An Inter-arrival Delay Jitter Model using Multi-Structure Network Delay Characteristics for Packet Networks

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1 An In-v D J Mo usn Mu-Sucu Nwok D Chcscs fo Pck Nwoks Ew J. Dn, Chsoph M. Wh, n Kh A. Tu Schoo of Ecc n Copu Ennn Okho S Unvs Sw, OK ABSTRACT D vsn pck nwoks xpnc vn s, sun n n-v j. Ths cn su n pfonc n - u councons ppcons f h j s o unccoun fo n h cv ppcon. Ths pp xns on n suon of nwok j fo - u councons ppcons. W xn h u-sucu chcscs of nwok n vop o fo suon of j. Th o s conf pc usn coc pck nwok j sscs.. INTRODUCTION Pck-swch nwoks bn us o pov ncv u councons, ncun voc, vo n svcs. Howv, pck nwoks no fo - u ppcons such s voc councons. Pck nwoks xhb non- bhvo h sous h pfonc of - councons sss. Pcu, s pcks ns fo souc o snon, h xpnc ffn s. As su, pcks v h snon wh vn s (bwn pcks) f o s j. Pck j su fo pcks kn ffn phs o h snon o vo cons s o f nks. Howv, j s p cus b vn quun s ncoun b pcks ous (nos). Nwok pcks cop wh oh nwoks ffc ous. Rous ssc upx ncon pcks, whch sus n h vn. In voc ov IP (VoIP) ppcon, nv j s o svon of h uo pbck ss. If h s no qu buffn on h cv ss hs s w o pck oss n cosponn oss of voc (sn pbck). D buffn o ovco hs pob cn o xcssv n o n n h ss. In hs pp, w xn h chcscs of nwok j o vop o fo nwok nv j. Scon scbs h chcscs of pck nwok n-v. Scon 3 psns ou nwok j o. Scon 4 vs copsons of ou o o pc coc nwok j. Fn, n Scon 5 su n concusons vn.. NETWORK JITTER DELAY PROPERTIES Whn - voc councon ppcon uss w pck nwok pon IP (Inn Pooco) o ns s of voc, f o s s, s upx nwok nos (ous) wh h oh ffc on h nwok c bckoun ffc. IP nwok nos hv no pos, so nwok ffc s svc on Fs n Fs ou (FIFO) bss. Thfo, quun s n j xpnc b pcks c su of w n svc s n h quu. J s of ss on pck nwoks sp of h quun s of h bckoun ffc h nos [] []. Th v sz of h s s s cop o h bckoun ffc, so os no snfcn conbu o h quun s. As s pcks v coss nwok ph h sp h bus pos (n quun s) of h nos on h ph [3]. If h sn, o h bwn pcks, of h s s s hn h bus pos of h no, h s s sp of h quun s whn h bus pos (o hn on sp fo h s bus po), Fu (). Howv, whn h sn s hn h bus Whn sv pcks v h no un vn nv (possb sunous), s f o s bus po.

2 pos, h s sps s of ffn bus pos (n ffn bus pos), Fu (b). Essn, sn s sp h bus pos wh s sn s sp h s whn h bus pos. W() Inv bwn spn of s whn bus pos Bp- Bp Bp+ () Inv bwn spn W() of s of bus pos Bp- Bp Bp+ (b) Fu. () T s spn of quun whn bus pos n (b) T s spn of bus pos of quu. W() s n nsnc of quun pocss n Bp psns h s of bus po. [3] Accon o L n Ms [3], hs spn scbs h u-sucu of, whch conss of sho non-son coponn, h s whn bus pos, n on- son coponn, h s of ffn bus pos. Th on- son coponn cn b o s Gussn nos pocss bcus h s no coon bwn h occuncs of bus pos of quu. Moov, h s sp whn h quu fo ch bus po hv no coon wh s sp fo oh bus pos. Th usucu chcsc of nwok s us n h nx scon o vop o fo j. 3. NETWORK JITTER DELAY MODEL chcsc o s sc chcsc s f o s h cossov. Sv schs hv vop copx os n pfo pc suon sus of nwok j ncun [] [] [5]. Ths sus show h nwok j foows Lpcn sbuon. Ynn n Kno ([5]) show h h pobb sbuon funcon wns n shons bs on ncss n ffc o, uzon, busnss, n bus nh. Wnn of h Lpcn pf snfs hh pobbs of on j s, wh shonn of h pf ps hh pobb fo s j s. Wh nvsn n pv j buffn oh, Rj. [6] po h spk phnon, conon wh spk n pck s s poc b ss of pcks vn v cos oh. Whn pck xpncs, h pcks foown h up n s su h v wh v s n-v s, sos os sunous. Rj. foun h h spk phnon c xponn, n ncopo n xponn cn funcon no h spk con j buffn oh. Whn hs j buffn oh c spk ws ow o c xponn o foow h sop of h spk un v off ppox zo sop, snn h n of h spk. Ths obvous ncs coon bu of n-v j s. In ou popos j o, s n fo pobb sbuons h hv no coon bwn sps, hus no sun spk chcscs. Thfo, n xponn cn funcon s us o su hs phnonon whn h Lpcn o Gussn sbuon poucs spk. Th Lpcn sbuon s us o o h s sc, non-son, pocss, n h sc son pocss s o wh v Gussn wh nos. J spks n subsqun j s foow h spk jusn pocu no bov. Th cobnon of h Lpcn sbuon, Gussn wh nos, n spk jusn pov ns o o h u-sucu chcscs of pck. Th popos o s shown n fu. L n Ms ([4]) su n nss of nwok ss h s spn nvs cn b o s non-son pocss, wh h on nvs cn b o s son pocss. Th pon whch h chns fo s s sc

3 Lpcn Dsbu Ds S sc s Av Gussn Wh Nos L sc s Fu. Popos J Mo Exponn Dcn D Spk Ajusn Ds foown spks Th Lpcn sbuon s us o n pck j vus bs on spcf n n vnc. Th chcsc quons () n () fo h Lpcn sbuon funcon vn s foows: X #" #! F ( X ) =, x "!, () X #" #! F ( X ) = #, x >!, () Fu 3 shows h Lpcn sbuon funcon pnon sun, pcks wh! = 49 n! = 5. Gussn wh nos s o h vus n b h Lpcn sbuon funcon o nouc h sc pops. Ths s on bs on spn h foows h cossov vu. Fo xp, vus b h Gussn wh nos pocss nvs bs on h cossov fo s sc o sc. Ths pocss os spn of h bus pos of h quu. Whn spk s c, bs on hsho, vus foown h spk uc xponn, own h o cch up wh h (spk) pck. Equon (3) vs h xponn c funcon us o o hs chcsc. Th nub of pocn pcks h ffc b h spk s no s h spk nv. In o fo h pcks foown h spk o cch up wh h spk h v j s whn spk nv shou b ss hn o qu o h n. x ~! ( ) = ( ), (3) wh,! = n n v! =. wh, () s h n-v j. Fu 4 povs pco scpon of hs j jusn pocss. D Spk D Spk Thsho 3 s h n Mn j J s D Spk Thsho Mn j spk nv () D Spk spk nv (b)! x f ( x) = Ruc bs on xponn cn funcon Fu 3. Gn Lpcn Dsbuon usn Lpcn Rno Nub Gno. Fu 4. J spk jusn pocu. () spk pouc fo o n (b) ucon of s foown spk.

4 4. JITTER MODEL COMPARISONS Expns w conuc wh Nwok Pfonc Appcon (NPf) h ws spcfc vop o coc pck nwok sscs fo VoIP. NPf s wn n Vsu C++ o op un h MS Wnows opn sss. Th po uns s sv/cn p bwn wo copus connc o n IP nwok (possb concn nwoks). Th ppcon ws spcfc sn o sn su voc copss ov IP nwoks, wh h fxb o ccoo vous us-spcf szs n sn s, ncun IP pck ps o su VoIP ffc such s f szs, pck sz (o fs p pck), sn, uon of suon, c. Dun suon NPf ppns pck squnc nubs on ouon pcks, n cos pck sn n v s (kpn ck of cv pck nubs). Ths nfoon s us o ccu pck ssc nfoon, such s pck n-v (j), n-o-n pck, pck oss, c. Accu n s cc fo hs ppcon; hfo h wo copu s (cn n sv) cocks us b cfu snchonz usn Nwok T Pooco (NTP) [7]. NPf s uh chcu h uss up TCP conncons fo cono n UDP conncon fo nsf. NPf ws us o coc nwok n-v s bwn PC connc o h W A Inn v n offc LAN (Loc A Nwok) n o PC connc o h Inn. Th pck c (s of voc ) sn su voc v 45s, 4 bs of po p pck, fo sv o cn. Th sun n-v j s cop wh h su fo h nwok j o. Th o ws us o n j vus bs on h ssc po b h NPf suon. Th j coc pc usn NPf h n of 45 s n sn von of Ths vus w us n nn h j o npus o copb sus. A cossov of 8 s, n spk sc of 3 s h n ws us fo Gussn nos spn n spk con jusn, spcfu. Fu 5 cops h coc j s fo NPf n h j s pouc b h popos u-sucu j o. Th o un n j of 45 s wh sn von of 5.5, vus qun h NPf. Fu 5 shows h boh h su n o j bus, wh h jo of h j s ppn n h n s xpc. Ths s so vn n h n-v j sbuon shown n Fu 6. Th sbuons foow Lpcn sbuon bou h n of 45s. D J 5 ) s 5 J ( s Pck Nub Mo Su J (LAN o Inn) D 5 s n D b b o P 5 Msu J (LAN o Inn) Pck Nub Fu 5. Msu vs. Mo J Ds Mo Su Msu In-v D J (s) Fu 6. J D Dsbuon fo Msu n Mo J Ds. Th n fo h bov suon n j o ws cop wh c uns ov LAN (connc o h W A Inn) o CDMA nwok conncon. Tc uns fo sv s of w cop fo h LAN o CDMA c o psnon of ffn vs of bus pos. Noz vnc chcscs cop b vn vnc vus of - ss. Ths chnqu s pc us fo sf-s non, s us n [8]. Th - ( ) ss x = { xk, k =,,, K}, of son ss x, cn b fn b sun h on ss ov

5 non-ovppn, jcn bocks of sz. Th vnc ccuons ssn copss h scs, wh = psnn h hhs nfcon n = fco of ucon n nfcon. Ths cn b xpss s, x k ( ) k =! x. (4) = k" ( " ) In hs copson n - ss of h vnc of h j s s us, us n quon (5) ( ) V( xk! ) ) + V( xk! ) ) + + V( xk! ) ) V( xk ) = A z o N Dc n A Vnc LAN o Inn LAN o CDMA Monn LAN o CDMA Nh LAN o CDMA Noon J Mo L, (5) Fu 7. A Vnc Copson. Fu 9 shows h sus of h vnc copsons. Fo sf-s ffc h vnc wou c sow ov h ffn scs, nnn sowh consn noz vnc vu [9]. Ths wou nc h h vnc sscs fo h ss wou b psv ov h vous scs n hus wou scb sf-s pocss. Howv, h su o n pc su ch c p, os xponn, wh h j o. Th j o os howv c sh sow hn h su, bu no nouh o concu s sfs. In copson, h ov vnc sscs of h o n h coc pp o hv xponn k c conssn wh on noh. Th j o foows h sho n on bus ns of h j coc fo cu pck nwoks. 5. SUMMARY AND CONCLUSION Th popos nwok j o hs pos fo us n on n sun pck nwok j. I cpus h u-sucu chcsc of nwok nv n psvs h bus chcscs of on sv scs. Ths o cn b us o su h ffcs of nwok j on h opon of voc n u ppcons n pck nwok nvonns, n s ffcs on spch n uo qu. A c ppcon of hs o s o vu h pfonc of pv j buffn ohs o pov oss pfonc n h fc of nwok j, wh nzn ov ss. 6. REFERENCES [] L. Zhn, L. Zhn, D. Xu, Chcscs of Nwok D n D J n s Effc on Voc ov IP (VoIP) IEEE Innon Confnc on Councons ICC, Vo., pp. -6,. [] C. Fuon, S. L, D J Fs-O n Scon-O Ssc Funcons of Gn Tffc on Hh-Sp Mu Nwoks IEEE/ACM Tnscons on Nwokn, Vo. 6, No., Ap 998. [3] Q. L, D. L. Ms, J-Bs D-Boun Pcon of W-A Nwoks IEEE/ACM Tnscons on Nwokn, Vo. 9, No. 5, Ocob. [4] Q. L, D. L. Ms, Invsn h Scn Bhvo, Cossov n An-pssnc of Inn Pck D Dncs, Pocns of IEEE Gobco, Vo. 3, pp , Ro Jno, Bz, 999. [5] T. Ynn, R. Kno, Voc Pck Inv J Ov IP Swchn, SBT/IEEE Innon Tco Sposu ITS 98, Vo., pp. 6-, 998. [6] R. Rj, J. Kuos, D. Tows, n H. Schuznn, "Apv Pou Mchnss fo Pckz Auo Appcons n W-A Nwoks," Pocns IEEE Nwokn fo Gob Councons INFOCOM 94, Vo., pp , 994. [7] D. Ms, Inn T Snchonzon: h Nwok T Pooco RFC-9, Inn Ennn Tsk Foc, Oc [8] W. Sns, Hh-sp Nwoks n Inns, Pnc- H, Nw Js,. [9] M. E. Cov, A. Bsvos, Sf-S n Wo W Wb Tffc: Evnc n Possb Cuss, IEEE/ACM Tnscons on Nwokn, Vo. 5, No. 6, pp , Dcb 997.