Mndrin sentences spoken by mle nd femle. Fig. 5 lists the E-mode score R of the voice qulity. It shows tht the optiml method hs the significnt improvement in the voice qulity over SD smoother, becuse our proposed optiml smoother truly optimizes with the dely nd loss impirments in trnsmission plnning of the E-model. 100 Rnk of E-model (score) 80 60 40 20 0 Smoothers SD Optiml 0 10 20 30 40 Number of Tlkspurt Fig. 5. The qulity scores of smoothers 5.3 Re-synchroniztion Effectiveness for the Positive Clock Drift A listening evlution experiment ws performed to nlyze the required proper number of silent pckets to segment the consecutive tlk-spurts well. It ws found in our experiments tht t lest three silent pckets (e.q. 10 ms per pcket in G.729) re required to seprte tlkspurts. We nlyze the G.729 voice sources used in our experiments nd find the percentge of the men ctive nd men silent segment length in tlkspurt re 0.51 nd 0.49 respectively, nd the mximum tlkspurt length is 257 pckets. k=3 is dopted to
Adptive VoIP Smoothing of Preto Trffic Bsed on Optiml E-Model Qulity 757 segment the consecutive tlkspurt. From the Eq. (12), we cn clculte the effective clock drift between the sender nd the receiver Cs Cr should be less thn or equl 3 to ( 257 0. 49 3) (( 257 ) 10 10 ) = 47. 8 (frme/sec). Normlly, the clock drift will not be over 47.8 (frme/sec) when sender of G.729 trnsmits 100 (frme/sec) to the networks. Consequently, the smoother cn void the buffer overflow well in our cse. 6 Conclusion This rticle proposes n dptive smoothing lgorithm tht utilizes the complete E-model to optimize the smoothing size to obtin the best voice qulity. The buffer re-synchroniztion lgorithm is lso proposed to prevent buffer overflow by skipping some silent pckets of the til of tlk-spurts. It cn efficiently solve the mismtch between the cpture nd the plybck clocks. Numericl results hve shown tht our proposed method cn get significnt improvements in the voice qulity which blnces the trget dely nd loss. References [1] Tien P. L., Yung M. C.: Intelligent voice smoother for silence-suppressed voice over internet. IEEE JSAC, Vol. 17, No. 1. (1999) 29-41 [2] Rmjee R., Kurise J., Towsley D., Schulzrinne H.: Adptive plyout mechnisms for pcketized udio pplictions in wide-re networks. Proc. IEEE INFOCOM. (1994) 680-686 [3] Jeske D. R., Mtrgi W., Smdi B.: Adptive ply-out lgorithms for voice pckets. Proc. IEEE Conf. on Commun., Vol. 3. (2001) 775-779 [4] Pinto J., Christensen K. J.: An lgorithm for plyout of pcket voice bsed on dptive djustment of tlkspurt silence periods. Proc. IEEE Conf. on Locl Computer Networks. (1999) 224-231 [5] Ling Y. J., Frber N., Girod B.,: Adptive plyout scheduling using time-scle modifiction in pcket voice communictions. Proc. IEEE Conf. on Acoustics, Speech, nd Signl Processing, Vol. 3. (2001) 1445-1448 [6] Knsl A., Krndikr A.: Adptive dely estimtion for low jitter udio over Internet. IEEE GLOBECOM, Vol. 4. (2001) 2591-2595 [7] Anndkumr A. K., McCree A., Pksoy E.: An dptive voice plyout method for VOP pplictions. IEEE GLOBECOM, Vol. 3. (2001) 1637-1640 [8] DeLeon P., Sreenn C. J.: An Adptive predictor for medi plyout buffering. Proc. IEEE Conf. on Acoustics, Speech, nd Signl Processing, Vol. 6. (1999) 3097-3100 [9] Cole R., Rosenbluth J.: Voice over IP performnce monitoring, Journl on Computer Commun. Review, Vol. 31. (2001) [10] Atzori L., Lobin M.: Speech plyout buffering bsed on simplified version of the ITU-T E-model. IEEE Signl Processing Letters, Vol. 11, Iss 3. (2004) 382-385 [11] Sun L., Ifechor E.: New models for perceived voice qulity prediction nd their pplictions in plyout buffer optimiztion for VoIP networks. Proc. ICC. (2004) [12] ITU-T Recommendtion G.107,: The E-model, Computtionl Model for use in Trnsmission Plnning. (2003)
758 S.-F. Hung, E.H.-K. Wu, nd P.-C. Chng [13] Huebner F., Liu D., Fernndez J. M.: Queueing Performnce Comprsion of Trffic Models for Internet Trffic. GLOBECOM 98, Vol. 1. (1998) 471 476 [14] Fujimoto K., At S., Murt M.: Sttisticl Anlysis of Pcket Delys in the Internet nd its Appliction to Plyout Control for Streming Applictions. IEICE Trns. Commun., Vol. E84-B, No. 6. (2001) 1504-1512 [15] Brzusks V., Serfling R.: Robust nd efficient estimtion of the til index of oneprmeter preto distribution. North Americn Acturil Journl vilble t http://www.utdlls.edu/~serfling. (2000). [16] ITU-T SG12 D.106: Estimtes of Ie nd Bpl for rnge of Codecs. (2003)