Simulation and Modeling of Packet Loss on Self-Similar VoIP Traffic

Transcription

1 Concaon and Manageen n Technologcal Innovaon and Acadec Globalzaon Slaon and Modelng of Pace Loss on Self-Slar VoIP Traffc HOMERO TORAL, JAIME S. ORTEGON, JULIO C. RAMIREZ, LEOPOLDO ESTRADA 3 Deparen of Scences and Engneerng Unversdad De Qnana Roo CHETUMAL, QROO, MÉICO Deparen of Basc Scences and Engneerng Unversdad Del Carbe CANCUN, QROO, MÉICO Deparen of Elecrcal Engneerng 3 Cenro de Invesgacón y Esdos Avanzados del I.P.N GUADALAJARA, JALISCO, MÉICO horal@qroo.x Absrac: - Ths paper nvesgaes he pace loss effecs on he VoIP Jer, and presens a ehodology for slang pace loss on VoIP Jer races h self-slar characerscs. Becase of s splcy and effecveness, he o sae Marov odel or Glber odel s sed o generae pace loss paerns. We proposed a ne odel for self-slar VoIP raffc, hs odel are based on voce raffc easreens, and alloed o relae he Hrs paraeer and pace loss. I s fond ha he relaonshp beeen Hrs paraeer and pace loss obeys a poer-la fncon h hree fed paraeers. Snce a nber of recen sdes have shon ha self-slar IP raffc has negave pac on neor perforance, s poran o consder odels ha capre hs behavor for he desgn and perforance analyss of coper neors. Key-Words: - VoIP, Hrs Paraeer, Pace Loss, Jer, To-Sae Marov Model Inrodcon Voce over IP (VoIP) has eerged as an poran Inerne applcaon and deands src qaly of servce (QoS) levels. Hoever, he crren Inerne only offers bes-effor servces de o s shared nare and canno garanee he QoS, VoIP s sscepble o sffer parens, hch resl n voce qaly degradaon. The QoS level of VoIP applcaons depends on any paraeers; n parclar, delays (fxed and hp://.qroo.x varable) and pace loss rae have an poran pac on voce qaly. These paraeers are coplcaedly relaed o each oher and affec voce qaly. I s dffcl o desgn and confgre every paraeer o op vale and ee voce qaly obecves, hle ananng effcen sage of neor resorces. Therefore s necessary o pleen adeqae raffc odels o evalae he voce qaly. In he lerare, has been shon ha: Pace loss rae s brsy n nare and exhbs a fne eporal dependency [-],.e, he probably of he crren pace beng los s dependen pon heher he pas fe paces have been receved or los. Specfcally, f a los pace s represened by he sybol one and a receved pace by he sybol zero, hen he pace loss process can be odeled as a fne eory bnary rando process,.e., a bnary Marov process [3]. Acal neor raffc s self-slar n nare [4-6]. The fac ha neor raffc exhbs selfslary eans ha s brsy a a de range of e scales. Therefore, self-slar processes are ofen sed for IP raffc odelng. An aracve propery of he self-slar processes s he degree of self-slary, hch s expressed as a fncon of a sngle paraeer, called Hrs paraeer. The an conrbons of hs paper are hreefold: ) An analyss of he pace loss effecs on he VoIP Jer. ) A ehodology for slang pace loss on VoIP Jer races. ISBN:

2 Concaon and Manageen n Technologcal Innovaon and Acadec Globalzaon 3) A ne odel for self-slar VoIP raffc. The paper s organzed as follos. In secon, e provde soe bacgrond on he QoS paraeers of VoIP applcaons. Secon 3 presens he heory of self-slar processes. A ne odel for self-slar VoIP raffc s proposed n secon 4. In secon 5 slaon resls are dscssed. Secon 6 concldes he paper. QoS Paraeers Several paraeers nflencng voce qaly on IP neors ay be expressed n ers of delays and pace loss rae. One ay delay (OWD) and delay Jer are he os crcal paraeers nflencng voce qaly, hogh excessve pace loss rae can draacally decrease he voce qaly perceved by sers of VoIP applcaons.. Jer When paces are ransed fro sorce o desnaon over IP neors, hey ay experence dfferen delays. The Iner-Arrval Te (IAT) of he paces on he recever s no consan even f he pace Iner-Deparre Te (IDT) on he sender sde s consan. As a resl, paces arrve a he desnaon h varyng delays (beeen paces) referred o as Jer. The Jer s calclaed accordng o RFC 3550 [7]. If S s he RTP esap for he pace of sze L, and R s he arrval e n RTP esap ns for pace of sze L. Then for o ay be expressed as: paces and -, J ( L) ( L) R S ) ( R S ) J = ( K K K K, () IAT ( K, K ) = J ( L) + IDT( K, K ) here J ( L), () s he dfference beeen he OWD of o paces, and -; ( K K ) = ( S K S ), K IDT s he ner-deparre e (n or experens, IDT= {0s, 0s, 40s, and 60s}) and IAT ( K K ) = ( R K R ), K s he ner-arrval e or arrval Jer for he paces and -. In he crren conex, s referred o as Jer.. Pace Loss Rae There are o an ranspor proocols sed on IP neors, UDP and TCP. Whle UDP proocol does no allo any recovery of ranssson errors, TCP nclde soe error recovery processes. Hoever, he voce ranssson over TCP connecons s no very realsc. Ths s de o he reqreen for real-e (or near real-e) operaons n os voce relaed applcaons. As a resl, he choce s led o he se of UDP hch nvolves pace loss probles. On he oher hand a nber of sdes have shon ha VoIP pace loss s brsy n nare and exhbs eporal dependency [-]. So, f pace n s los hen norally here s a hgher probably ha pace n + ll also be los. The os generalzed odel o capre eporal dependency, s a fne Marov chan [3]. Becase of s splcy and effecveness, a o sae Marov odel or Glber odel s ofen sed o slae pace loss paerns. Fgre shos he sae dagra of hs -sae Marov odel. Fg.. To-sae Marov odel In hs odel, one of he saes (sae ) represens a pace loss and he oher sae (sae 0) represens he case here paces are correcly ransed or fond. The ranson probables n hs odel, as shon n Fgre, are represened by p and q. In oher ords, p s he probably of gong fro sae 0 o sae, and q s he probably of gong fro sae o sae 0. Dfferen vales of p and q defne dfferen pace loss condons ha can occr on he Inerne. The probably ha n consecve paces are los s gven by p ( q) n. If ( q ) > p, hen he probably of losng a pace s greaer afer havng already los a pace han afer havng sccessflly receved a pace. Ths s generally he case n daa ranssson on he Inerne here pace losses occr as brss. Dfferen vales of p and q represenng dfferen neor condons, ha e are consdered n or experens. ISBN:

3 Concaon and Manageen n Technologcal Innovaon and Acadec Globalzaon In eqaon (3), PLR corresponds o he average pace loss rae and b corresponds o he average brs lengh. p PLR= b=, (3) p+ q q Fro eqaon () can be fond a relaonshp beeen Jer and Pace Loss Rae. If he pace - s los, IAT( K, K ) = J ( L) + IDT, herefore, f n consecve paces are los, hen: IAT ( K, K n ) = J ( L) + ( n+ )( IDT), (4) The eqaon (4) descrbes he pace loss effecs on he VoIP Jer. 3 Self-Slar Processes Traffc processes are sad o be self-slar f ceran propery of he processes s preserved h respec o scalng n space and/or e [4-6]. In hs secon, a bref overve of self-slar processes s gven. Consderng a dscree e sochasc process or e seres = ( ; Ν) h ean µ, varance σ, aocorrelaon fncon r and aocovarance fncon (ACV) γ, 0 ; here can be nerpreed as he raffc vole a e nsance, or Jer. To forlae he phenoenon of scale nvarance, he aggregaed process s defned as ( Ν) ; here seres each er =, (5) () s obaned by averagng he orgnal over non-overlappng blocs of sze, and () s gven by = ; =,,3,..., (6) = ( ) + Here, H ss h selfslary paraeer H,.e. Hrs Paraeer 0 < H < f: s self-slar d H =, (7) here = d denoes eqaly n dsrbon. γ denoe he aocovarance fncon of Le (). The process s called exacly second order self-slar h Hrs paraeer H f H H H γ = σ ( + ) + ( ), (8) for all. s called asypocally second-order self-slar f H σ H H l γ = ( + ) + ( ), (9) Eqaons (8) and (9), express he fac han H and are reqred o have exacly or asypocally he sae second-order srcre. Fro eqaon (7) follos ha H = var σ, (0) Le r = γ σ denoe he aocorrelaon fncon. For 0 < H < H ~ H( H ) r, () In parclar, f < H <, r asypocally η behaves as c for 0 <η <, here c > 0 s a consan, η and r = = H =. Tha s, he aocorrelaon fncon decays sloly, hch s he essenal propery ha cases o dverge. When r obeys a poer-la, he correspondng saonary process s called long range dependen (LRD). s shor range dependen (SRD) f he s = r < does no dverge. Follong are soe sple facs regardng he γ. vale of H and s pac on ISBN:

4 Concaon and Manageen n Technologcal Innovaon and Acadec Globalzaon, = 0 γ = for H = Ths s he ellnon propery of he Gassan nose. 0, 0 γ < for 0 < H < ( ) > 0 γ for 0.5< H <. Properes and 3 are ofen ered anperssen and perssen correlaons, respecvely. 4 Slaon and Modelng of Pace Loss 4. Mehodology for Slang Pace Loss Le = { : =,..., N} be a VoIP Jer race h selfslar characerscs [9], Hrs paraeer 0 < H 0 < and pace loss rae PLR 0. In order o bld an accrae odel for pace losses, he o-sae Marov odel (Glber odel) s sed o represen he pace loss process or pace loss paern. The pace loss paern s represened as a bnary seqence P= { P : =,..., N}, here P = eans a pace loss, P = 0 eans a receved pace correcly and = 0.,0.,...,. In hs odel, dfferen vales of p and q defne dfferen pace loss paerns. We appled J dfferen pace loss paerns over a e ndo W l of o slae pace loss. The relaonshp beeen Jer and pace loss fro eqaon (4) s sed o apply he pace loss paerns o by eans of he algorh shon n Table. As s ell recognzed ha on Inerne pace losses occr n brss, varos e ndos Wl of sze N, are sed o represen dfferen pace loss brss levels. W l = l l+ = l+ N,,..., l< : l=,,..., N N +, () here l and are he l-h and -h eleen of e seres and represen he ndo begnnng and endng, respecvely. Table Algorh for slang pace loss: A) Generang pace loss paern B) Applyng pace loss paern FOR n = o l = 0 FOR n= l A) B) o IF (pace as los) = ELSE = 0 END IF FOR n= + = 0 o N FOR n= o IF ( = ) N [ n] = [ n] + [ n ] END IF = FOR n= o N IF ( ) ˆ [ ] = [ n ] = + END IF By eans of he above algorh he ne e seres ˆ are obaned, here = 0,,,... J. For each ˆ he pace loss rae and he Hrs Paraeer ere calclaed, and he fncon ( PLR H ) f, as generaed. For he Hrs paraeer esaon, all ehods pleened n SelQoS [8] ere sed. 4. Proposed Model Fro or slaons, e fond ha he relaonshp beeen Hrs paraeer and pace loss rae can be odeled by a poer-la fncon, characerzed by hree fed paraeers, 0 < H ˆ 0 < 0. 5, a > 0 and b > 0, as he follong: M ( PLR) b H Hˆ + a, (3) here = 0 H M s he Hrs paraeer of he fond odel, Ĥ 0 s he Hrs paraeer hen PLR = 0, H 0 and PLR 0 are he Hrs paraeer and pace loss rae of orgnal race respecvely. 5 Slaon Resls In hs secon, applyng he ehodology proposed n secon 4, slaon resls are presened. The slaons are accoplshed over VoIP Jer races correspondng o Table. ISBN:

5 Concaon and Manageen n Technologcal Innovaon and Acadec Globalzaon Daa Se Se Se Se 3 Se 4 Table Descrpon of sed VoIP er races Measreen Perods Sep/07/007, 0:00a- 04:00p Sep/0/007, 0:00a- 04:00p Sep//007, 0:00a- 04:00p Sep//007, 0:00a- 04:00p Toal N of 4 Jer 4 Jer 4 Jer 4 Jer CODEC-Voce Daa Lengh(s) G.7-0s G.7-0s G.7-40s G.7-60s G.79-0s G.79-0s G.79-40s G.79-60s G.7-0s G.7-0s G.79-0s G.79-0s G.7-40s G.7-60s G.79-40s G.79-60s PLR PLR<0.75% PLR>0.75% In hs able, can be seen ha VoIP Jer races ere colleced n he follong ay: The easreen perods ere 60 nes (call draon e). For each easreen perod (an hor), for daa races ere obaned and for dfferen CODEC confgraons ere sed. For beer references of he sed daa ses n hs paper, see [9]. Fgre llsraes he relaonshps beeen pace loss rae and Hrs paraeer. The fncons faly f PLR, H, s resl o apply " J " pace loss paerns o e seres over a e ndo. The e seres represens a VoIP Jer race of he daa ses and descrbed n able. In hs fgre, f PLR, H represens a each pon of he fncon ne e seres f PLR, H s generaed by I VoIP Jer races. Where I s he oal nber of VoIP Jer races colleced n able. ˆ. The fncon Hrs Paraeer (H-VAR) Pace Loss Rae (%) =0. =0. =0.3 =0.4 =0.5 =0.6 =0.7 =0.8 =0.9 =.0 Fg.. Relaonshp beeen pace loss rae and Hrs paraeer: f ( PLR, H ) vs. f ( PLR, H ) The dfference beeen he fncon correspondng f PLR, H and he fncon f PLR, H, as o easred resls correspondng o slaon resls qanfed n ers of ean sqare error: MSE = PLR PLR Max PLRMax Mn PLRMn [ f ( PLR, H ) f ( PLR, H )] =,,...I Table 3 shos he fed paraeers and MSE PLR H f PLR, H beeen f, and correspondng for each e ndo. Table 3 Fed paraeers for Fg. H Ĥ a b MSE ( PLR ) f, 0 = = = = = = = = = = ( PLR H ) f, As shon n fgre and able 3, f ( PLR, H ) = 0.4 provdes he bes ach o he fncon f ( PLR, H). The sae analyss for represenaves VoIP Jer races correspondng o daa ses and s repeaed over a ndos sze =0.4. The resls are sarzed n fgre 3 and able 4. Fgre 3 shos he fncons f = 0.4( PLR, H ), and f ( PLR, H ). The fncons f = 0.4( PLR, H ) are ISBN:

6 Concaon and Manageen n Technologcal Innovaon and Acadec Globalzaon generaed by VoIP races h dfferen voce daa lenghs and CODEC ypes. Hrs Paraeer (H-VAR) Pace Loss Rae (%) G.7-0s G.7-0s G.7-40s G.7-60s G.79-0s G.79-0s G.79-40s G.79-60s Fg. 3. Relaonshp beeen pace loss rae and Hrs paraeer: f 0.4(, ) vs. f ( PLR, H ) PLR H Table 4 shos he fed paraeers and MSE PLR H f PLR, H beeen f, and = 0.4. Table 4 Fed paraeers for Fg. 3 Ĥ a b MSE f.4 PLR, H 0 0 G.7-0s G.7-0s G.7-40s G.7-60s G.79-0s G.79-0s G.79-40s G.79-60s ( PLR H ) f, In fgre 3 and able 4 s shon ha he relaonshps beeen Hrs paraeer and pace loss can be good odelng by eans of he poer-la fncon proposed n secon 4. 6 Conclsons Several facors nflencng voce qaly on IP neors. These paraeers are coplcaedly relaed o each oher and s dffcl o desgn and confgre every paraeer o op vale and ee voce qaly obecves, hle ananng effcen sage of neor resorces. Therefore s necessary o pleen adeqae raffc odels o evalae he voce qaly. In hs paper e have presened a ehodology for slang pace loss on VoIP Jer races. In hs ehodology he pace loss effecs on VoIP Jer and he o sae Marov odel are sed. Based on he above ehodology, e have proposed a ne odel for self-slar VoIP raffc. The ne odel alloed o relae o poran paraeers, he Hrs paraeer and pace loss. We fond ha Hrs paraeer s relaed o pace loss by a poer-la h hree fed paraeers. Slaon resls sho he effecveness of or odel n ers of MSE. References: [] M. Yan, S. Moon, J. Krsoe and D. Tosley, Measreen and odellng of he eporal dependence n pace loss, Proc. IEEE INFOCOM 99, Ne Yor, NY, pp , March 999. [] R. Sngh and A. Orega, Modelng of eporal dependence n pace loss sng nversal odelng conceps, Proc. h Pace Vdeo Worshop, Psbrgh, PA, Apr. 00. [3] ITU-T Recoendaon G.050, "Neor odel for evalang leda ranssson perforance over nerne proocol," Inernaonal Teleconcaons Unon, Geneva, Szerland, 005. [4] W.E. Leland, M.S. Taqq, W. Wllnger, and D.V. Wlson, On he Self-Slar Nare of Eherne Traffc (Exended Verson), IEEE/ACM Transacons on Neorng, Vole, sse, pp. -5, 994. [5] K. Par and W. Wllnger, Self-Slar Neor Traffc and Perforance Evalaon, John Wley & Sons, Inc., chaper, 000. [6] O. I. Shelhn, S. M. Solsy, and A. V. Osn, Self-Slar Processes n Teleconcaons, JohnWley & Sons, Ld, chapers and 3, 007. [7] RFC 3550, RTP: A Transpor Proocol for Real-Te Applcaons, Inerne Engneerng Tas Force, 003 [8] J. Raírez and D. Torres, A Tool for Analyss of Inerne Mercs, Mexco, Proceedngs CIE, Mexco, D.F., pp , 005. [9] H. Toral, D. Torres, C. Hernandez and L. Esrada, Self-Slary, Pace Loss, Jer, and Pace Sze: Eprcal Relaonshps for VoIP, Proceedngs CONIELECOMP, Pebla, Mexco, pp. -6, 008. ISBN: