61756042 Queuing Theory
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":0:3%047":0:3%047:39:39
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3974/:.9433974/:.943
%0%0 89:/89:/ 4141 ,93,93 308308 88 .,0/.,0/ 6:0:36:0:3 90479047
33 0307,0307, ,, 6:0:06:0:0 88 14720/14720/ 0303 09070907 :398:398 706:73706:73807;.0807;.0 .42243.42243 7010770/7010770/ 9494 ,8,8 .:8942078.:8942078 ,9,9 147147 9090
807;.0807;.0 1,.91,.9 89,3/89,3/ /0/0 ,9,9 147147 9090 .:894207.:894207
$420$420 .:8942078.:8942078 ,9,9 0303 9090 949,949, 3:2-073:2-07 4141 .:8942078.:8942078706:73706:73 807;.0807;.0 0.00/80.00/8 9090 3:2-073:2-07 4141 807;.0807;.0 1,.9081,.908
$420$420 807;.0807;.0 1,.9081,.908 89,3/89,3/ /0/0 0303 9090 949,949, 3:2-073:2-07 4141807;.0807;.0 1,.9081,.908 0.00/80.00/8 9090 3:2-073:2-07 4141 .:8942078.:8942078 706:73706:73807;.0807;.0
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35:984:7.035:984:7.0
%035:984:7.089084:7.01742..:894207.4208%035:984:7.089084:7.01742..:894207.4208438906:0:0438906:0:0
%035:984:7.04190.:89420794906:0:388902%035:984:7.04190.:89420794906:0:388902
.,3-013904731390.,3-013904731390
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84:7.0":0:0
$07;07$07;07$07;07
$0;072 05,79:70
17429088902
":0:34/0
!43941,77;,39088902
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77;,.,7,.90789.877;,.,7,.90789.8
$04190,77;,545:,943$04190,77;,545:,943
!,9907341,77;,,9906:0:388902!,9907341,77;,,9906:0:388902
0,;4741,77;,80,;4741,77;,8
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$04190,77;,545:,943$04190,77;,545:,943
!45:,943!45:,943 808808 ,70,70 .438/070/.438/070/ 9494 -0-0 09070907 :3290/:3290/ 003139031390 4747 290/290/ 00 13901390
99 88 .438/070/.438/070/ 9494 -0-0 3139031390 11 9090 7,907,90 ,9,9 .. 84:7.084:7.0
0307,9080307,908 9090 .:8942078.:8942078 88 349349 ,110.90/,110.90/ -- 9090 3:2-073:2-07 4141.:8942078.:8942078 33 9090 807;.0807;.0 8890288902
9073,9;09073,9;0 84:7.084:7.0 88 .438/070/.438/070/ 13901390 11 9090 7,907,90 88,110.90/,110.90/ -- 9090 3:2-073:2-07 4141 .:8942078.:8942078 33 9090 8890288902
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!,9907377;,99088902!,9907377;,99088902
:8942078:8942078 ,77;0,77;0 ,9,9 807;.0807;.0 1,.91,.9 ,..47/3,..47/3 9494 84208420343343 8.0/:08.0/:0 4747 080080 9090 ,77;0,77;0 7,3/427,3/42
33 6:0:36:0:3 90479047 9090 3:2-073:2-07 4141 ,77;,8,77;,8 507507 :39:39 4141 920920
.,3.,3 -0-0 0892,90/0892,90/ -- 574-,-9574-,-9 /897-:943/897-:943 343343 ,8,8!48843!48843 /897-:943/897-:943
%0%0 2,472,47 10,9:7010,9:70 4141 9898 /897-:943/897-:943 88 9,99,9 3:2-073:2-07 41415045050450 ,77;3,77;3 ,9,9 ,, ;03;03 920920 88 349349 ,9,9 ,, 31:03.0/31:03.0/ --
9090 3:2-073:2-07 4141 570;4:8570;4:8 ,77;,8,77;,8
77;,77;, 7,907,90 88 ;03;03 -- 82-482-4 ,2/,,2/,
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0,;474190,77;,0,;474190,77;,
.:89420743390807;.0/4083490990220/,90.:89420743390807;.0/4083490990220/,90807;.090.:8942072,807;.090.:8942072,
89,39088902:39807;0/89,39088902:39807;0/
24;01742430,933094,3490724;01742430,933094,34907
0892,9090,93920/0./0030;07940,;00892,9090,93920/0./0030;07940,;0
%0178995041.:894207489,39088902,70%0178995041.:894207489,39088902,70.,0/,85,9039.:8942078.,0/,85,9039.:8942078
%0490794,70.,8810/,825,90394770303%0490794,70.,8810/,825,90394770303.:894207.:894207
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":0:3039":0:3039
%003941,30.,3-00907290/47:3290/%003941,30.,3-00907290/47:3290/
33 ,, 8,088,08 /05,792039/05,792039 070070 9090 .:8942078.:8942078 47/07847/078 ,70,7070.0;0/70.0;0/ 90709070 88 3434 70897.94370897.943 4343 9090 3:2-073:2-07 4141 47/07847/078
9,99,9 .,3.,3 .420.420 33 8484 9,99,9 ,, 6:0:06:0:0 4141 ,3,3 8080 .,3.,3 147214720303 90709070 88 44 2929 4343 9898 8080 9090 507288-0507288-0 6:0:06:0:0 888,/8,/ 9494 -0-0 3139031390
0303 90709070 88 ,, 2929 4343 8080 4141 6:0:06:0:0 99 88 8,/8,/ 9494 -0-0 13901390
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$07;.00.,382$07;.00.,382
3.090.:894207,8039070/9088902147807;.0903.090.:894207,8039070/9088902147807;.090807;.088902,81443.,7,.90789.807;.088902,81443.,7,.90789.
9209,03147807;.09209,03147807;.0
807;.01,.9807;.01,.9
807;.0/8.530419088902807;.0/8.530419088902
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$07;.0920$07;.0920
$07;.09202,-00907.4389,39477,3/42$07;.09202,-00907.4389,39477,3/42
1807;.09208.4389,3999,08908,20,24:39411807;.09208.4389,3999,08908,20,24:394192094807;.00,..:89420792094807;.00,..:894207
%082-4/08.7-390807;.07,908a,3/90:398%082-4/08.7-390807;.07,908a,3/90:398,703807;.0507:39920,703807;.0507:39920
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$07;.01,.908$07;.01,.908
:2-07:2-07 4141 .,3308.,3308 830830 .,330.,330 5,805,80 .,80.,80 88 0700709090 ,77;,8,77;,8 5,885,88 974:974: 4343 430430 89,94389,943 33 47/0747/07 9494.425090.425090 9090 706:70/706:70/ 807;.0807;.0
9494 -449-449 90,97090,970 9.099.09 3/43/4
2:95,802:95,80 .,330.,330 3;4;083;4;08 9090 89:,943889:,9438 070070 9090:398:398 9494 -0-0 807;0/807;0/ 5,885,88 974:974: ,, 8070880708 4141 89,94389,943 33 ,,806:03.0806:03.0
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":0:0 $07;.01,.9
":0:0 $07;.01,.9
$07;.01,.9
$30.,330
$305,80
$30.,330
:9505,80
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":0:0
$07;.01,.9
$07;.01,.9
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1,.9
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7;.0
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$07;.0/8.530$07;.0/8.530
":0:0/8.53070107894907:0-..:89420783":0:0/8.53070107894907:0-..:894207839030,709470.0;0807;.09030,709470.0;0807;.0
489889028:806:0:0/8.530343,89017893489889028:806:0:0/8.530343,89017893
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5,-09.,47,30/5,-09.,47,30/
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55.,94341":0:38890255.,94341":0:388902
42207.,807;.08890242207.,807;.088902
:830883/:897,88902:830883/:897,88902
$4.,807;.088902$4.,807;.088902
%7,385479,943807;.088902%7,385479,943807;.088902
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507,93.,7,.90789.841507,93.,7,.90789.841
6:0:3889026:0:388902 &9,9431,.9471479088902&9,9431,.9471479088902
;07,03:2-0741.:89420739088902;07,03:2-0741.:89420739088902
;07,03:2-0741.:89420736:0:0;07,03:2-0741.:89420736:0:0
;07,09200,..:8942078503/83906:0:0;07,09200,..:8942078503/83906:0:0
!74-,-99,9807;.0-0/0!74-,-99,9807;.0-0/0
!74-,-941850.1.3:2-0741.:894207839088902!74-,-941850.1.3:2-0741.:894207839088902
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49,9438%0723440849,9438%07234408
49,943 9,9 ,8 -003 :80/ 147 8:22,73 90 2,3.,7,.90789.8 41 5,7,0 6:0:0 ,8 :3;078, 89,3/,7/0/1472,9
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80 41 .,3 84:7.0
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,8.49,9438,8.49,9438
77;,7,9077;,7,90 %0,;07,07,90,9..:8942078,77;0%0,;07,07,90,9..:8942078,77;043906:0:0890,77;,7,9043906:0:0890,77;,7,90
$07;.0920$07;.0920 %0,;07,0920706:70/94807;.0430%0,;07,0920706:70/94807;.0430.:8942078807;.0920%0:39814790807;.092084:/-0.:8942078807;.0920%0:39814790807;.092084:/-0
903;07804190:398147,77;,7,90903;07804190:398147,77;,7,90
:2-07:2-07 4141 .:894207.:894207 33 9090 8890288902 $$ 90809080 ,70,70 9090,;07,0,;07,0 3:2-073:2-07 4141 .:894207.:894207 33 9090 8890288902 -49-49 ,93,93 -03-03807;.0/807;.0/
;07,0;07,0 ,93,93 920920 33 9090 8890288902"" 99 88 9090 ,;07,0,;07,0920920 0,.0,. .:894207.:894207 33 9090 8890288902 -49-49 ,93,93 -03-03 807;.0/807;.0/
;07,0;07,0 ,93,93 920920 33 9090 6:0:06:0:0 $$ 99 88 9090 ,;07,0,;07,0920920 0,.0,. .:894207.:894207 ,98,98 33 9090 6:0:06:0:0
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4/04/0++++
%88,830.,3306:0:324/0%88,830.,3306:0:324/0
%0,77;,920,8,54843/897-:943,77;,7,908/03490/%0,77;,920,8,54843/897-:943,77;,7,908/03490/--
77;,8,70174231390545:,94377;,8,70174231390545:,943
%06:0:0/8.5308$090.:8942078,70807;0/%06:0:0/8.5308$090.:8942078,70807;0/431789.4201789807;0/-,88431789.4201789807;0/-,88
%070843830807;.089,943%070843830807;.089,943
%020,3,77;,7,9080889,39020,3807;.07,90%020,3,77;,7,9080889,39020,3807;.07,90
%0,9385,.0,;,,-0147.:89420783906:0:0831390%0,9385,.0,;,,-0147.:89420783906:0:0831390
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$$++
%824/08/1107039174224/0370850.99490%824/08/1107039174224/0370850.99490.,5,.9419088902.,5,.9419088902
07090.,5,.94190889028290/94.:894207807090.,5,.94190889028290/94.:8942078
4343
%0701470/110703.006:,9438/07;0/324/0,843,8%0701470/110703.006:,9438/07;0/324/0,843,833
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4/0'4/0'
$$++++ %0%0 6:0:086:0:08 33 .. ,77;,8,77;,8 4747 /05,79:708/05,79:708 2,2, 349349
144144 5484354843 /897-:943/897-:943 ,70,70 .,0/.,0/ ,8,8 343343 5484354843/897-:943/897-:943
%8%8 24/024/0 .438898.438898 4141 /039.,/039., 0543039,0543039, 807;.0807;.05,8085,808 33 8070880708 0,.0,. 99 20,320,3 807;.0807;.0 920920 4141
3030 807;.0807;.0 /408/408 349349 89,7989,79 :39:39 ,, 5,8085,808 ,;0,;0 -003-003.425090/.425090/
807;.0807;.0 89,94389,943 33 .. .:894207.:894207 5,88085,8808 974:974: 5,8085,808 8,8, ,;0,;0 9090 807;.0807;.0 920920 14431443 7,37,3/897-:943/897-:943
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,7,.90789.8417,3/,7,.90789.8417,3/
897-:943897-:943 %07,3/897-:9438:801:147/013390807;.0%07,3/897-:9438:801:147/013390807;.0
92041,.:894207470.0;08/039.,70509943841,92041,.:894207470.0;08/039.,70509943841,5,79.:,7807;.05,79.:,7807;.0
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3.,8041.4389,39/897-:94341.:8942073907,,7;,3.,8041.4389,39/897-:94341.:8942073907,,7;,
9208903/949208903/94++
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29,94341$30.,33029,94341$30.,330
":0:34/0":0:34/0 %0%0 ,93,93 85,.085,.0 2,2, -0-0 290/290/
%0%0 ,77;,,77;, 7,907,90 88 /0503/039/0503/039 !49039,!49039, .:8942078.:8942078 ,70,70/8.4:7,0//8.4:7,0/ 17421742 -03-03 039073039073 9090 6:0:06:0:0 11 9090 4-807;04-807;0
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%0%0 545:,943545:,943 4141 .:8942078.:8942078 2,2, -0-0 13901390
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:9,330":0:34/08:9,330":0:34/08
33 ,, 2:9502:950 6:0:36:0:3 8890288902 9494 4747 24702470 807;07807;07 ,70,70,;,,-0,;,,-0 9494 ,3/0,3/0 9090 .:894207.:894207 44 ,77;0,77;0 147147 807;.0807;.0
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4/0;$4/0;$$$++++
%8,2:9.,33024/03.5,7,0807;.089,9438%8,2:9.,33024/03.5,7,0807;.089,9438,70807;3,8306:0:0,70807;3,8306:0:0
807;.089,9438574;/08,20807;.0807;.089,9438574;/08,20807;.0
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$07;.089,9438,;00543039,807;.09208920,3$07;.089,9438,;00543039,807;.09208920,3.:894207803907336:0:0807;0/-,807;.0.:894207803907336:0:0807;0/-,807;.089,943889,9438
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":0:034/0380708":0:034/0380708
33 70,70, 1010 89:,943889:,9438 070070 9090 ,77;3,77;3 .:894207.:894207 5,88085,8808974:974: 8:..088;08:..088;0 3:2-073:2-07 4141 807;.0807;.0 .,3308.,3308 33 47/0747/07 9494.425090.425090 88 807;.0807;.0 ,70,70 343343 ,8,8 6:0:086:0:08 33 8070880708 4747":0:08":0:08 33 %,3/02%,3/02
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