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11.15b

Template for the M/M/s Queueing Model
Data Results Range Name Cells
l = 1 (mean arrival rate) 1 L = 0.3333333333 L G4
m = 4 (mean service rate) 0 Lq = 0.0833333333 Lambda C4
s = 1 (# servers) 0 Lq G5
0 W = 0.33333 Mu C5
Pr(W > t) = 0.0497870684 0 Wq = 0.08333 n F13:F38
when t = 1 0 P0 G13
0 r = 0.25 Pn G13:G38
Prob(Wq > t) = 0.0124467671 0 Rho G10
when t = 1 0 n Pn s C6
0 0 0.75 Time1 C9
0 1 0.1875 Time2 C12
0 2 0.046875 W G7
0 3 0.01171875 Wq G8
0 4 0.0029296875
0 5 0.0007324219
0 6 0.0001831055
0 7 0.0000457764
0 8 0.0000114441
0 9 0.000002861
0 10 0.0000007153
0 11 0.0000001788
0 12 0.0000000447
0 13 0.0000000112
0 14 0.0000000028
0 15 0.0000000007
0 16 0.0000000002
17 0
18 0
19 0
20 0
21 0
22 0
23 0
24 0
25 6.66133814775094E-16
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0.75 0.1875 4.6875E-2 1.171875E-2 2.9296875E-3 7.32421875E-4 1.8310546875E-4 4.57763671875E-5 1.1444091796875E-5 2.86102294921875E-6 7.152557373046875E-7 1.7881393432617188E-7 4.4703483581542969E-8 1.1175870895385742E-8 2.7939677238464355E-9 6.9849193096160889E-10 1.7462298274040222E-10 4.3655745685100555E-11 1.0913936421275139E-11 2.7284841053187847E-12 6.8212102632969618E-13 1.7053025658242404E-13 4.2632564145606011E-14 1.0658141036401503E-14 2.6645352591003757E-15 6.6613381477509392E-16

Number of Customers in System

Probability

11.15c

Template for the M/M/s Queueing Model
Data Results Range Name Cells
l = 1 (mean arrival rate) 1 L = 0.5 L G4
m = 3 (mean service rate) 0 Lq = 0.1666666667 Lambda C4
s = 1 (# servers) 0 Lq G5
0 W = 0.5 Mu C5
Pr(W > t) = 0.1353352832 0 Wq = 0.1666666667 n F13:F38
when t = 1 0 P0 G13
0 r = 0.3333333333 Pn G13:G38
Prob(Wq > t) = 0.0451117611 0 Rho G10
when t = 1 0 n Pn s C6
0 0 0.6666666667 Time1 C9
0 1 0.2222222222 Time2 C12
0 2 0.0740740741 W G7
0 3 0.024691358 Wq G8
0 4 0.0082304527
0 5 0.0027434842
0 6 0.0009144947
0 7 0.0003048316
0 8 0.0001016105
0 9 0.0000338702
0 10 0.0000112901
0 11 0.0000037634
0 12 0.0000012545
0 13 0.0000004182
0 14 0.0000001394
0 15 0.0000000465
0 16 0.0000000155
17 0.0000000052
18 0.0000000017
19 0.0000000006
20 0.0000000002
21 0.0000000001
22 0
23 0
24 0
25 0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0.66666666666666663 0.22222222222222224 7.4074074074074084E-2 2.469135802469136E-2 8.23045267489712E-3 2.7434842249657062E-3 9.1449474165523556E-4 3.0483158055174517E-4 1.0161052685058171E-4 3.3870175616860571E-5 1.1290058538953523E-5 3.7633528463178412E-6 1.2544509487726136E-6 4.1815031625753788E-7 1.3938343875251262E-7 4.6461146250837533E-8 1.548704875027918E-8 5.1623495834263925E-9 1.7207831944754643E-9 5.7359439815848806E-10 1.9119813271949605E-10 6.3732710906498674E-11 2.1244236968832893E-11 7.0814123229442962E-12 2.3604707743147657E-12 7.8682359143825519E-13

Number of Customers in System

Probability

11.15d

Template for the M/M/s Queueing Model
Data Results Range Name Cells
l = 1 (mean arrival rate) 1 L = 1 L G4
m = 2 (mean service rate) 0 Lq = 0.5 Lambda C4
s = 1 (# servers) 0 Lq G5
0 W = 1 Mu C5
Pr(W > t) = 0.3678794412 0 Wq = 0.5 n F13:F38
when t = 1 0 P0 G13
0 r = 0.5 Pn G13:G38
Prob(Wq > t) = 0.1839397206 0 Rho G10
when t = 1 0 n Pn s C6
0 0 0.5 Time1 C9
0 1 0.25 Time2 C12
0 2 0.125 W G7
0 3 0.0625 Wq G8
0 4 0.03125
0 5 0.015625
0 6 0.0078125
0 7 0.00390625
0 8 0.001953125
0 9 0.0009765625
0 10 0.0004882813
0 11 0.0002441406
0 12 0.0001220703
0 13 0.0000610352
0 14 0.0000305176
0 15 0.0000152588
0 16 0.0000076294
17 0.0000038147
18 0.0000019073
19 0.0000009537
20 0.0000004768
21 0.0000002384
22 0.0000001192
23 0.0000000596
24 0.0000000298
25 0.0000000149
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0.5 0.25 0.125 6.25E-2 3.125E-2 1.5625E-2 7.8125E-3 3.90625E-3 1.953125E-3 9.765625E-4 4.8828125E-4 2.44140625E-4 1.220703125E-4 6.103515625E-5 3.0517578125E-5 1.52587890625E-5 7.62939453125E-6 3.814697265625E-6 1.9073486328125E-6 9.5367431640625E-7 4.76837158203125E-7 2.384185791015625E-7 1.1920928955078125E-7 5.9604644775390625E-8 2.9802322387695313E-8 1.4901161193847656E-8

Number of Customers in System

Probability

11.16a (1 min)

Template for the M/M/s Queueing Model
Data Results Range Name Cells
l = 0.5 (mean arrival rate) 1 L = 1 L G4
m = 1 (mean service rate) 0 Lq = 0.5 Lambda C4
s = 1 (# servers) 0 Lq G5
0 W = 2 Mu C5
Pr(W > t) = 0.0820849986 0 Wq = 1 n F13:F38
when t = 5 0 P0 G13
0 r = 0.5 Pn G13:G38
Prob(Wq > t) = 0.0410424993 0 Rho G10
when t = 5 0 n Pn s C6
0 0 0.5 Time1 C9
0 1 0.25 Time2 C12
0 2 0.125 W G7
0 3 0.0625 Wq G8
0 4 0.03125
0 5 0.015625
0 6 0.0078125
0 7 0.00390625
0 8 0.001953125
0 9 0.0009765625
0 10 0.0004882813
0 11 0.0002441406
0 12 0.0001220703
0 13 0.0000610352
0 14 0.0000305176
0 15 0.0000152588
0 16 0.0000076294
17 0.0000038147
18 0.0000019073
19 0.0000009537
20 0.0000004768
21 0.0000002384
22 0.0000001192
23 0.0000000596
24 0.0000000298
25 0.0000000149
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0.5 0.25 0.125 6.25E-2 3.125E-2 1.5625E-2 7.8125E-3 3.90625E-3 1.953125E-3 9.765625E-4 4.8828125E-4 2.44140625E-4 1.220703125E-4 6.103515625E-5 3.0517578125E-5 1.52587890625E-5 7.62939453125E-6 3.814697265625E-6 1.9073486328125E-6 9.5367431640625E-7 4.76837158203125E-7 2.384185791015625E-7 1.1920928955078125E-7 5.9604644775390625E-8 2.9802322387695313E-8 1.4901161193847656E-8

Number of Customers in System

Probability

11.16a (1.5 min)

Template for the M/M/s Queueing Model
Data Results Range Name Cells
l = 0.5 (mean arrival rate) 1 L = 3 L G4
m = 0.6666666667 (mean service rate) 0 Lq = 2.25 Lambda C4
s = 1 (# servers) 0 Lq G5
0 W = 6 Mu C5
Pr(W > t) = 0.4345982085 0 Wq = 4.5 n F13:F38
when t = 5 0 P0 G13
0 r = 0.75 Pn G13:G38
Prob(Wq > t) = 0.3259486564 0 Rho G10
when t = 5 0 n Pn s C6
0 0 0.25 Time1 C9
0 1 0.1875 Time2 C12
0 2 0.140625 W G7
0 3 0.10546875 Wq G8
0 4 0.0791015625
0 5 0.0593261719
0 6 0.0444946289
0 7 0.0333709717
0 8 0.0250282288
0 9 0.0187711716
0 10 0.0140783787
0 11 0.010558784
0 12 0.007919088
0 13 0.005939316
0 14 0.004454487
0 15 0.0033408653
0 16 0.0025056489
17 0.0018792367
18 0.0014094275
19 0.0010570706
20 0.000792803
21 0.0005946022
22 0.0004459517
23 0.0003344638
24 0.0002508478
25 0.0001881359
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0.25 0.1875 0.140625 0.10546875 7.91015625E-2 5.9326171875E-2 4.449462890625E-2 3.33709716796875E-2 2.5028228759765625E-2 1.8771171569824219E-2 1.4078378677368164E-2 1.0558784008026123E-2 7.9190880060195923E-3 5.9393160045146942E-3 4.4544870033860207E-3 3.3408652525395155E-3 2.5056489394046366E-3 1.8792367045534775E-3 1.4094275284151081E-3 1.0570706463113311E-3 7.9280298473349831E-4 5.9460223855012373E-4 4.459516789125928E-4 3.344637591844446E-4 2.5084781938833345E-4 1.8813586454125009E-4

Number of Customers in System

Probability

11.23a

Template for the M/G/1 Queueing Model
Data Results Range Name Cell
l = 0.05 (mean arrival rate) L = 3 L G4
1/m = 15 (expected service time) Lq = 2.25 Lambda C4
s= 15 (standard deviation) Lq G5
s = 1 (# servers) W = 60 OneOverMu C5
Wq = 45 Rho G10
s C7
r = 0.75 Sigma C6
W G7
P0 = 0.25 Wq G8

11.23b

Template for the M/G/1 Queueing Model
Data Results Range Name Cell
l = 0.05 (mean arrival rate) L = 3.2439025 L G4
1/m = 16 (expected service time) Lq = 2.4439025 Lambda C4
s= 11.62 (standard deviation) Lq G5
s = 1 (# servers) W = 64.87805 OneOverMu C5
Wq = 48.87805 Rho G10
s C7
r = 0.8 Sigma C6
W G7
P0 = 0.2 Wq G8

11.27a (1)

Template for the M/M/s Queueing Model
Data Results Range Name Cells
l = 150 (mean arrival rate) 1 L = 6.0112359551 L G4
m = 60 (mean service rate) 2.5 Lq = 3.5112359551 Lambda C4
s = 3 (# servers) 3.125 Lq G5
0 W = 0.0400749064 Mu C5
Pr(W > t) = 0 0 Wq = 0.0234082397 n F13:F38
when t = 1 0 P0 G13
0 r = 0.8333333333 Pn G13:G38
Prob(Wq > t) = 0.702247191 0 Rho G10
when t = 0 0 n Pn s C6
0 0 0.0449438202 Time1 C9
0 1 0.1123595506 Time2 C12
0 2 0.1404494382 W G7
0 3 0.1170411985 Wq G8
0 4 0.0975343321
0 5 0.0812786101
0 6 0.0677321751
0 7 0.0564434792
0 8 0.0470362327
0 9 0.0391968606
0 10 0.0326640505
0 11 0.0272200421
0 12 0.0226833684
0 13 0.018902807
0 14 0.0157523392
0 15 0.0131269493
0 16 0.0109391244
17 0.009115937
18 0.0075966142
19 0.0063305118
20 0.0052754265
21 0.0043961888
22 0.0036634906
23 0.0030529089
24 0.0025440907
25 0.0021200756
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 4.4943820224719093E-2 0.11235955056179774 0.14044943820224717 0.11704119850187263 9.7534332084893871E-2 8.1278610070744883E-2 6.7732175058954069E-2 5.644347921579506E-2 4.7036232679829218E-2 3.9196860566524348E-2 3.2664050472103627E-2 2.7220042060086352E-2 2.2683368383405293E-2 1.8902806986171077E-2 1.5752339155142566E-2 1.3126949295952138E-2 1.0939124413293448E-2 9.115937011077874E-3 7.5966141758982281E-3 6.3305118132485228E-3 5.2754265110404363E-3 4.3961887592003637E-3 3.6634906326669693E-3 3.0529088605558076E-3 2.54409071712984E-3 2.1200755976082002E-3

Number of Customers in System

Probability

11.27a (2)

Template for the M/M/s Queueing Model
Data Results Range Name Cells
l = 150 (mean arrival rate) 1 L = 5 L G4
m = 180 (mean service rate) 0 Lq = 4.1666666667 Lambda C4
s = 1 (# servers) 0 Lq G5
0 W = 0.0333333333 Mu C5
Pr(W > t) = 0 0 Wq = 0.0277777778 n F13:F38
when t = 1 0 P0 G13
0 r = 0.8333333333 Pn G13:G38
Prob(Wq > t) = 0.8333333333 0 Rho G10
when t = 0 0 n Pn s C6
0 0 0.1666666667 Time1 C9
0 1 0.1388888889 Time2 C12
0 2 0.1157407407 W G7
0 3 0.0964506173 Wq G8
0 4 0.0803755144
0 5 0.0669795953
0 6 0.0558163294
0 7 0.0465136079
0 8 0.0387613399
0 9 0.0323011166
0 10 0.0269175971
0 11 0.022431331
0 12 0.0186927758
0 13 0.0155773132
0 14 0.0129810943
0 15 0.0108175786
0 16 0.0090146488
17 0.0075122074
18 0.0062601728
19 0.0052168107
20 0.0043473422
21 0.0036227852
22 0.0030189877
23 0.002515823
24 0.0020965192
25 0.0017470993
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0.16666666666666663 0.13888888888888887 0.11574074074074073 9.6450617283950615E-2 8.0375514403292186E-2 6.6979595336076822E-2 5.5816329446730692E-2 4.6513607872275577E-2 3.8761339893562986E-2 3.2301116577969163E-2 2.6917597148307635E-2 2.243133095692303E-2 1.8692775797435859E-2 1.5577313164529883E-2 1.2981094303774907E-2 1.0817578586479089E-2 9.0146488220659085E-3 7.5122073517215901E-3 6.2601727931013255E-3 5.2168106609177716E-3 4.347342217431477E-3 3.622785181192897E-3 3.0189876509940814E-3 2.5158230424950682E-3 2.0965192020792238E-3 1.7470993350660199E-3

Number of Customers in System

Probability