On the pathwise optimal Bernoulli routing policy for homogeneous parallel servers
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Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. On the pathwise optimal Bernoulli routing policy for homogeneous parallel servers Ger Koole. N˚ 2443 Decembre 1994. PROGRAMME 1 Architectures paralle`les, bases de donne´es, re´seaux et syste`mes distribue´s. ISSN 0249-6399. apport de recherche. 1994.
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(39) FIFI= \n_L =lJ DVY[_N\`uEG!YVL JxN\YV`vN+WgWg`+l_Y[N\`vFPWg`!L#WZY[Y[WZU_`GcgN]J.JdcZEiYvh ! / N#J.a_aXcZj t 9GO D6Y[F :3 9< 9 @ B [= F GC=D[ b0FdY[NPY[!U_JdY0!N#T\J.nEKN\lk^_T\N0YVU_N ! xJdcg^_N\`PFxG VHh ?J.n_L ^_n.YGWZ
(40) c I 0 |JJ J.n_Kl
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(54) =" 0O DRq 3 9
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(57) =
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(59) = [=D27 WZI Kh F.6 T\J.n?Y[UrWgnZ9Fx!JIn1JIEGEuWZxJdcN]IN\n.Ymj{N]Wgn_HsT\FInk`uY[EG^_T]Y[N\lfEGFIL2Y%F9`K^kT\T\N\`K`uWZ.N %N\EGn_F.^XcZcZWN[qkaN\EvWgLMr N\n.Y[` WgJ.nsEKEvY[WZxUkJxN cXfJ.Fd`cZcgF\`KN\+T\WgF.n_n_Hl %N[Jiqkt.a& N\/ÌEvWgLMWZY[N\U9n.a_Y{EKY[F.U_j_JdJ.YjX`KWZN\cZn_WZYlkt&`£ Y[9KU_O Npp8JIEG5 EuDWZ;YVWgU_n_NHSBT\^_EK`u`uY+YVFIN[Lqka{N\N\E EuYVWgF0LMN\N\J.n.T[YbU cgN\;JI^_l_N\`p^_NbYVF#+JWZY[U[`va_tXEGLMFIjkLMJIN]jXYVWZEucZWgWZTYt < WZY[WZdU?Jxc_a_JdEGFIY6jk;JI^_jXN\WZ^_cZWZNmYtOd[ 5|iun_plkN\OmN\lY[hU_Y[N U_NpEGY[`uFdY0Y[JdN[c_qka_a{EGN\FIEuWgj_LJ.jXN\nIWZcZY!WZYcgtN\J.Fdl_`+`KN\YVnkFMlXJ.Wgn_nHP[JIJ.n#`utXJ.LEKEvLMWZxN]JdY[cXEvY[WgFPT r^kJIEGN\Eu^_WZxN0JdO+cfhBWg`p T\UXF.WgEKTVEKU?N\T]Wg`Y rJ.n#d/Ì . J K E u E ^_J.EKnkEvl_WZxN\JxE cfh{YVUX`vWgtX`0LMT\LMF.n_N]`uYVYVEuEKWg^_TST]FIYGESWgFIJIn{`vh tkJ.L` LMr< N]9YV Eu9KWg4OTx p `@5 N]YSD
(60) D@^_ `0`v9Y[ J.5|EuY+p +0O WZDVY[U&7MY[5U_QN b0`utXF\L LMT\F.N]Y[n_EvlXWgT0WZYGWgJ.FIEKn1EvWZxJxJxcg`Gcg`]F&dF.iunn?YVH.U_N\n_N N\YEKtXJdacfhkN%FdN U_JiINPY[U_JdY ! ! ! 9$ D :3 9< 9
(61) = \=D7 r< 3 9 Qp O = \=Vp O DI r< 3 9
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(63) GC=4p 0O D/ r< 3 9# / 0 \= I G p O =p 0O D? /$N~UkJ\IN ! ! 3 9 / 0 Ep O =4 $ GC=Fp 0O DRq 3 9 np O =
(64) 0 ? GC=4p O D J.n_l ! ! 3 9# / 0 [=4 I G p O =Vp O DWq 3 9
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(66) 0 GEp OO =4p 0O D? iun_lkN\N\lhXYVU_N BEK`uY!Wgn_N\;^_JdcZWZYtsfFdcZcgF\ ` j.t=Wgnkl_^_T]YKWgF.nfF. `GN\T\FIiun_n9lT\JIWgn_`GN\N6;GH^_Jd7 cZWZY Xt=hX!»FxN cZcgFiT\ JIns`+jIJIts`G`K^_Wgn_Ll_NP^kT] NYKWgM F.nM XWgh_n?J.`!JdcZY[c@U_T\NPJIT\`GN\J.`i`KN"E % "M7 X hk»JIFxn_cZcgl9Fi U_`+FdcgY[l_Ev`!WZrYVWgJdEuWZcZ;cZtxWgJx cZm+cZt9U_NP»FIT\E JI v`GN 7 v k7 d m+ U_WgN` `vWgL#WZcgJ.! E!Y[FYVU_JxY+J.jFiINxkR0`K`G^_LM! N%Y[U_N\EGN]fF.EKN "M kd b0Fi !! NmUkJ\IN :3 9< 9 / O \=
(67) =D 7 r< ! 3 9 / 0 p O = =Vp 0O D/ r< ! 3 9# / 0 [=4 vp OO =Vp 0O D 7 r< 3 9 / 0 p O = =Vp 0O D/ r< 3 9"9 Qp 0O DI 9 O D=4 vp OO =4p 0O D? Ç. n>@>.
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(70) GC=Vp OD ! q 3 9 npOO = / GC=Vp ODn7 :3 9< 9
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(72) =GC=D+WZY[U|G8JC Kh %p 3 &$'#& * q 5 q r< $! , ->
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(75) =4 I 0 \=D 7 r< ! 3 9#
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(77) =
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(79) &9C vp 0O D[T m+UXWg`£cgN\JIlk`YVF!JInPF\IN\EGJxcZc;a_EGFIj_J.jXWZcZWZYt0FdxwuFdWgnXWgn_H+;^_N\^kN%Ob^_n_l_N\ E 1 Fd r & 9G\O p\D !5 9 &pP0O Dv7 5 /$N~T\F.n_lXWZYGWgFInJxcg`GF#F.n=YVU_NSYtka{N0FdJ.EKEuWZdJxcf , FInk`uWgl_N\E!J#`vtkLLMN]YVEuWgT J.EKEvWZxJxcfk@WgEG`uY+!N~T\F.n_`vWgl_N\EpY[U_NST\JI`G" N M X m+U_N\n{h_j.Lt 9$ D ! ! ! < < L9< 9
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(167) Unite´ de recherche INRIA Lorraine, Technopoˆle de Nancy-Brabois, Campus scientifique, 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LE` S NANCY Unite´ de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unite´ de recherche INRIA Rhoˆne-Alpes, 46 avenue Fe´lix Viallet, 38031 GRENOBLE Cedex 1 Unite´ de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex Unite´ de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902 SOPHIA-ANTIPOLIS Cedex. E´diteur INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) ISSN 0249-6399.
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