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A B C D E F G H I J
Problem 9-22 (a)
Queuing Model M/M/s (Exponential Service Times)
Input Data Operating Characteristics
Probabilities
Number of Units Probability
Cumulative
Probability
10.1389 0.3056
30.0965
0.5177
50.0670 0.6651
70.0465 0.7674
90.0323 0.8385
10 0.0269 0.8654
11 0.0224 0.8878
12 0.0187 0.9065
11
41
42
43
44
46
48
52
53
54
55
56
67
68
69
70
71
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
10.8333333 1 5 0.16667 0.833333 4.166667 54.166667 5
30.0964506 2.1805556 0.133547009 0.43213 0.277778 0.022196 0.85553 0.022196 0.85553
50.003349 2.2971001 0.004018776 0.43457 0.166667 0.000349 0.833683 0.000349 0.833683
95.341E-07 2.3009753 5.88577E-07 0.4346 0.092593 2.61E-08 0.833333 2.61E-08 0.833333
10 4.451E-08 2.3009758 4.85527E-08 0.4346 0.083333 1.92E-09 0.833333 1.92E-09 0.833333
11 3.372E-09 2.3009759 3.64808E-09 0.4346 0.075758 1.3E-10 0.833333 1.3E-10 0.833333
12 2.341E-10 2.3009759 2.5162E-10 0.4346 0.069444 8.16E-12 0.833333 8.16E-12 0.833333
13 1.501E-11 2.3009759 1.60374E-11 0.4346 0.064103 4.77E-13 0.833333 4.77E-13 0.833333
24 2.027E-26 2.3009759 2.10035E-26 0.4346 0.034722 3.28E-28 0.833333 3.28E-28 0.833333
25 6.758E-28 2.3009759 6.99111E-28 0.4346 0.033333 1.05E-29 0.833333 1.05E-29 0.833333
26 2.166E-29 2.3009759 2.23777E-29 0.4346 0.032051 3.22E-31 0.833333 3.22E-31 0.833333
27 6.685E-31 2.3009759 6.89825E-31 0.4346 0.030864 9.55E-33 0.833333 9.55E-33 0.833333
28 1.99E-32 2.3009759 2.05072E-32 0.4346 0.029762 2.73E-34 0.833333 2.73E-34 0.833333
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A B C D E F G H I J
Problem 9-22 (b)
Queuing Model M/M/s (Exponential Service Times)
Input Data Operating Characteristics
Arrival rate (l)1Average server utilization (r)0.4167
Service rate (m)2.4 Average number of customers in the queue (Lq)0.2976
Probabilities
Number of Units Probability
Cumulative
Probability
00.5833 0.5833
40.0176 0.9874
60.0031 0.9978
80.0005 0.9996
90.0002 0.9998
10 0.0001 0.9999
11 0.0000 1.0000
12 0.0000 1.0000
11
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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
20.086806 1.4166667 0.109649123 0.6552 0.208333 0.018905 0.435572 0.018905 0.435572
40.001256 1.5155285 0.001401899 0.6592 0.104167 0.000107 0.416774 0.000107 0.416774
67.27E-06 1.5168891 7.81012E-06 0.6592 0.069444 3.84E-07 0.416667 3.84E-07 0.416667
82.25E-08 1.5168968 2.37695E-08 0.6592 0.052083 8.61E-10 0.416667 8.61E-10 0.416667
91.04E-09 1.5168968 1.09376E-09 0.6592 0.046296 3.5E-11 0.416667 3.5E-11 0.416667
10 4.35E-11 1.5168968 4.53532E-11 0.6592 0.041667 1.3E-12 0.416667 1.3E-12 0.416667
11 1.65E-12 1.5168968 1.71116E-12 0.6592 0.037879 4.44E-14 0.416667 4.44E-14 0.416667
12 5.72E-14 1.5168968 5.9221E-14 0.6592 0.034722 1.4E-15 0.416667 1.4E-15 0.416667
13 1.83E-15 1.5168968 1.89287E-15 0.6592 0.032051 4.13E-17 0.416667 4.13E-17 0.416667