Measurement of One-Way Internet Packet Delay
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(25) hE FE8>, FX 7,/.- @ HTU@e.>=?Ô@D4*8 7E781ÌA@CD,/ÔTA0H81@D.-O=?6-6981=ZN?NÊ/@D47@D.;:J8>=?4AÊ81.1:<Ù)CWÈQ=|81Ì38>ÌA@6>:/Ô@¤C;Ì7:<.;:/CÎ 81@D.1=?6w8>=[CD6-:/6-=Z4 @ HTU@e.>=?Ô@D4*8 5XVÆ^ÌA@PA= @D.1@D47CD@¤=[681Ì7:J8 4A,JÈ :<N?NF81ÌA.>@e@CD,/ÔTA0H81@D.;6 Eg2 :/47P +¹:/.>@Ê/@e4A@D.;:J81=Z4AÊ× MÔÎuN?=ZK5@¤81.1:<Ù)C¤Û7,JÈ6eEÈQ=|81Ì H ≈ 0.9 :/47P ρ ≈ 0.1 X¤Æ^ÌA@e6>@C,/ÔTA0A8>@D.;6 :/.>@Ê/@D47@D.;:J8>=?4AÊÐÉh,<81Ì Ô@D.1Ê/=?4AÊ381.1:<ÙC:<4UPÝC.1,5616w=?4AÊ81.1:<Ù)C/Xß-47@Ì0A47PH.1@ePÝTA.>,HCD@e616w@B6W:<.1@ 0U6w@BPÐ×Ñ,5.-81.1:<ÙCÊ5@D4A@e.1:<8>=?,/4Ð=?4@DË/@e.>ÇÐCD,/ÔTA0H81@D.BXÆ^ÌA@Ê5@D4A@e.1:<8>@eP38>.;:JÙCÛ7,JÈ6%:<.1@ÉA.1,/K5@D4 07T=Z481ÌA@V.1,/0A8>@D.;6¢Þ 5E*Þ-Òm:<47P)+Þ m=Z4:WÈM:Ǥ8>Ì7:<8 ,/×@eË/@e.>ǤÛ7,JÈ =?6·Ô@e.>Ê5=Z47Ê%8>ÌA@V8>.;:JÙC CD,/Ô=?4AÊ)×Ñ.1,/Ô C,/ÔTA0A8>@D. O :<4UP8>ÌA@¤.>@B698V,/× ÏÚ×Ñ,5.V@eË/@D.1ÇÛU,JÈVÓ^=?6-C.1,5616w=?4AÊ81ÌA@¤.1,/0H81@D.;6 ,54AN?Ç/XSY=?4A@Q8>.;:/CD@e6SÌ7:Ë5@^ÉU@e@D4Ê/@e4A@D.;:J81@eP=Z4)@ Th@D.1=?Ô@e4*8 :56IÈM@DN?NE5ÈQÌA=?C;Ì):/.>@Q6>ÌA,JÈQ4:516 0
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(29) ! &! ++ . ! ' ! + -#! -#! #- ! ,-. #! '. ± ± ± ± ± ± ± ± ±. #! & #! /- & #! +&'+ #! . & #! . & #! ' #! & - #! + . . ,#+ ! - - . ! - ' & #- ! ' ,#+ ! ' &! &! '#! ' '#! '. #! .
(30) . ! .. ! . .. ! + ! + ! . . .
(31) . ! & ! & ! & ! & ! & ! & ! & ! & ! & . "! $#&%(')(* % . ,+ % ' . % && '# % ++ % +& ' % #, -+ % '# % , + -+ % . ' -. . ! . !' #! + . ! +#! +#! +#! . '#! -. Æ^Ì7@ÐC,/ÔTA0A8>@D.RO Ê/@D47@D.;:J8>@B6=Z4¡81ÌA=?6CD:/6>@8>.;:JÙCLÈQ=Z8>Ì :/47P X ß-4¨81ÌA@ CD,/4*8>.;:<.1Ç/EC,/ÔTA0A8>@D.;6 EM2 :<47P¡+ Ê/@e4A@D.;:J81@ϯ@e:5C;Ì¡,/×V81αÌA@D=ÔÓ1.281.1:<Ù)CLÈQρ=Z8>=Ì α0.4= 1.2 :<47P X%Æ^ÌA@D=?.V81.1:<ÙCW=[6-É7.>,5K/@D4307T=?4Ð8>Ì7@¤.1,/0H81@D.;6-Þ 5EgÞVÒ:/47PÐÞ=Z4*8>,LÔ@D.1Ê/=?4AÊ)81.1:<Ù)C ρ = 0.1 Ï Ó:<4UP C.1,5616m81.1:<ÙCÏ ÓbX M@DN?,JÈ 8>Ì7@e6>@TAN?,<8;6=Z8=?6:<N[6w,6wÌ7,JÈQ48>ÌA@R8>Ì7.>,50AÊ/ÌAT70H8 Ï 3ÉAT76;ÓÔ@e:/6>0A.1@eP:<881ÌA@mPH@e6w8>=?47:<8>=?,/6 4 :<4UP)8>Ì7@ :56>6>,HC=[:J8>@BP)ÌA=[6981,/Ê5.1:/ÔLX 4UPH@D.14A@e:<8>ÌR=|8^=?6 6>ÌA,JÈQ4¤8>ÌA@ßQàÆQÆÝÔ@B:/6>0A.1@ePm=?4¤81ÌA=[6¥@ HTU@e.>=?Ô@D4*8¥81,/Ê5@8>Ì7@D.SÈQ=|81ÌW81ÌA@Q:/616w,HC=[:J81@ePmÌ7=?6w8>,5Ê/.;:<ÔX ßàÆQÆ =?6Q,5É76>@D.1Ë/@eP8>,)Ì7:Ë5@m6wTA=?K/@B6:/6^Ì7=ZÊ5Ì:56 8¤Ô)6eX 70A.w81ÌA@D.1Ô,/.1@/EH=Z8V=[6:<N[6w,,5É76w@e.>Ë5@eP 81Ì7:J8Q81ÌA@ßàÆQÆÌA=[6981,/Ê5.1:/Ô¹Ì7:/6Q:ÌA@B:Ë*Ç81:<=?N X =?47:<N?N?Ç/ E 7Ê50A.>@ 6wÌA,JÈ681ÌA@%Ô@B:/6>0A.1@ePÔ@B:<4R:/47PRË:/.>=[:<4UC@ ,<×SßàÆQÆ,5ÉH81:/=Z4A@BP)×Ñ,5.:<N?N 81ÌA.1@D@% @ HTh@D.1=ZÔ@D4*8;6DXSÍu8Q=?6^,5É76>@D.1Ë/@eP)8>ÌA@m6w8>.1,/4AÊPH@DTh@D4UPH@D47CD@%,<×y81ÌA@%Ô@e:<4:<4UP)8>Ì7@mË:/.>=[:<4UC@ ,548>.;:JÙCC;ÌU:<.;:/Cb81@D.1=?6w8>=[CD6¤:<47PN?=?4AKá0H8>=?NZ=?Õe:<8>=?,/476eX A0A.>8>ÌA@e.eES=Z8=[6:<N[6w,Ð,5É76>@D.1Ë/@eP#81Ì7:J8=|8=?6 81ÌA@ α TU:<.;:<Ô@81@D.Q,<×8>Ì7@mÊ/@D47@D.;:J8>@BP81.1:<ÙC 8>Ì7:<8Ô,*6981NZÇR=Z4AÛ70A@D4UC@e6Q8>ÌA@W.1,/0A8>@D.QÉh@DÌU:Ë*=?,/.Q:<8 N[:<.1Ê/@ ρ X¢Æ^Ì7=?6M=[6,/×CD,/0A.;6w@V8>ÌA@mCD,/476>@eØ*0A@e47C@-,<×Ø*0A@e0A@D=?4AÊÉU@eÌ7:Ë=Z,5.eE*ÈQÌA=[C;Ì89ÇTA=[CD:/NZN?Ç)6wÌA,JÈ6 Ì7@e:ËÇ*Î8;:<=?NZ@BPPH@eN?:Ç3Th@D.>×Ñ,/.1Ô):<47CD@Lϯ@/X Ê7X?EFà#@e=ZÉ70ANZN¢PA=?6w8>.1=ZÉ70H8>=?,/4UÓ =?4#8>ÌA@)CD:56w@,<×8>.;:JÙCÈQ=|81Ì $y,/4AÊ/ÎuÞV:<4AÊ5@ +-@DTh@D47PA@D47CD@/X. . . . . ÁW¾LÄ (Ã#2yÅDÁW¾ O³PH@BPH=[CD:J81@ePÔ@B:/6>0A.1@DÔ@D4*8M6>ÇH6981@DÔ ×Ñ,5.MCD,/N?NZ@BCb8>=?4AÊÌA=?Ê/ÌHÎØ*07:<N?=|89Ç81.1:<Ù)CV8>.;:/CD@e6M:<47PÔ@e:/6>0A.>Î =?4AÊ@BÒ<@-PH@eN?:ÇÌ7:56Éh@D@e4.1@DTh,/.>8>@BPgXÆ^Ì7@-Ô@e:56w07.>@eÔ@e4*8=?4H×Ñ.1:56981.>0UCb8>07.>@ PH@e:/N?6MÈQ=Z8>ÌT7.>,5ÉANZ@eÔ)6 N?=?K/@W6>Ç*4UC;ÌA.>,54A=?Õe:J81=Z,54FEHÌA=?Ê/ÌHÎ:/CeC0A.;:/CDÇ=Z481=ZÔ@e6w81:/ÔTA=Z47Ê:<47PTA.1,HC@B6>6>=Z47Ê,/×SÔ0ANZ8>=?TANZ@%81.1:5C@B6 CD,/N?NZ@BCb81@eP:<8RËJ:<.1=Z,5076)Ô@e:56w07.>@eÔ@e4*8TU,5=Z4*8;6DX O Ô@e:56w07.>@eÔ@e4*8R698107PHÇ ,<פPA@DN[:Ç68>ÌA.1,/07Ê/Ì ÍG³.1,/0H81@D.;6 Ì7:/6%Éh@D@e4.1@DTh,/.>8>@BPgX)Æ^ÌA@)Ô@e:56w0A.1@DÔ@e458m6>@8>07T=[6%.1@DTh,/.>8>@eP#=?4á:PH@D81:/=ZN?@ePÈ^:Ç 81,/Ê5@8>Ì7@D.VÈQ=Z8>ÌÐ8>ÌA@6w@D8-,<×I@ Th@D.1=?Ô@e4*816 PH,/4A@5X Ü @eË/@D.;:<Ny=ZÔTh,/.>81:<4*8-6w81:<8>=[6981=?Ce6VÌU:Ë/@mÉh@D@D4.>@DÎ Th,/.>8>@BP¤:/ÉU,50H8¥81ÌA@^PH@DN[:Ç%×Ñ,/.S:V.1,/0A8>@D.S:<4UPm×Ñ,/.S: C;Ì7:<=?4W,<×U.>,50H8>@e.16eXSß-0A..1@e6>0AN|8;6¥CD,/4 U.>Ô ,/8>ÌA@e. .1@e6>0ANZ816m.1@DTh,/.>8>@BP@e:<.1N?=Z@e.%8>Ì7:<8m8>ÌA@PA@DN[:Ç=?4ÍG .>,50H8>@e.16%=[6mÊ/@e4A@D.;:<N?N?ÇÐ=Z4AÛ70A@D4UC@ePáÉÇ8>.;:JÙC C;ÌU:<.;:/Cb81@D.1=?6w8>=[CD6eEBNZ=?4AKmC,547PH=Z8>=?,/476:<47PFE8>,-6>,/Ô@ @ 8>@e458BE<PH@8;:<=?N?6¥=?4¤Ì7:/.1PHÈ^:<.1@I=?ÔT7NZ@eÔ@e4*81:J81=Z,54 :/47P6>,<×Ú89È^:<.1@.1@DN?@e:/6>@e6eX¢ß-0A.¢×Ñ0H810A.1@-ÈM,/.1KÈQ=?N?NhÉh@%:<Éh,/0H8MÔ,HPH@eNZ=?4AÊ,<×F81ÌA@-,5ÉH81:/=Z47@eP).1@e6>0ANZ816eE 81,¤=?47CN?07PH@-TU,*6>6>=?ÉANZ@ C,5.>.1@DN[:J81=Z,5476I @ H=[6981@D4*8Éh@89ÈM@D@e4Ø*0A@D07@VN?@D4AÊ/8>Ì76M:J8^:/P w:5C@D4*8·47,PA@e6eX¢ß-07. Ê5,5:/Nh=[6^81/, U47P:¤×Ñ,5.>Ô0AN[:¤×Ñ,5.^8>ÌA@m@ÒJ@mPH@eN?:Ç=?4:)C;Ì7:<=?4R,/×¥.1,/0H81@D.;6DX 0. ,.
(32) OWTT for More Data Flows − Chain of Routers A: ρ = 0.4, α = 1.2 B,C,D: 50+50 sources with ρ = 0.1 0.1 P[X1<X<X2]. Mbps. 10. 5. 0. 0. 1000. 2000. 3000. 4000. 5000. 6000. 0 0. 7000. 2. 4 6 Bitrate [Mbps]. 8. 10. 2. 4 6 Bitrate [Mbps]. 8. 10. 0.06 P[X1<X<X2]. Mbps. 10. 5. 0. 0.05. 0. 1000. 2000. 3000. 4000. 5000. 6000. 0.04 0.02 0 0. 7000. OWTT [ms]. 150 100 50. P[X1<X<X2]. 0 0 −3 x 10 8. 100000. 200000. 300000. 400000. 500000 600000 Sample Number. 700000. 800000. var: std.dev: median: mean: max: min:. 6 4. 900000. 1000000. 9. 10. 57 7.55 2.42 5.1 107 0.409. 2 0. 0. 1. 2. 3. 4. 5 OWTT [ms]. 6. 7. 8. =?Ê/0A.1@QÒ 7yÆ^ÌA.1,/07Ê/ÌATA0A8Ô@e:56w07.>@BPW:J8¢C,5ÔTA0H8>@e.IO ϯ0ATATh@D.IN?@×Ú8;ÓS:/47P¤:<8SCD,/ÔTA0H81@D. ÏÑÉh@DN?,JÈVÓ 81,/Ê5@8>Ì7@D.%ÈQ=|81Ì8>ÌA@):/616>,CD=?:<8>@BPÐÌA=[6981,/Ê5.1:/Ô6ÏÑ.1=?Ê/Ì*8W6w=[PH@BÓX 47PH@e.>47@e:J81Ì 7¤ßQàÆQÆ Ô@B:/6>0A.1@eP ×Ñ,5.QÔ,/.1@%P7:J81:Û7,JÈ6^=?4:)C;Ì7:<=?4R,/×¥.1,/0H81@D.;6%ÏÑ @ HTh@D.1=ZÔ@e45+8 <Î *ÓÈQ=|81Ì:56>6>,HC=[:J81@ePÌ7=?6w8>,5Ê/.;:<Ô 4. . ^À &Q¾RÄ &2 WOVNZÔ@e6 X?Em:<N?=[PH=Z4UPH= Ü XS:/47P@DKJ:<076>KJ:/6 XZE
(33)
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(35) E ¢KÉU@e.>ÊOWXS:<47P ¥=?@ePANZ@e. X?3 E 4%5 6 7( ' 8 69 - , ;: < =-/ > ?. =-
(36) 8-/ E¢2Qß Ü ÆÒ ÆQ+Ï 5Ó ÒHEAÒ AX 2,547698;:<4*8>=?4A@B6>CD0W+¤X?E/2M:<.1N?616w,54%GX?EJGS,/Th@e61C0WO¤XZ@ E 1 A CB/ DB D =-/ bE Æ¥@eC;ÌA47=?Ce:<NFÞQ@eTU,5.w8BE MNZ@eK*=?4AÊ5@-Í476w8>=Z8>0A8>@W,/×Æ¥@eC;ÌA4A,5NZ,5Ê/Ç5EHÒ 7EÍ ÜAÜ Y 78<Î /X & &. . . . .
(37) .
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