A Dynamic Architecture for Reducing the Response Time and Avoiding the Congestion
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. A Dynamic Architecture for Reducing the Response Time and Avoiding the Congestion Mohammad Malli, Chadi Barakat, and Walid Dabbous. N° 5195 – version 2 version initiale May 2004 – version révisée October 2004 Thème COM. ISSN 0249-6399. apport de recherche.
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(49) x|Gc stQcbmpoeȹ|}cbmGv`vu`¢ vuo}^`cemGrnqz¯yc oO mx|}|Gvx6`t Acb|zÊxuQo}^`c o}vaMc º^Qc&uvo°Qu`vwmG^`cbmmpcb|GSvu`¢MoG^Qvm |}c t`cOmoÈ o}^`c]d¶{Àq&ryu`uQcbqo}vrsumpo}xoGcvm%q |}cbxoGcOvuo}^`cmpcb|Gsc&|%xuQoG^`cÇd vwm%mpcbusoQxsqz¯IoGrIoG^`c q&vc&uoÊ´½]%^Qc&u6µ xuQ xy|Gc tQ A`xoGcO >cb|Gvrnnvwq&xlSloG^`cerxy$cOmo}va xo}ry|x¢ycbuo½xuQ±mo}ry|}cb$vu xe°QchoG^>xooG^Qc Q|Grs`vuQ¢Mxy¢ycbusoLqbxu|GcOxyº^`c&uu`cbq&cbm}mGxy|Gls´ % c tQmGc ¸xsmoG^`cM|zxoGcMry¬Zc Ãn Aryu`cbuoGvwxJ¢y|}rº%oG^-r¬¶]d¶{Bq rsu`¢ycOmo}vrsu±ºvuQnrº ntQ|Gvu`¢oG^`c mGrº mozx|Go `^QxymGc M 1 M 8 I 1 4 1 4 ÈD¡sÊ ]%^`c¶c&u> ry¬`oG^`c%mGrº mpo}xy|po `^QxymGc%q&xue>c%q&xytQmGcbSlhoG^QcZrnq&q&t`|}|GcbuQq cZr¬>x½ Qxyqz¯sc ormGmxryu`¢oG^`c >xoG^vursu`chr¬,o}^`|}c&cq&xsmpcO%m %ȹv ÊZoG^`chQxyuQnºvwSoG^vwmmGxoGt`|zxo}cbrsuo}^`c QxoG^$mpcb|Gsc&|Z¾q vcbuso ÈÉq vcbuso mGc&u>nvuQ¢±|zxoGc|GcOxyqz^`cOm ½Ê ´³]%^QvmIq&xsmpcqbxu rsu`l-^Qxy ` Ac&u?v¬oG^Qc `|}rnntQq oIxxvxy`cQxu>nºvnoG^n¾ `c&wxlvmcbm}moG^Qxyu«oG^QcIa xÃSva tQa ºvu>nrº xt`cÈ 8 M #Ê´$ȹvvwÊh]%^`cMq rsu`¢ycOmo}vrsu ºvuQnrºxt`cMr¬o}^`cmG rº5mpo}xy|po `^>xymGcI|}cbxsqz^`cbmoG^Qc `)t ;c&|}vu`¢qbx Qxsq vol ÈÉq vcbuso mGc&uQ`vu`¢ |zxo}cM|GcOxyqz^`cOm M
(50) ʵ,oG^`cbu¸x¬ oGcb| x$q c&|Go}xyvu-oGvaMcyµx$ Qxyqz¯sc ohvmrsmporyu-oG^`c >xoG^¸mGc&|}ycb|¾ q&vc&uo%nt`c½oGr o}^`c|}xyuQnryaÄrsm}m `|}rnq cOmGmr¬6|zxoGc ºZcx|}c½xsmGmGt`aMvuQ¢È¹vurs ` >rmpvoGcoGrIq&xymGceÈDvwÊ µSoG^`c xxyvwx`c QxyuQnºvwSoG^ 5vwmuQro½|}cbxsqz^`cb$^Qc&|}cOÊ´Iȹvvv Ê *Zc&¬¹ry|}c |}cbxsqz^`vuQ¢MoG^`cI`)t ;c&|}vuQ¢q&xy Qxyq&volry| o}^`cexxyvwx`c QxyuQnºvwSoG^±ryuo}^`ce >xoG^-mpcb|Gs c&|¾q vcbuobµ;x Qxsqz¯yc o½vm½rmoryu$o}^`ce >xoG^-x¬ oGcb|o}^Qxo xyu¸xyc&|zx¢sc uSt`ae>cb| r¬ Qxsqz¯yc ozmhc tQxyJoGr ^Qxsm>cbc&u mGtQq&q&cbm}m¬¹tQl«o}|}xyuQmpaMvopo}cb-oGr$o}^`cq vc&uob´ % cu`ryoGc o}^`c q vcbuo%ºvuQnrºBmpvÅ&ch|}cbxsqz^`cbxo%oG^Qcc&uQr¬oG^`c mGrº9mpo}x|Go `^Qxsmpchvu$qbxymGc ȹvvv Ê 1 È¹Ê mGr M K 4 8 ÈÉyÊ 1. ]%^`cea xÃnvaet`a mpcbuQnvu`¢|zxoGc oG^Qxoq&xyu>ce|GcOxyqz^`cO$xoLo}^`c cbuQr¬Jo}^`cemGrºmpo}xy|poL `^>xymGc q&xyu Acc Ãn `|}cbm}mGcbSl ozx¯Svu`¢IoG^`caMvu`vaet`aÆrsc&|¶oG^Qcxsmo%oG^Q|GcbcaIcbuoGvryu`cOqbxymGcbm # M K 4 M # 8 12# M È sÊ C > jSa xy%mpvÅ&cq ryuo}c&uo}meq&xu¸Acq&ryaM `c oGcbl o}|}xyuQm¬¹cb|G|}cb³ntQ|Gvu`¢$oG^QcmGrº mpo}x|Go `^>xymGcy´ %V^`c&u o}^`c q rsuoGc&uomGvÅbcvmLxy|G¢scyµnvo½mozx|Go}m%Ac&vu`¢MoG|zxu>mpaMvopoGcOvu$o}^`c mprº mozx|Go% Q^QxymGcyµno}^`c&u«q&ryuoGvuSt`cbm . . .
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(52) ©¦ Ó . vo}moG|zxuQmGaMvm}mpvryuvu$oG^`c q&ryu`¢scbmpoGvryu$xyrsv`xyuQq c `^Qxsmpcs´®u$o}^`cu`c ÃSoLoº¶rmGcbqo}vrsuQm%º¶cvuSycOmo}v¢xo}c o}^`cbmGcoºZr qbxymGcbmb´. §¨ .¥ Ï §© Ó Ï ¦ Ï Ô ¦ Ï ¥ ÓSÒ ¥&¦O¨n§¦¨`¥ Ï ®uIo}^`vmq&xymGcyµyºZcLq&ryuQmGv`c&|JoG^>x o *44%|Grst`uQS¾äoG|}v >mx|}c¶|}c t`v|}cb oGr q rsaM `c&oGc%o}^`cLnrºu`rsxsÁ´]%^`c `rºu`rxyc&uQQm>c&¬¹ry|}c ]d¶{3oG|zxu>mpaMvwmGmGvrsu|zxo}c|GcOxyqz^`cOm ´¶]%^`c xoGc&u>q lq&ryaM Aryu`cbusozm^Qxsc o}^`ch¬¹ryrºvu`¢Ic Ãn `|}cbm}mGvrsuQ%m & ) !=1 > 4 C M xyuQ ) , !=1
(53) v¬ M # `µ È Ê º^Qc&|}cyµ 1 8 È Ê # ¿o¬¹rsrºLmZoG^Qxobµ K &1 M > # C 4 K ÈDsÊ xyuQÁµ K ÈpbsÊ M # 1 M > M C 4 # 8 ;c&uQq&cyµSº^`c&uoG^`coG|zxuQmp¬¹c&|Zvm%q&ryaM `c oGcO vu oG^`chmGrºVmpo}x|GoZ Q^QxymGcLAc ¬¹ry|}c|}cbxsqz^`vu`¢ `µoG^`c o}|}xyuQmp¬¹c&|¶oGvaMcv m K & )- "!=1 M > # C 4 M xyuQ & )-, 7!=1 K v¬ M > M C 4 # ´ ÈpyOÊ. §¨ .¥ Ï §© Ó Ï ¦ Ï Ô ¦ Ï © Ó Ï ¥&¦ Ó ¨ Ó ¹Ô¨ © Ï ¨`¥ Ï ]%^Qcq ryuo}c&uo mpvÅ&c vwmryu`¢sc&|oG^Qxyu³>cbvu`¢«xsqz^`vc&ycO±vu oG^`cmGrºmpo}x|Go `^QxsmpcsµmGrvoeq&ryuoGvuSt`cbmhvo}m o}|}xyuQmGaIvwm}mpvryu vuo}^`cq ryuQ¢ycbmpoGvryuxsryvw`xu>q cL `^>xymGceȹrs|Zvuo}^`chmo}cbxy`lmozxoGcʺ^Qc&|}cLoG^Qco}|}xyuQmpaMvwm¾ mGvryuvmq&ryaM `c oGcO$x¬ oGcb|%oG^QxooG^`c mGc&u>nc&||zxo}c^>xym%|}cbxyqz^Qcb . '. '. . . '.
(54) 6. M > K C 4 # M . pÈ OyÊ % c c&xtQxoGceoG^`cMºvuQnrº c&ÃS Acbq oGcO«o}rAcM|GcOxyqz^`cO±xoo}^`cMc&uQ-r¬ZoG^`c mGrºmozx|Go `^>xymGceSl o}^`ch¬¹ryrºvu`¢Ic Ãn `|}cbm}mGvrsu . & !=1. . 8. . M # 1 1 1 . v¬ Èpb¡sÊ v ¬ 1 M . M > ' 4 C v¬ 1 M > 0 4 C M . jSr>µº¶c¶c&Ãn `|GcOmGmo}^`cuSt`a Ac&|ry¬>|}ryt`uQQm º^`vwqz^evwmJ|}c t`v|GcOoGrh|}cbxsqz^ oG^QcºvuQ`rºÀmGvÅbc*& ! ÈDvÉ´ cy´µno}rI|}cbxsqz^
(55) yÊ%mGvu>q choG^Qc>cb¢yvu`u`vu`¢Mr¬oG^`coG|zxu>m¬¹cb|Lxym M . v¬ 1 C > 1 Èp&Ê v ¬ 1 M . > 0 4 C K v¬ 1 M > 0 4 C M . % cu`ryoGc 4 oG^QcuSt`a Ac&|Zr¬6mGrºVmpo}x|Go|}ryt`u>`m|}c t`v|GcOIoGro}|}xyuQm¬¹cb| & 0 "!Á`xo}xSloGcOmvu o}^`c q&xsmpcº^`cb|G coG^QchoG|zxuQmGaMvm}mpvryuvmq ryaM `c o}cbx¬ o}c&|%oG^>xooG^Qc mpcbuQnvu`¢M|}xoGch|GcOxyqz^`cOm $ÈDmGc&c st>xoGvryu³ÈyÊGʵno}^t>%m v¬ 1 1 &4
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(57). ÈpOyÊ v¬ 1 M > ' 4 C M . ±vm oG^`cxsc&|zx¢sceuSt`ae>cb| r¬ Qxsqz¯yc ozmhº^`vwqz^¸vm oG|zxuQmGaMvoGoGcb³mGtQq&q&cbm}m¬¹tQl-vu³oG^QcmprºWmozx|Go Q^QxymGcM>c&oºZcbc&u-oG^`cMo}vaMc º^`cbu±o}^`cMoG|zxuQmGaMvoGoGvu`¢$`)t ;c&|vwm m}xoGtQ|}xoGcb-xuQ±oG^QcMoGvaIc º^Qc&u oG^`c o}|}xyuQmp¬¹c&|vwmq&ryaM `c o}cbrs|½x >xyqz¯yc&orsm}mLvwmrnq&q&t`|}|GcOÁ´ %-cIc&xytQxoGc vu«oG^QcbmGcoºZrq&xsmpcOmLxymoG^`c ¬¹rsrºvu`¢ . M
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(66) K 0 1 M . xu> . ÈpbsÊ. > ' 4 C 0 v¬ 1 M > 4 C M . %] ^`ca xÃSva tQa·uSt`a Ac&|ry¬½SloGcOmIoG^Qxoq&xu3Ac«mpcbusovu3oG^`c«qbxymGcº^Qc&|}co}^`c$oG|zxu>mpaMvwmGmGvrsu vwm q&ryaM `c o}cb¸x¬ o}c&| oG^Qxo oG^QcmGc&uQnvu`¢«|zxo}c |GcOxyqz^`cOm È o}^`cq&ryuQnvoGvryu¸vu tQxoGvryu ÈpOyÊvm m}xo}vmp°QcOQʵ`qbxu>cc&ÃS Q|GcOmGmGcbxym ! .
(67) . v¬ 1 & !=1 # M 46 v¬ 1 $M . ÈäsÊ v¬ 1 M > ' 4 C M . ;c&uQq&cyµ6º¶cIqbxu-c&xtQxo}c o}^`ceoG|zxuQmp¬¹c&|oGvaMce|}c t`v|}cbo}rq&ryaM `c o}c o}^`cIoG|zxuQmp¬¹c&|vu-oG^QcMq&ryun¾ ¢scbmpoGvryu$xyrsv`xyuQq c½ `^Qxsmpchry|vuoG^`c mpoGcOxynlmpo}xoGcÈDv¬oG^`c q&ryuoGcbuomGvÅ&cxrºLmzʵ`xsm% K & )-, 7!=1 , 0 "! ÈänOÊ º^Qc&|}c , vwmIoG^Qc«]d¶{Äxsc&|zx¢sc oG^`|}rytQ¢y^` `t`oMvu3oG^`cq&ryu`¢scbmpoGvryuÀxsryvw`xu>q c Q^QxymGc¸È¹ry| vu3oG^`c mpoGcOxynlmozxoGcÊ´¼Q|Grsa b ¿µnºZchtQmGcoG^`ch¬¹rsrºvu`¢Mc Ãn `|}cbm}mpvryu # , 12# M ÈäyyÊ C º^Qc&|}cyµ . . . . jSr>µ.
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