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On-Demand Layer Addition (ODL) : Making Multi-Layer Multicast Transmissions Cheaper

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(1)On-Demand Layer Addition (ODL) : Making Multi-Layer Multicast Transmissions Cheaper Vincent Roca. To cite this version: Vincent Roca. On-Demand Layer Addition (ODL) : Making Multi-Layer Multicast Transmissions Cheaper. [Technical Report] RT-0239, INRIA. 2000, pp.17. �inria-00069933�. HAL Id: inria-00069933 https://hal.inria.fr/inria-00069933 Submitted on 19 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. On-Demand Layer Addition (ODL): Making Multi-Layer Multicast Transmissions Cheaper Vincent Roca. N ˚ 0239 F´evrier 2000 ` THEME 1. ISSN 0249-0803. apport technique.

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(19) IJ>KLA M) FN>O+QPQ %A R. œ Ž j h Q ”  v j hfj w Q­vtj–h w h j w ” w ”th^j ” Q h Ÿ¸Qej w h^j `eu c^T h]` ›)\^§ Tr`tc cT c Q T _lh c4T7__ s$h _IT7u _ ”tT]”tc^\w c \^w•TjHv c_l‘Kc u j _\^c^ \rc `tQ s€_lc> _ hc T jlŽ cfT v T]u.` T vtI” T T h TV_I\f\4c \ w Ušu _l_lc^c^T T ”S«  ‘’‘¥T stsT ¥Hd€c Tr¯ \fc sU`e‘’c u._I\^c S o ” T v \^TU je” TYs hfj c j u j ‘$‘ w’ T µ T ³Z g $ | &(' jHh´g °ž³ ŸËµ ³U$ * ' h T]‘ w T]\ jav c Q T–s$T hfw’je”ew u]_l‘-5 jOje”ew’v jlŽ8” _lc^__I\ Ž _ h _I\ Ušw _ ”QT€ves j­j h \4\ w ¥e‘’w T ¥Hh.d¨› c Q T PPrmi› °žc h TV_lc^‘•d wyv u h TV_I\^T]\c Q T v T]cž jHh^ c h _„¬-u7_ vt” c Q T h^j `ec^T h ‘ j _ ” T.IT vjav ¥ h _ v u Q T]\  c TVu!T IT S Õ w c Q” T v \^T Ÿ U je” T7s hfj c j u j ‘’\]—e_l‘’‘Sc Q T h^j `tcfT h \]—HT]IT vw•Ž c Q T.d ”ej­vej c¥T.‘ jav šc j c Q T U`e‘•c w u]_I\^c ”ew \^c h^w ¥t`ec w’jav c h T.Ta—  j T]T]sh wyvOŽ™javth ” Uš_lch^w’j jav@Ž™jHh”t”$c hQew \€ h^j `tQVs $Æ2W ' ›  jHh vtwy” v \^c^_ v w u!TI—h"_ Ž™h^jaj h `tcfT h€Q h ` v$hfvej w’v wygvJ°ž³ W ŸËh µ ³v  T]T]st\_¶£wËu › jHv› c^T!bew c Qe j w c Q c vQ T \ vt` ” u!h^Tv _ Q¨ h `tw s _h¹ * TV›i\^\^© T]\]—nw•c jHZv TY$\f›c4} _lcfTw _ _+jah c U"” T w wyv T]_au jlŽ:`t µ s T [g s ,]` \_^T`0a\^bc^_lcc^d¢T.› X T  c `tc-_ d ` T T]_lc T]u.T IT $ ' T]u!c aT]\U T T.c4_ ‘’\ u._I\^T ³Z ‘ $ |l} ' h T x ` w’h T]\ c Q _Ic€T]_au Qªhfj `ecfT h7jlŽ c Q T ”ej Uš_ wyv@ T.TVst\€_ vt” T!btu Q _ v ITV\ \fc4_lc^T Ž™jah T]_Iu Q S PQ T-³ œ7©Og ·s hfj c j u j U€”ew `e\fc ‘’hfc ww ¥tu._a`e\fc c¨w•jH v h^jc h `tT]s T › ›o Pv Qew` \ v `tw’vO\^Ž™T jH” h Uš hf_Ij c `tw’jas-v' w w \‘•‘®c _lQ ‘yT\ j­v h `tT \fx T ` ” wyh T–¥Hd \^`$U€u Q `e‘’_šc w \^u.c^_a_l\fc^c T › hfj `ecfT h \c j u h T]_lc^T“c Q T+‘ j u._I‘  w T] jlŽ c Q T ³ $ Ya{ ' h T x ` wyh T]\`t\ wyv C³ ©Hµg=¶ ³“`e‘’c w u._a\fc ©Hj ` h u!T µw \^u j IT h d gih^jlŸ S \ w’v C_C\^s$_ h \fT Ÿ U je” Ts hfj c j u j ‘®‘ w’ T g °ž³ Ÿf© e c\ jj `u j h ‘u!¹ T$Æ¥$W TV{ u '´j c UjTVw’\nvOŽ™_ajHu!h c U w ITah —lTVc U Q T>j cf‘ Tj u]”e_lj ‘$Uš³ _ ©Hw’v µY\ g jIsŽ T.c TQ h T-_ s vth veTVj \fT` v v u!u!T TV\ jlw Ž c4\´_s \ h j T]` \^Th u.v T u.T wyv g¶ f+c h Q TšU‘ TVj \^u]\4_l_l‘ aT ”e¹ j cU"j _ _lw’vK‘’‘ ›”ewyÕ h TVQ u!cfT ‘’v dT.au jaT hvtv _ T]u!v c^T.T  ” ³ ©Hµg sj T.T h \]—I QeQ j ” c Q T v"›´Ž™PjHhQerw _ h4v” c Q h4vT U"Ÿ T]\4\4wy” _l ITrc j7hfw’jjec”eQ w T h sjOT.jeT ”eh wy\ v ›:P¶ Qtwvt\ ” w’vOŽ™jHh Uš¹ _Ic w’ja vw \is$T hfw’je”ew u]v-_l‘’‘•w•dŽ h Q T Ž£h TV\h^Qj T ” _ Q vt” Ušvej _˜dš_I‘’\ ¥h.T7i u._au T $Æ2W ' \i° c^T T.c  T–s$T u 5 _ \fc4_lcfT c^_ T]\×se‘y_Iu!TYT.aT c T– `ts _I\ U"T]U€¥T S o vt” ¯ v _l‘’‘•d_­U`e‘’c w u._I\^c_ ”t”$h TV\^\ w \ h TV\fT h aT ”  Qew ‘’T u!‘y_I\4\ µ _ ”$”th TV\^\^T]\r_ h T7_š\^u]_ h u!T h TV\ j ` h u!T w c Q ° g  Y$› . gj. P>OMkl6 ;

(20) nmkoVprq? O[FN%M. ³ j wyvew U sw h.7]› w’v ­v c Q QeT w v `tU€¥Th hrjIŽ wyU€v `thf‘•jec w” u]_I\^c× hfvj `tst\r`thf\^j T ”¨j w j\_I‘•œY‘Sc µYQ m T7U ¶žœjavh T µ w Ušs jHhvtc4”_ v m cr_I\rh c Q T]”t\^”eT–w _aw’jastvse¹‘ w u]_lQ c w•jHv w \r_ h TYc j ¥w T]u j” U"jT cs Q T]st\^`thT‘’_‘’” _˜daTh ° h T v ” c c h w \_ v stw’\4ja_IU vswT \4\¶ w’×ja› v T › \4u Qc m T]U"T]`$\ |Iu!› T€| °žc_ h T.mT]‘ w T]\ s ja} v c c ¹ Q u T>Q s‘E— h h T]\^T v u.T QjIh Ž _ Â^w ºTVÃUšº.h ÊÈ_ Ԙº.QeÂ2jOtfjÀ„Â3_˜Ê£dIº.T»$Ğj º_ Ò ”tu ja”Cc v jH ahT]\^”tc —hfw’jajc v _lu c jHv \ c hfij hT]‘e‘•\^‘8u \4wQ ` TVQeU"cfw’vT T Ž™Q cjah ‘y_˜dIT T c _ \^U \^\ \ T Z ³u$ '˗tZ $ ƒ.'  T T–T]_Iu T]u.T IT u \fTV\ic _ s¨_š‘y_˜dIT  c c T } .

(21) ¯t½.Å-beT ę” Çtº€\^T.Ã.c ÁejIÂ3Â^Ž º._˜»$„Ä8_ Îew ‘yÀV_IÀ„¥e¾)‘’T–À Ӗ‘’_˜Â^daºTú!h \ÊÈԄ›´º.œY¿µ› m \ j _l‘ w \rc j“º.»¢¼I½.¾•ºęÇtº ¿!ÀlÁeÂ^ú ĞÀ­ÁO¿.º"À„»¾ÐÅ­ÄÈÇ$º ¾’¼„ÅIº.¿€ÄÈÇ$¼„ļ„Â^º"¼IÃ.ÄËÁ$¼„¾È¾ÐÅ-Â4º4Ñ.ÁeÊÈÂ^ºÒ Õ T­_l‘y\ j \ Qtj  c Q _Icc Qew \7s hfj c j u j ‘u._ v ‘•TV_ ” c j \ w vtw ¯u]_ v c–\^_˜ wyv a\Y Q T v `t\^T ”  w c Q+h^j `ec^T h ¯$‘’cfT hfwyv CcfT]u Q$vew’x `eTV\ ‘ w’ T P$ |IQ { ' hjahP jIŽ  Q $ ƒ 'KT]IT vCh€w•Ž w _šja\ hw’v I‘’vtT–sw 7 U” `e‘’c w u._IŽ™j\^crj h^j `t«šs © w \`tw’\fjaT v ”C|w’v ” c Q _lc>w u._a\fQ T › œYµYm hfj j j ›© w’jav } ”ew Q T TV\fc c TCst_IsT \ a_ T _I\ ‘•‘ >\ TVu!c T.c4_ ‘’\€c T s c u ‘ T]u.c \^c^` TV\€c T ¥T v v T.¯$c^\ w’jajlv ŽiœY”ewµm  w c Qvew jHv h–u.wy`tveUw `ew ‘y_lwsc 7 w ITw•jH_ v vt”h^v$j ” `ec^T h hfŸ ¥$_Iv \^T ” ¯$‘•c^T hfh^ww’v v \^u Q T]U"h T]\ ›×P›­Q T © v \^T]w•u.jHc v w’javZ”eY-w wyv c hfje” `$hu!T]\ w c4\ ” w UšjHseh^‘•T¢Ÿ › U"T c4_lc — \^u]`t\^\^T]\c U"T c _l‘ _lc —8_ s T]\^T c4\YT.bts$T U"T c^_I‘ T]\4`e‘’c^\ T]u!c & \^u]`t\4\fTV\ T.‘y_lc^T   wyv _l‘’‘•d¨iT7u jav u.‘’` ” T ›  9 < %   )7)-52 °jHv hn”tc Qeh^jw \i\^T]u.c w’jav h×T _I\4\^`$vtU”ewyT v ¶ W jH¹ h´c veQ j _IcnTV_Iu Q ‘’_˜daT j hw \×u._ hh4h^ww T ”jHhv _ ¿.ºžÎtw ¼„Â4¼„Äžº ”t”$Áeh ¾ÆÄEʣü˜›:¿3o>ÄKŽ ÍIÂ^À„h Á˜Î¢Q ›)PQj T h h T Ž™jah T j ęÇtºY¿.À„v$Áe”eÂ4w’Ã4v º _ v ”t” \ st\i_7‘y_˜dIT ¥Hd­\^T cist_au T.c4\c _ st_ c u]`e‘’_ U€`t‘•c u]_I\^cn_ TV\^\ cfT c TY\ ` u!T>\^c st\n\^T T. s\_t^_au`0 aT]b c^c\d c j _­ h^j ”`$sSŽ —$c Q T€\ jlŽ c wyŸ v \^c^_lc^T  w TVsec h¥H¹3d›  U€`eÂ^‘’ºc Ãw º!u.ÊÈ_aԄ\fº!c  h^j ”$`t”cfT h ja\ h>¶ \^”$T]hfu.j c w’jav Y› }O¹nŽ™h jah c Qek jaw \>w’ve wyhfv j `tjHsh \f‘ j ‘•w’d v ”ew \^Q _asts$TV_ j h \ w ¶ T › ” › `t\^T]\>_ T _I`e‘’c &šU `tcfT]\>c UT _ \ st\_š‘’_˜daT ¥Hd ‘•TV_˜ šc T _I\4\ u _IcfT U`e‘•c Q w u]_I\^c hh^j `ts ›:j Õ ›iT © _l‘y\ j w•jH_av¨\^\4`t} U"vT ¶Ë|H¹ 7 c Q _IcQ c h _ v \4U jIŽ´w \4œY\ w’µjav m \×_ hQ T v Ã.Á Q Áe¾’¼„ÄËÊÈԘºj — w˛ T ›´h TVu!T ww’jaw’v v "‘yh _˜dITveh j nh T x ` › w’h T]\ h T]u.T w  wyv _I‘•‘Kc T7‘y_˜dIT \×¥$T]‘  TVu!c _ _l‘’d T]\×c T `t\^T  T c T]\^T7cž _a\^\4`tUšsec \×_ T c>U"T.c. . . . 9%.  

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(23) R OGFNBM #t #t. œYµmw vCº.»¢Ò žÄ¸À fº!»±Ò΢Â^À„ÄžÀVÃ4Àl¾ jah4Hw’v wyv h x ,„h jHv je” ›PQ h Ž™jah œYµmQ _I\ vej h T x ` wyh T]U"T v c v T w c Q T h jHv c Q T \h^_ j `ec^T hiŽ ` v u.c w’jav _I‘ w c w T]\ vt—Ija hrjav c Q T hfj _`ec wyTv ­`e_ TVvt\fc ” °^T]²Y\4s³ g \^s Tih^U j c j u T j ‘y\ w’v T `tT \^T › T œYµm¦h T]‘ w T]\ jHv ¥ j c Q c Q T \ j ` h u!T–_ vt” c Q T h TVu!T w IT h \ wy” T]\ «w c w \rc Q T Â^ºÃ4º.ÊÈԄº! \ h TV\^s jav \ w ¥ w ‘ w cžd-c j _I\ šŽ™jHh _ ”t”ew c w’jav _l‘ ‘yw _˜dIT h \ j Q QT v ¿!_IÀlstÁes Â^h^Ãj º s hfjw _lc^T h ¶ T › ›–”$w•Ži”eQew w w•\YjHv u jav aT]\^c w’h jav u Q jav v c h^j ‘) U ” jO” j`e‘•”eT"j \^_˜dej \Y\ je¹ _ h v$” wc jCh.h ›×TV\^œ s jaŽ v$”j c h j

(24)  Q  vU"h TV\^Ž \4_l aT]\ ¶ › › °žc › w•Žr\ Qt`tws\7c Uš_„c b w T U€`tU v `$U€c ¥Tu h–T]jl_IŽ cfT7‘’_˜_ daT h \ c Q _I\7_l‘8¥‘’T._˜T dav@T h \rT]_I u Q TT ”¹3_a›"\ PT Q T­c \ j ` h u!Tš\ _l¥H‘y\ dCj _ u Q TVT]uu.T \ITsT h^w’jO”tw uu]_l`‘’‘•d\fT c Q _lTc7u.TV_ _Iu Q T U`t`e\^T‘’c w u.T _I \^c hfj `this w w \הt`$h^\fj T ” ¥H”Sd › jav T jah U jHh T h TVu!T w aT h \n¥Hd-\fT vt”ewyv   U"T]\4\4_l ITV\ › ° Ž:vej ¥ je” d h T]\4s jHvt” \]—Oc Q T v c Qtw \ ¶Evtj  `t\^T.‘’T]\4\ ¹ ‘y_˜dIT \ s$s$T. R1 requests layers 2 and 3. layer_3 (highest layer). layer_3 (highest layer). the source queries then drops layer 2. receivers request layer_2 layers 1/2/3. source queries then drops layer 3. query then drop layer 2 ... query then drop layer 1. R2 requests layer 1. source queries then drops layer 0. layer_2. layer_1 layer_0 (base layer). ... ... .... layer_1 layer_0 (base layer) t0 (tx start) t1. t2. time. continuous tx. low-end receiver R2. t1. t2. t3. t4. time. high-end receiver R1. low-end receiver R2. "!$#&%'%'())+*&,#+*. .-/102)+"!$#&%'%'())+*&,#+* high-end receiver R1. jHv w a` h TQ W «"h P®h _ v h\4U w \4\ w•hjHv \ jav ”S› T]_au Q ‘y_˜dIT h  w c Q _\fd v u Q$hfjHvej `t\ jHh _I\^d v u Qth^javej `t\–\fc4_ h c jlŽ c Q T h TVu!T w IT h \38 w c QœYµm ‘•d¨c T7 T]d-_ T]_a\×_ T–`t\^T w h ¶ ¹ vt”+¶ ¹ j h h v v Q j h w Q vt” w Qej Q œYµm hfj j j ›PQ h h_ T– cž ajš` h T]T]\u.T W w IT _ h \]—H_ _ Qew ¥ QeŸ T u vt”UšhstTV_ u!T Tw I‘’T_˜h5daT 476 Uš _ Qej_I I\4T]`tU"¥tT\4u h^cw ¥_IT]c×\rc c j T7_l\ ‘’‘ ` Ž™j u!` T–h  ‘y_˜cdIT h _ \]—e_ vt ” c _"‘ j `e cŸ cT vtT ”Ch T]u!T w as T h 49c 8 u  ‘ Qtj­javT ‘’d T \4`t¥t\4u h^w ¥T]\rc j c Q T–¯ h \^crcž j ‘y_˜dIT h \ ›®Õ T u jHv \ wy” T h cž j­Hw’vt” \ jlŽ _Istse‘ w u._lc w•jHv \ « S _ v _Istse‘ w u._lc w•jHv€”ejaw’v _ jav Tic w U"Tׯ$‘’T×c h _ v \ Ž T h׶ ¯$ H` h TYW ¶ _ ¹  Q T h Ti³³ª² $ Y ' w \_a\^\4`tU"T ”¢¹«®Q T h T×_I‘•‘Oc Q T h T]u.T w IT h \ U€`t\^c>¥T h TV_ ” d-¥T Ž™jHh T–c Q T7c h _ v \4U w \4\ w’jav \^c^_ h c^\ ¶ \fd v u Qth^javtj `t\r\^c^_ h c ¹3› S _ v _astse‘ w u]_lc w’jav”tjIwyv u jHv c wyv ` j `t\>¯$‘•Tc h _ v \ Ž T h \ ¶ ¯$ a` h TW ¶ ¥ ¹^¹«>Q T h T h T]u.T w IT h \>u]_ v _ h^h^w aT _lc_ v d¨c w U"T ¶ _I\^d vOŸ u Qth^javej `t\r\fc4_ h c ¹› hfj  w H` h T¦WI—riT\^T.Tc Q _lc¨`t\ wyv œYµm T v _a¥e‘’T]\­c Q T“\ j ` h u!Tc j h TVU"_ w’v _a\-u!‘ j \^T_I\-s j \4\ w ¥e‘’Tc j c Q T“_au!c^`$_l‘ h T x `  wyh TVU¤ U"T v c^\ jIŽ c Q T h TVu!T w IT h \^T.c ›  jah wyv \^c^_ v u!T-‘y_˜dIT h \ | _ vt”¦} _ h T x ` w u  ‘•d ”th^j stsT ” _ Ž cfT h c Q _Ic 4 6 Q _a\7¯ vew \ Q T ” Y.

(25) h T]u.T w  wyv Cc Q T­ Qtj ‘’T¯‘•T ›"PQ T­sT h^w•je” \– Q T v c Q Tš„_ h^w’j `t\‘y_˜dIT h \_ h T wyvt” T]T ” `t\^T ” _ h T h T]s h T]\^T v c^T ”wyv ¶E” _ h^ , ‘ w Q c ¹ h T]d”K›Y›Pp Q j T€ QeQ w cfTš_ jšh T]Ž _a\>h u jHh^h ”tT]w’\4”s jHvevtj ” c j _`t\^T.” ‘’T]\4v \ s h TV\fT v v u!T jlŽ c Q T€‘yv _˜dIT Q h \ ¶Ëw vej¨h T]Q u.T w IT h _ h v dU w jahh T ¹  Q T v+vtœY” µmQ w \ w vtj c w`tc \^Tw \ ” T.c^T]u!c^c^T T ”c ¥H_ld-c \c Q T _ \ j ` ih T u.T ›PQew \ c w \_I\4”e\4w`t\4U"u.`$T \^\^T _ ”¨w’dCv ‘’\^_IT]cfu.T c w’u!jad¨v ¥Y$T.› |ecž×› T.T c Tc U"T c T‘’_a\fc TVu!T IT ‘•TV_˜ITV\_ c T€c U"T NIL. NIL. LAYER_REQ recv’d && accepted. LAYER_REQ recv’d && refused. layer already exists. layer doesn’t exist. send LAYER_REQ. LAYER_ASKED set layer_asked_timer send ADD_LAYER. ACCEPT. REFUSE send DROP_LAYER. DROP_LAYER received layer_asked_timeout ADD_LAYER received. ACTIVE. set softstate_timer unset drop timer. ACTIVE. softstate_timeout. IS_THERE_SOMEBODY PRESENT recv’d send PRESENT_OK. send QUERY set drop_timer. QUERY received. WAIT_BEFORE_ANSWER. drop_timeout. SEND_ECHO. PRESENT_OK recv’d (sombody else answered...). CHECK_DROP not yet possible. possible. DROP_LAYER. unset timers DROP_LAYER received. set wait_timer. DROP_LAYER received wait_timeout. SAY_PRESENT send PRESENT. set wait_ack_timer. send DROP_LAYER "remove" layer. PRESENT_OK recv’d. wait_ack_timeout DROP_LAYER received. NIL.  %'(#+ . .-/    #. NIL.  w H` h T |t«r¶¸©Hw Ušse‘ w ¯$T ”¹  w’vtw c^T © c^_IcfT–³“_au Qew’v T]\ Ž™jah TV_Iu Q ‘’_˜daT h u jHv c h^j ‘’‘•T ” ¥Hd œYµmn› P _I¥t‘•TšW «iœYµm \ w v _l‘ ws7 _lc w’jav U"T]\4\^_I IT]\ › 

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(46) £ŒI‰]ˆ Ü ®Ù  Š Ý    ‹ ´‹ ÚÙ Š \ wyv ª_+u]`tU€`e‘y_lc w aTC\4u Q T ” `e‘ w’v ª\4u Q T]U"TUTV_ v \"c Q _lc"‘’_˜daT h  u._ v jav ‘•d ¥T ”thfj stsT ” w•Ž c Q T h T w \ vej ‘’_˜daT h  › ° v s Qeh w_Iu.c” w u!T–u h jHv 5h w u!w c^\ ” jIŽ cfT v c^”_  T–se‘yQ _Iu!T v › ° v x¯$ H` h h T } iT7›®_a\^§ \4`tU"T c Q _lQ crc Q T‘y_Ih \^c h w TVu!T w h aT h h ‘•TV_˜veIj T]\×_lc×v c wQtU"h^jaT vtws 7 › ”  jHh T]_Ih u Q { ‘’_˜davtT ” h c \ TVst_ c^w ` T Q \ T]cfT]u.hcfT|"Q _lc´c T vCT.”$behfc j `eT ” d\^c^_IŽ™ja Ih T T]wyu]v _I`t”t\^Th^j c T>‘’”_˜dawyTv \´Q c w’Uh T \ih4vS_ › T ci\fd u T —l‘y_˜dIT \ _ W U`t\fcrr_ crc _Ic‘’_˜daT _I\¥T.T sts$T ¥$T T–¥T s$s$T c T c4` . . . . . QUERY.... timeout=>dropped!. layer_2 (highest layer) QUERY.... timeout=>.... dropped!. layer_1 QUERY.... timeout=>.... dropped!. layer_0 (base layer). ‘y_˜w dI aT ` hrh T|t› }t« ° v cfT h^” TVs$T vt” T v u!T jIŽ ‘’_˜daT h \r w c Q _-u]`tU€`e‘y_lc w aT€\4u Q T]U"T 3¢‘ j iT h ‘’_˜daT h \ ”th^j s w \ ” T]‘’_˜daT ” ¥Hd¨c Q Ts h T]\^T v u!T jlŽ time. t_0: receiver leaves. . 9%gj. o

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(184)  6  (*)*+.- ¹f¹  V ¶ $¹ /   ¶   3 45® ¶    3 ¶ YO¹ P  ¶ $ ¹  -Ù £‹e‰  Ý  ˆ    Ü £‰ 3254   10 oYvªw Ušs jah c^_ v c Ž _au!c jah–w \ c Q T-°^²Y³ g IT h \ w’jav+w’v `t\^T-_lc€c Q T h T]u.T w IT h \ ›­Õ w c Q °^²Y³ g ¢Wa—®_ h T]u.T w IT h ‘’T]_˜ wyv _ h^j `ts ”ej TV\ vej c´c h dšc jw’vOŽ™jHh U _ v de¥ jO” d ›PQ T h T Ž™jHh T ” _lc^_€\fT v cic j c Qew \n hfj `ts  T]T]st\ 5 j  w’v €` v c w ‘c Q T ‘ j u._I‘¢U`e‘•c w u]_I\^c h^j `ec^T h ”ew j h Q h w vej€h w h v jHh Q v c(\98 c^ a;:C9   ±›IPQ ” Ž x h hfw’je” '<>=@?BA CDE.)F — w \7\4W u | &€IT \^T]\´u jac vtT ” \ T $ÐWa\ 2W ' ›iœYT]µu.mT Iu.T _ vC_ ”twd­\4u U j aT hTYc _lQ cnT c ” TTVst_ T!h bec^7c` h 6 T jlŽ c Q T7‘y_I\^c h T]u!T w aT h ¥T T Ž™jah T T–_a°^`e²Y‘’c³ g `e±T W dšw•Ž s$« T —   ¶ '!(" #   $  C ¹ 68 (*),+.-HGH<>=I?JA CDE.)KF ¶& ¹ Žw’v x w•jHv ¶ ¹€w Ž Q v œYµm·”tj vej Q j¦h ” Q s hML v jlŽ g › PQew w v ”_ t”e° w c w’jav T _I‘ `th _lTVc _I\ jav c & j-” T!\ ¯ v _lT ‘y\^TI_ —nc T    st_ h _aUTVT]\ cfT h c \4Uš_lT.‘’‘y‘•s T h c c Q _ T v `tW |u.T¨&"c\^T]u T jHvt” \ › ‘’_IcfT u!d °^²Y³ ±W \ \š_ W{  .  . . . . .  . . .

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