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A B C D E F G H I J
Queuing Model M/M/s (Exponential Service Times)
Input Data Operating Characteristics
Probabilities
Number of Units Probability
Cumulative
Probability
10.1875 0.4375
30.1055 0.6836
50.0593 0.8220
70.0334 0.8999
90.0188 0.9437
10 0.0141 0.9578
11 0.0106 0.9683
12 0.0079 0.9762
Problem 9-17 (a) & (b)
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A B C D E F G H I J
Computations
n or s
(lam/mu)^n/n!
Cumsum(n-1)
term2 P0(s) Rho(s) Lq(s) L(s) Wq(s) W(S)
0 1
10.75 1 3 0.25 0.75 2.25 30.15 0.2
30.070313 2.03125 0.09375 0.470588 0.25 0.014706 0.764706 0.00098 0.05098
50.001978 2.1147461 0.002326517 0.47235 0.15 0.000194 0.750194 1.29E-05 0.050013
92.07E-07 2.1169998 2.25724E-07 0.472367 0.083333 9.69E-09 0.75 6.46E-10 0.05
10 1.55E-08 2.117 1.67768E-08 0.472367 0.075 6.43E-10 0.75 4.28E-11 0.05
11 1.06E-09 2.117 1.1355E-09 0.472367 0.068182 3.92E-11 0.75 2.62E-12 0.05
12 6.61E-11 2.117 7.05386E-11 0.472367 0.0625 2.22E-12 0.75 1.48E-13 0.05
13 3.82E-12 2.117 4.04877E-12 0.472367 0.057692 1.17E-13 0.75 7.81E-15 0.05
24 1.62E-27 2.117 1.66937E-27 0.472367 0.03125 2.54E-29 0.75 1.7E-30 0.05
25 4.85E-29 2.117 5.00166E-29 0.472367 0.03 7.31E-31 0.75 4.87E-32 0.05
26 1.4E-30 2.117 1.44107E-30 0.472367 0.028846 2.02E-32 0.75 1.35E-33 0.05
27 3.89E-32 2.117 3.99858E-32 0.472367 0.027778 5.4E-34 0.75 3.6E-35 0.05
28 1.04E-33 2.117 1.06996E-33 0.472367 0.026786 1.39E-35 0.75 9.27E-37 0.05
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A B C D E F G H I J
Problem 9-17 (c)
Queuing Model M/M/s (Exponential Service Times)
Input Data Operating Characteristics
Arrival rate (l)15 Average server utilization (r)0.3750
Service rate (m)20 Average number of customers in the queue (Lq)0.1227
Number of Units Probability
Cumulative
Probability
0 0.4545 0.4545
1 0.3409 0.7955
2 0.1278 0.9233
3 0.0479 0.9712
15 0.0000 1.0000
16 0.0000 1.0000
17 0.0000 1.0000
18 0.0000 1.0000
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53
64
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67
68
6 0.0002472 2.11672363 0.000282506 0.472365 0.125 1.91E-05 0.750019 1.27E-06 0.050001
7 2.648E-05 2.11697083 2.96631E-05 0.472366 0.107143 1.68E-06 0.750002 1.12E-07 0.05
8 2.483E-06 2.11699731 2.73982E-06 0.472367 0.09375 1.34E-07 0.75 8.93E-09 0.05
9 2.069E-07 2.11699979 2.25724E-07 0.472367 0.083333 9.69E-09 0.75 6.46E-10 0.05
10 1.552E-08 2.117 1.67768E-08 0.472367 0.075 6.43E-10 0.75 4.28E-11 0.05
21 4.655E-23 2.11700002 4.82766E-23 0.472367 0.035714 8.45E-25 0.75 5.63E-26 0.05
22 1.587E-24 2.11700002 1.64303E-24 0.472367 0.034091 2.74E-26 0.75 1.83E-27 0.05
23 5.175E-26 2.11700002 5.34949E-26 0.472367 0.032609 8.52E-28 0.75 5.68E-29 0.05
24 1.617E-27 2.11700002 1.66937E-27 0.472367 0.03125 2.54E-29 0.75 1.7E-30 0.05
25 4.852E-29 2.11700002 5.00166E-29 0.472367 0.03 7.31E-31 0.75 4.87E-32 0.05