queue - # ρ= λ µ = &$ − ρ * ρ " ! . $ = ρ...

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Unformatted text preview: # ρ= λ µ = &$ − ρ * ρ " ! . $ = ρ &$ − ρ * = ρ2 &$ − ρ * ! = #λ = ρ $ = &$ − ρ *λ &$ − ρ * µ "#"#$ % + 0. % &$(,* $#&'()* − & µ −λ * $#&'()* -. / & > *= 1 ρ ! " !# $ % 1(3 4 1(3 = & # % 5& * % % 6&* λ2 &% & ! * + & $ & ! * 2 * 2&$ − λ$ & ! ** $ $ & !* = " λ$ & ! * = ρ " µ λ 2σ 2 + ρ 2 = 2&$ − ρ * % & !* = σ 2 # 7 ' 2! = σ2 &$ # µ * 2 # = ρ 2 &$ + ' 2 ! * 2&$ − ρ * σ2 8 8 ! & ' −$ & ρ * & ρ * &$ − ρ * −$ = ∑ + 9 9 =. %( % " ' )% % # −$ . # ρ= λ µ " ! . $ 1- ( ρ) 9 . - . $ 2 :: ; - ( ρ) 9 − . - ;<$ ;<2 :: = ρ +$ 9&$ − ρ * 2 . 8 (ρ = *' + > ? ) @ * * + 8 )) &8 * &* #) λ A$ µ *= ( = ρ &$ − ρ * $) ,- ρ + ($ − ρ ) * − ρ + +$ ) &$( 14 * = [ρ ($ − ρ )] ∗ $ − ρ + (+ − +ρ + $) {{ } {* − ρ }} + +$ = λ *"# λ ≥$ µ * ; -$ & #) λ A $* µ , *- $ , *;0$ . λ = ∑ . =. µ λ $ = µ .9 . $ + λ $ λ .9 + ∑ µ 9 µ . =$ . . −$ . . . = .$ . $ λ λ = 9 µ µ = = $ λ λ 9 µ µ .− . .= +$ +2 ++ ,- ++ + . &$( 14 * = ∑ . =. ++ . . = . = +$ ∑& . − ++ * . &* &* = λ = λ - "' )% ) ( )% % *$ $ ' # 3B % $# µ 4 −$ ⋅ 4 & * = =$2 3 + 4. = $ 4 = $− ∑ !µ =$ λ =$2 )- -$2: 3 λ = ∑λ 3 =$ !/ ) !! 0 1/ ) !! "! 22 . "' )% ) ( )% % *$ $ ' # ; C D ρ= λ µ *= ( λ &$ − ρ * $) 4. = $ 4 = $− ∑ !µ =$ λ =$2 &= $ *4 −$ ⋅4 =$ 2 3 &! = & + $ µ $ ! )#' . $. . $E . 2. . 2E . H. . HE . =. . =E . E. . EE . F. . FE . J. . JE . G. . GE . I. . IE $. $2 $= $F $G 2. 22 2= 2F 2G H. H2 H= HF HG =. =2 == =F =G E. E2 E= EF EG F. F2 F= FF FG J. J2 J= JF JG G. G2 G= GF GG I. I2 I= IF IG $. . .$$$ . .2F= . .E.. . .GHH . $2GE . $GG= . 2FFF . HFG$ . E... . FJ22 . I.I. $ 2.J$ $ FHHH 2 2E.. H 2... = G$FE G $... $G .E.. . ...F . ..2. . ..HI . ..FI . .$$. . .$FF . .2HI . .HHH . .=E . .EIH . .JFJ . .IJF . $22J . $E2H . $GJH . 22GE . 2JFJ . HHHH . FJ=G $ H==I 2 G==$ J FJH$ . ..$I . ..H. . ..=H . ..F$ . ..G= . .$$2 . .$=J . .$GI . .2HI . .H.. . .HJ$ . .=E= . .I=. . $JJG . H$2G . EH2. . GGGG $ =I.J 2 $2F$ = IH22 $2 2J2= . ..H$ . ..=$ . ..EH . ..FJ . .$EG . .H2= . .F.= . $.E$ . $JH. . 2JJ. . =2.E . FEG$ $ .... $ E2G2 2 HGEE H I.F. J .GIH $F IHFF . ..EI . .$2$ . .22J . .HI. . .FF . $.=J . $F.I . 2=$$ . HE=$ . E$2G . JHFE $ .EE. $ E$G$ 2 2$F= H H2FI E 2FJE I 2GGE 2$ FHG= . ..=J . ..I. . .$EG . .2FF . .=2E . .FEI . .II$ . $=E2 . 2.GE . 2I=J . =$$= . EFI= . JGHJ $ .JJJ $ =GEJ 2 .J.G 2 IHJE = H..= F FF.I $$ E$JG 2F HJ2F . ..FE . .$$. . .$G. . .2G2 . .=2J . .FH$ . .I$2 . $2I2 . $G.$ . 2=JE . HHF= . =EH2 . F.J$ . G$.2 $ .G.= $ ===$ $ I=HF 2 F=G$ H FGJG E 2IJI G .JFG H JII2 H$ $2J. . ..JJ . .$22 . .$GI . .2GH . .=$2 . .EI. . .G2J . $$=2 . $EEE . 2.I2 . 2JGE . HFG. . EGJ$ . FH$H . G22E $ .J.J $ HIFJ $ G.=. 2 =$IG H 2==$ = ==J$ F H$HH I E$.2 $F .HJI HE GIEF . ..G= . .$2J . .$GI . .2JH . .HGI . .E=$ . .J=2 . $..F . $H=E . $JJI . 2HH. . H.H2 . HI$G . E.HJ . F=E= . G2=J $ .EHH $ H=J$ $ J2GG 2 2H2= 2 I$$H H GEEG E 22F= J H==$ $. IEI2 $G H22H =. FG2= . ..GJ . .$2G . .$G= . .2F. . .HF$ . .=I2 . .FFH . .FGH . $$F= . $E$G . $IF= . 2E2= . H222 . =.I. . E$J2 . FE2$ . G2.2 $ .H$. $ 2IJ2 $ FHF= 2 .JHF 2 F=J. H =$F. = =G.E F .$GH G HGFI $2 =$GH 2. F$F. =E =JFI . .$2E . .$JE . .2=H . .HH. . .==H . .EI. . .JJE . $..G . $H.2 . $FFF . 2$$I . 2FJJ . HHF= . =2$$ . E2E. . FEH. . G$.I $ ..F. $ 2=G= $ EE2= $ IHFF 2 =2IH H .JH2 H IH$G E $$EF F G2$. . ..GE . .$$I . .$F= . .22= . .H.. . .HIG . .E2H . .FJI . .GJF . $$$I . $=2. . $JGI . 22=H . 2JIF . H=FI . =2GG . E2HF . FE.$ . JIG. . IJGG $ 2.$. $ =JE2 $ G$FE 2 2=FE . .$$H . .$EH . .2.E . .2J$ . .HEJ . .=FH . .EIE . .JF$ . .IFF . $2$= . $E2. . $GI$ . 2H=$ . 2GGE . HE=H . =HHH . E2FJ . E=HJ . JG2J . IE.F . .$.E . .$=$ . .$GJ . .2=E . .H$G . .=$. . .E22 . .FFH . .GH= . $.=H . $2.G . $F.H . $IJ= . 2=$I . 2IE2 . HFII . =HE2 . ..IJ . .$2I . .$FG . .22. . .2GH . .HF$ . .=EI . .EJJ . .J2H . .GII . $$$$ . $HFJ . $FJH$ . 2.=. 0 5 6 7 8 9 "# #$% !& : ; 0 5 6 7 ...
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This note was uploaded on 04/28/2011 for the course IME 642 taught by Professor Pm during the Spring '11 term at IIT Kanpur.

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