{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple P lot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "# Maple worksheet to demonstrate us e of Ph(t)/Ph(t)/Infinity procedures" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "# from Nelson and Taaffe (1999). Last update 6/30/99 ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }} {PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra ce have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "A := matrix(3,3,[.2,.1,.7, .4,.2,.4, .8,.2,0.]);\n" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7%$\"\"#!\"\"$\" \"\"F,$\"\"(F,7%$\"\"%F,F*F27%$\"\")F,F*$\"\"!F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "lambda := vector(2,[7.,9.]);\n" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%'lambdaG-%'vectorG6#7$$\"\"(\"\"!$\"\"*F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "B := matrix(3,3,[0,1,0, 0,0, 1, 0.3, 0.7, 0]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrix G6#7%7%\"\"!\"\"\"F*7%F*F*F+7%$\"\"$!\"\"$\"\"(F0F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "mu := vector(2, [2+sin(t), 2+sin(t/2)]); \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG-%'vectorG6#7$,&\"\"#\"\" \"-%$sinG6#%\"tGF+,&F*F+-F-6#,$*&F*!\"\"F/F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "# Evaluate the moment differential equations at time t = 5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "read(`c:/TeXpapers/TaaffePap ers/WebUpdate10152003/PhPhInfNumericEmpty7.txt`):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 47 "mdeq := PhPhInfNumericEmpty(A, lambda, B, mu );\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%mdeqG73/%\"tGf*6#F'6\"6#%ao Copyright~(c)~1993~by~the~University~of~Waterloo.~All~rights~reserved. 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_jmOFbjmFdjmOFhjmC$>F`[m-F][n6#&F`[nFiblOFc[nZ%C$>FaqFh[n&FaqFiblF*YF* F*F*F*/-%'N2N2A2GF)f*F)F2F7F*C(>F;F<>F@%F@>FDFE>FDFK>FMFN@$Ffim@)Fj imOF^jmF_jmOFbjmFdjmOFhjmC$>F`[m-F][n6#&F`[nF_uOFc[nZ%C$>FaqFh[n&FaqF_ uF*YF*F*F*F*/-%#P1GF)f*F)F2F7F*C(>F;F<>F@%F@>FDFE>FDFK>FMFN@$Ffim@) FjimOF^jmF_jmOFbjmFdjmOFhjmC$>F`[m-F][n6#&F`[nFduOFc[nZ%C$>FaqFh[n&Faq FduF*YF*F*F*F*/-%#P2GF)f*F)F2F7F*C(>F;F<>F@%F@>FDFE>FDFK>FMFN@$Ffim @)FjimOF^jmF_jmOFbjmFdjmOFhjmC$>F`[m-F][n6#&F`[n6#F^oOFc[nZ%C$>FaqFh[n &FaqF[eoF*YF*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "mdeq( 5);\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#73/-%\"tG6#\"\"&F(/--%#N1G6#F &F'$\"3IxTHZ='y:\"!##p.#*!#=/--%%N1A2GF-F'$\" 39p1[zi#\\P#F7/--%'N1N1A1GF-F'$\"3y5'[0.rq)>F0/--%'N1N1A2GF-F'$\"3U " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "# show the moment differential equations \+ for this queue starting empty and idle" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "read(`c:/TeXpapers/TaaffePapers/WebUpdate10152003/PhP hInfSymbolic7.txt`):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "PhP hInfSymbolic(A, lambda, B, mu);\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6B/ -%%diffG6$-%#P1G6#%\"tGF*,&*&$\"$o\"!\"#\"\"\"F'F0!\"\"*&$\"$['F/F0-%# P2GF)F0F0/-F%6$F5F*,&*&$F.F/F0F'F0F0*&$F4F/F0F5F0F1/-F%6$-%#N1GF)F*,(* &$\"$Z\"F/F0F'F0F0*&$\"$3\"F/F0F5F0F0*&,&\"\"#F0-%$sinGF)F0F0FBF0F1/-F %6$-%#N2GF)F*,**&$\"$V$F/F0F'F0F0*&$\"$_#F/F0F5F0F0FKF0*&,&FMF0-FO6#,$ *&FMF1F*F0F0F0F0FSF0F1/-F%6$-%'N1N1A1GF)F*,2*(FMF0FLF0F_oF0F1*&$\"++++ !o\"!\"*F0F_oF0F1*&$\"%_B!\"$F0-%%N1A1GF)F0F0*&$\"%G " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 69 "# compute the mean and variance of number in t he queue for 0 < t < 50" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 " # (the mean and variance appear to be the same for this example)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "read(`c:/TeXpapers/TaaffePap ers/WebUpdate10152003/PhPhInfMoments7.txt`):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "PhPhInfMoments(A, lambda, B, mu, 0, 50);\n" }}{PARA 13 "" 1 "" {GLPLOT2D 624 624 624 {PLOTDATA 2 "6&-%'CU RVESG6$X,%)anythingG6\"6\"[gl'!%\"!!#_q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F=F=" 1 2 0 1 10 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 1 "N1+N2" "N1N1A1+N1N1A2-N1^2+N2N1A1+N2N1A2-2*N2*N1+N1N2A1+N1N2A2+N2N2A1+N2N2A2- N2^2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "# compute the mean, variance and cdf of t he sojourn time of a customer" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "# arriving at time 5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "read(`c:/TeXpapers/TaaffePapers/WebUpdate10152003/PhPhInfNumericIn it7.txt`):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "read(`c:/TeXp apers/TaaffePapers/WebUpdate10152003/PhPhInfSojourn7.txt`):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "sojourn := PhPhInfSojourn(A, lambda, B, mu, 5):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "sojo urn[1]; # mean\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"3=(zd " 0 "" {MPLTEXT 1 0 23 "sojourn[2]; # variance \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+u3$*H_!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "sojourn[3]; #cdf\n" 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"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "# Create initial conditions that correspond to 1 customer in the queue and no new arrivals" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "InitP := vector(2, [0,0]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% &InitPG-%'vectorG6#7$\"\"!F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "InitN := vector(2, [.3, .7]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&InitNG-%'vectorG6#7$$\"\"$!\"\"$\"\"(F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "InitNN := vector(2):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 29 "InitNN[1] := matrix(2,2, 0);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%'InitNNG6#\"\"\"-%'matrixG6#7$7$\"\"!F-F," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "InitNN[2] := matrix(2,2,0); \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%'InitNNG6#\"\"#-%'matrixG6#7$ 7$\"\"!F-F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "InitNA := ma trix(2, 2, [0,0,0,0]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'InitNAG -%'matrixG6#7$7$\"\"!F*F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "# create a procedure to evaluate the moment differential equations with these" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "# initial co ndition in place at time t = 5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "mom := PhPhInfNu mericInit(A, lambda, B, mu, 5, InitP, InitN, InitNA, InitNN);\n" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%$momG75/%\"tGf*6#F'6\"6#%aoCopyright ~(c)~1993~by~the~University~of~Waterloo.~All~rights~reserved.GF*9$F*F* F*/-%#M1GF)f*F)6&%$resG%)solnprocG%)outpointG%&ndsolG6#%inCopyright~(c )~2000~by~Waterloo~Maple~Inc.~All~rights~reserved.GF*C(>%8_EnvDSNumeri cSaveDigitsG%'DigitsG>F<\"#9@%/%-_EnvInFsolveG%%trueG>8&-&%&evalfG6#F; 6#F->FD-FGFI>8%f*6#%#mxG6+F5%#dtG%$datG%(odeprocG%#x0G%$valG%$digG%\"n G%\"iG6#%inCopyright~(c)~2002~by~Waterloo~Maple~Inc.~All~rights~reserv ed.GE\\s#Q0soln_proceduresF*=F*6#;\"\"\"\"#>E\\[l4F[o\")%3r#=\"\"#\")[ 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