Queueing Analysis of Simple FEC Schemes for IP Telephony
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Queueing analysis of simple FEC schemes for IP Telephony Eitan Altman — Chadi Barakat — Victor Manuel Ramos Ramos. N° 3998 September 2000. ISSN 0249-6399. ISRN INRIA/RR--3998--FR+ENG. THÈME 1. apport de recherche.
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(37) ',51 * * +** 1 * /. ck ρ = 0.1. 0.9995 0.999 0.9985 K=5 K=10 K=20 K=50 K=1000. 0.998 0.9975. ρ = 0.6. 1 Audio quality Q(α). Audio quality Q(α). 1. 0.9 0.8 0.7 K=5 K=10 K=20 K=50 K=1000. 0.6 0.5. 0.997 0. 0.2. 0.8. 1. 0. ρ = 0.9. 1 0.9 0.8 0.7 K=5 K=10 K=20 K=50 K=1000. 0.6 0.5 0. 0.2. 0.2. 0.4 0.6 Amount of FEC α. 0.8. 1. ρ = 1.5. 1 Audio quality Q(α). Audio quality Q(α). 0.4 0.6 Amount of FEC α. K=5 K=10 K=20 K=50 K=1000. 0.9 0.8 0.7 0.6 0.5. 0.4 0.6 Amount of FEC α. 0.8. 1. 0. 0.2. 0.4 0.6 Amount of FEC α. 0.8. 1. ¢ x l|sb ]X¼ a1jmU~³p]UbºKlUbalUbkjm{j}axp´q¯x5i,]jm|b*~E® °±]Uba¯p]UbH|l Ebas±ixÅkbH~|b*asbkj}ib*ik®(\^]UbD`djmx³xKpbas{|sbap jmpx5t}tm¦ÀilU]³'ba]j*/x5t}s^x5i^p]jmp^p]Ub z5t i iX{|st}jm|xzxpÂqotm¦Àjm³t}sx xjmz'{j}bap±xUasbkj}i b*i^°±xp] ¦¨j}ipbas¶p]jm¯p]UbDKjmxox¯º8ljmzxp´q °¶bdt}p¦«st}` sbapsx5ba/x|"p]Ubsb*~Ql|U~UjmKpxQ¦¨t}s`djmpx5t}¾®"\^]|x5ii]Ut}l|z5~ªUt}p'bdil|s{|sx5ix|U® U~|b*b*~E¡(baba$x:`Lt}sboit}{|]|x5ipx5kjmpb*~$i ]Uba`Lb*ix:°±]|x5 ]²jyix| z5bsb*~Ql|U~UjmKp{j} bapx5i j}~|~|b*~:ptY{|st}pb*apj³°±]Ut}z5b|z5t/µtm¦ {j}bapi©¡xpx5i[/Utk°±Sp]jmp¢£¶¤tm¦«pba:]j}i1jm t©bas jmzz|UbaKjmpxb±7b 'b*apk¡ i b*b ( *Q¡/c¡/c c ,´® ÄbapxilU ]Li]Uba`Lb*ip]Ub¶UbaKjmpxb±7b Eb*aptm¦Ej}~|~Qx| p]Ubsb*~Ql|U~UjmUaqYx5i i`djmzz5basp]jmt}l|si ]Uba`Lb ¡ixU*b[p]Ubjm`Lt}l|8pDtm¦Xj}~|~|b*~yxQ¦«t}s`djmpx5t} {'bas[{j} bapx5ii`djmzz5bas K«ixU*bjYix| z5b{j}bap{|st}pb*api1j³°±]Ut}z5bL st}l|{:tm¦ {j}bap;i M>® $Dt}pbD]Utk°¶babask¡Up]jmp^¦¨t}s^ilU]Yi ]Uba`Lb*i±°XbH/Utk°½p]jmp±x³kj}ibtm¦zx ]Kp±ps -j dHp]Ubtkbas jmzz *t}8psx|l|px5t}tm¦¢£X¤x5i {t ixpx)b (c ¡¾c c ,´®X\^]|x5i,`Lt}px jmpb*i,lUi,ptjmjmzq8Åkb`Lt}sb{|sb*ax5ibazq p]UbHx`{j}apDtm¦¢£X¤)xYt}l|s ix`{|zx5ipx5[i ]Uba`LbxYkj}ibtm¦zx ]8p,ps -j d ® D7b &UUb¶p]UbX¦«l|Uapx5t} a -_ ÀjmU~*t}Uix5~|basp]Ub¶kj}i bX°±]Ubasb¶p]Ub¶|l Ebasx| kjm{j}axpÂq1jmpp]Ub¶t}ppz5baUb* x5iÀUt}p(j Eb*apb*~Kq[p]Ub±jm`Lt}l|Kp(tm¦¢£X¤D®}\^]|x5ix5ijmt}{|px`x5ipx5. !. . . . . "!#$.
(38) * *-,
(39) / , #/ !#"%$ , & / ρ = 0.1. 0.99999 0.99998 0.99997 K=5 K=10 K=20 K=50 K=1000. 0.99996 0.99995. ρ = 0.6. 1 Audio quality Q(α). Audio quality Q(α). 1. ck. 0.9 0.8 0.7 K=5 K=10 K=20 K=50 K=1000. 0.6 0.5. 0.99994 0. 0.2. 1. 0. ρ = 0.9. 1 0.9 0.8 0.7 K=5 K=10 K=20 K=50 K=1000. 0.6 0.5 0. 0.2. 0.4 0.6 Amount of FEC α. 0.8. 1. ρ = 1.5. 1 Audio quality Q(α). Audio quality Q(α). 0.4 0.6 0.8 Amount of FEC α. K=5 K=10 K=20 K=50 K=1000. 0.9 0.8 0.7 0.6 0.5. 0.2. 0.4 0.6 Amount of FEC α. 0.8. 1. 0. 0.2. 0.4 0.6 Amount of FEC α. 0.8. 1. ¢ x l|sb]ļ ajmU~Yp]Ub[ºKlUbalUbkjm{j}axpÂq³x5i±Ut}p ]jm|b*~E® i *bajmsx5tL°±]Ubasbxp x5ibasq³{|st}jm|z5bptib*bp]UbKjmxy|st}l| ]KpH8qY¢£¶¤D¡tm¦Ä*t}l|sibx ¦p]|x5i Kjmx"b>n/x5ipi©®ÀÁµb[]j*b ¡ aO_ m_ " a^H» »|a $ " aJ_ K }pM » J a _ $ a_ ¢ÀxU~Qx| H°Xt}l|z5~S{'bas`xplUiptba jmzljmpbp]Ub³jmlU~Qx5tº8ljmzxp´q ¦¨t}sj"basq z5t©°¸ps -j dxKpbaU i
(40) xpÂq ®(Áµb,pt/t} gxd£º`® K }pMjmU~L°¶bb>nQ{jmU~|b*~ Àx¯j\Àjkq8z5t}s i basx5b*ik®ªÁµb¦¨t}l|U~$p]jmpdjmzz±p]Ub &Usip*t8b dax5ba8pidtm¦Dp]Ub³ibasx5b*i _§jmsb b*º8ljmzpt¯Åkbast|¡jmU~ p]jmp[p]UbL*t/b dax5baKp x5iUbaKjmpxbdjmU~µb*º8ljmzpt _ ® ^x5i p]Ub*t/b dax5baKpDtm¦ x5i±p]Ub\Àjkq8z5t}sDibasx5b*i,tm¦ ¶jmU~ykjm³bkjmz5al|z<jmpb*~yKq. .
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(46) ',51 * * +** 1 * /. ca. ^\ ]KlUik¡¦¨t}sDi`djmzz ¡ ,kjmb°±sxppbaµj}in_ » ,jmU~p]UbKjmx¦«st}` p]Ub1j}~|~Qxpx5t} tm¦Ä¢£¶¤ kjmb*t}Uix5~|basb*~j}i UbaKjmpxb ®Á@xp]p]|x5iDix`{|z5b¢£X¤i ]Uba`Lb ¡ °¶bDz5t ibDx³jmlU~Qx5tº8ljmzxp´q°±]Ubayj}~|~Qx|¢£¶¤baba¦¨t}s,jbasqLz5tk°½ps j-dHx8pbaUixp´q®X\^]|x5i z5t i i±xYºKljmzxpÂq³~|b*asbkj}ib*i,°±xp]Yp]UbHxUasbkj}i bxY|l Ebas,ixÅkb ® (+ ¯%À ,% D $Dtk°[¡O°XbX*t}Uix5~|basBp]UbÄ`Lt}sbbaUbas jmz/kj}ib(°±]Ubasbp]UbXi{j}ax|,'bap´°¶b*bap]UbXt}sx xjmzK{j}bap jmU~xpiHsb*~Ql|U~UjmUaqx5iD sbkjmpbasp]jm²c ®[\^]Ub1x5~|bkjoba]|xU~p]|x5iHp´q/{'b1tm¦¶i{j}ax|³x5iDp]jmp z5t i ib*ix:sbkjmzXUbap°Xt}sQipbaU~ªptjm{|{'bkjmsxS|l|sipijmU~ªp]8lUi1i{j}ax|"p]Ubsb*~Ql|U~UjmUaq ¦«st}` p]Ub¶t}sx xjmz|{j} bap(Kq`Lt}sbXp]jmt}Ub¶{j}bap(x`{|st©b*i(p]Ub¶{|st}jm|xzxp´q1ptDsbapsx5bab xpDx kj}ib1p]Ubt}sx xjmz{j} bapx5iHz5t ipk® U~|b*b*~E¡¾jL{j} bapz5t iiD`LbkjmUiHp]jmpDp]Ubº8lUbalUb1x5i ¦«l|zzjmU~¸p]Uba@p]Uby{|st}jm|xzxp´q¸tm¦[z5t ix|:p]UbYUb>nQpL{j}bap¯x5id]|x ]Ubasdp]jmp]Ubyipbkj}~Qq ip jmpb{|st}jm|xzxpÂqµtm¦Xz5t ix|yj{j} bapk®\^]Ubi{j}ax|³ xb*ip]Ubsb*~Ql|U~UjmUaq tm¦^j{j}bap `Lt}sb³ ]jmU*bYp!t &UU~²jUt}$¦«l|zz±|l 'basdjmpp]Ub¯'t}ppz5baUb*'¡±jmU~$p]KlUipt'b³*t}ssb*apzq sb**baxb*~E®ÁµbHUt}pbHp]jmp±p]UbH{|]UbaUt}`LbaUt}ytm¦Àp]Ub*t}ssbaz<jmpx5t}Y'bap´°¶b*bayz5t ii b*i¶tm¦{j}bapi °^j}ijmzsbkj}~Qqª`Lt/~|baz5b*~$jmU~$iplU~Qx5b*~Sx$t}p]Ubas{jm{bas~i ] ( */¡Xc¡¶c c ,´®w"bkj}il|sba`LbaKpi]jkb jmz5i ti]Utk°±Yp]jmp `Lt ip tm¦p]UbHz5t iib*i jmsb[*t}ssbaz<jmpb*~ ( |¡UQ¡Qc ,´® zbasb ¡|°¶bjmsbx8pbasb*ipb*~Yx &UU~Qx|dp]Ub{|st}jm|xzxpÂq³p]jmp {j}bapD¹d»²¼"x5i±z5t ip xba p]jmp {j}bap¹x5i jmz5i tz5t ipk®(\^]|x5i,°±xzzB xblUi a Ä°±]|x5 ]yxYpl|sy xb*i lUi,p]Ub[b>n/{|sb*i ix5t}³¦¨t}s,p]UbjmlU~Qx5tLº8ljmzxp´q K«£º®9 M>®^8xU*b°Xb1j}iil|`Lbp]jmp,p]Ubiq/ipba`·x5i xdxpiÄipbkj}~Qqip jmpb ¡K°Xb kjmt}`xpÄp]Ub±xU~|b>nL¹yjmU~Lil|Uipxpl|pb,xp8qÅkbast|® bap ~|baUt}pb p]Ub1|l EbasixÅkb1jO¦«pbasHp]Ubj}~|~Qxpx5t}µtm¦X¢£X¤²u lUipj}iDxp i~|7b &UUb*~xµ/b*apx5t}ªQ®HÁµb1]jkb °±]|x5]"`LbkjmUi ®XÁµbjmsb[xKpbasb*ipb*~"xYp]Ub[{|st}jm|xzxpÂqYp]jmp ® ¢t}s(p]Ub,bkj}ib±tm¦kjmz5al|z<jmpx5t}°Xb±*t}Uix5~|basÄp]Ub±kj}ib ¼ ®Áµb^'bazx5bab±p]jmp(p]|x5i(x5i(º8l|xpb baUt}l| ] xba p]jmp[jz<jmsbi{j}ax|¯bap°Xb*ba p]Ubt}sx xjmz({j}bapjmU~p]Ub1sb*~Ql|U~UjmUaq z5bkj}~|i,ptdjm³x`{t}sp jm8puvxppbasjmU~yj1{'t8t}s±x8pbas j}apx8xpÂq® µt}s~|bas[ptyt}|p jmx:jmªb>nQ{|zx5axpb>n/{|sb*i ix5t} ¦¨t}sp]Ub{|st}jm|xzxp´q ¡°¶b &Usip{|stk/x5~|b1jmb>n/{|zx5axpDi jm`{|z57b {jmp] b>n/{|sb*iix5t}Y¦¨t}s,p]Ubbaba8pDtm¦z5t iitm¦(p]Ub {j} bapkjmssq/x|Lp]UbHsb*~Ql|U~UjmUaq¡ xbaYp]jmp±p]Ub[t}sx xjmzB{j} bap,xpibaz ¦°¶j}i z5t ipk®.
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(55) ',51 * * +** 1 * /. c~}. 292 ¾ÁµbÄ{|st8*b*b*~xp]UbX{|st/tm¦UKqxU~QlUapx5t}¾®\^]|x5iBsbaz<jmpx5t}x5iÀ}jmzx5~[¦«t}s p]jmp xp±x5i±}jmzx5~o¦¨t}s Q ®(Áµb[i]Ut©° p] jmp±xp,x5i± jmzx5~o¦«t}s '» a¡ . ÄÇ. . . µ 1 1 . . _. _ $ _ $ . . _ a _ a . . . . . . . _ _ " . . .
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