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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
Arrival rate (l)20 Average server utilization (r)0.6667
Probabilities
Number of Units Probability
Cumulative
Probability
00.0318 0.0318
10.1058 0.1376
30.1960 0.5100
50.1089 0.7822
90.0215 0.9570
10 0.0143 0.9713
11 0.0096 0.9809
12 0.0064 0.9873
Problem 9-21 (8 a.m. – 10 a.m.)
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52
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67
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71
13.3333333 1-1.428571429 -2.3333 3.333333 -4.7619 -1.42857 -0.2381 -0.07143
36.1728395 9.8888889 -55.55555556 -0.0219 1.111111 -12.1655 -8.83212 -0.60827 -0.44161
53.4293553 21.205761 10.28806584 0.0318 0.666667 0.653339 3.986672 0.032667 0.199334
90.1400057 27.825566 0.222361972 0.0357 0.37037 0.004663 3.337997 0.000233 0.1669
10 0.0466686 27.965572 0.070002843 0.0357 0.333333 0.001248 3.334582 6.24E-05 0.166729
11 0.014142 28.01224 0.020290679 0.0357 0.30303 0.000315 3.333648 1.57E-05 0.166682
12 0.0039283 28.026382 0.005439226 0.0357 0.277778 7.46E-05 3.333408 3.73E-06 0.16667
13 0.0010073 28.030311 0.001354597 0.0357 0.25641 1.67E-05 3.33335 8.33E-07 0.166667
24 5.707E-12 28.031625 6.62712E-12 0.0357 0.138889 3.81E-14 3.333333 1.91E-15 0.166667
25 7.609E-13 28.031625 8.77952E-13 0.0357 0.133333 4.82E-15 3.333333 2.41E-16 0.166667
26 9.755E-14 28.031625 1.11896E-13 0.0357 0.128205 5.87E-16 3.333333 2.94E-17 0.166667
27 1.204E-14 28.031625 1.37395E-14 0.0357 0.123457 6.9E-17 3.333333 3.45E-18 0.166667
28 1.434E-15 28.031625 1.62746E-15 0.0357 0.119048 7.85E-18 3.333333 3.92E-19 0.166667
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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
00.0009 0.0009
20.0204 0.0274
40.0755 0.1482
60.1119 0.3608
80.0888 0.5561
90.0740 0.6301
10 0.0617 0.6917
11 0.0514 0.7431
12 0.0428 0.7859
Problem 9-21 (10 a.m. – 2 p.m.)
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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
222.2222222 7.6666667 -9.523809524 -0.5385 3.333333 -7.32601 -0.65934 -0.18315 -0.01648
482.3045267 79.271605 -123.4567901 -0.0226 1.666667 -6.98519 -0.31852 -0.17463 -0.00796
6121.932632 271.3155 -1097.39369 -0.0012 1.111111 -13.2844 -6.61771 -0.33211 -0.16544
896.7719303 509.37445 580.631582 0.0009 0.833333 2.663433 9.3301 0.066586 0.233252
971.6829114 606.14638 276.4912295 0.0011 0.740741 0.895016 7.561683 0.022375 0.189042
10 47.7886076 677.82929 143.3658227 0.0012 0.666667 0.349164 7.015831 0.008729 0.175396
11 28.9627925 725.6179 73.52093473 0.0013 0.606061 0.141539 6.808205 0.003538 0.170205
12 16.0904403 754.58069 36.20349059 0.0013 0.555556 0.057227 6.723894 0.001431 0.168097
13 8.25150783 770.67113 16.93730554 0.0013 0.512821 0.022637 6.689303 0.000566 0.167233
24 9.5742E-05 785.77186 0.000132566 0.0013 0.277778 6.49E-08 6.666667 1.62E-09 0.166667
25 2.5531E-05 785.77196 3.48154E-05 0.0013 0.266667 1.61E-08 6.666667 4.03E-10 0.166667
26 6.5465E-06 785.77199 8.80389E-06 0.0013 0.25641 3.86E-09 6.666667 9.66E-11 0.166667
27 1.6164E-06 785.77199 2.14639E-06 0.0013 0.246914 8.96E-10 6.666667 2.24E-11 0.166667
28 3.8486E-07 785.77199 5.0513E-07 0.0013 0.238095 2.01E-10 6.666667 5.02E-12 0.166667
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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
Arrival rate (l)25 Average server utilization (r)0.6944
Service rate (m)6Average number of customers in the queue (Lq)0.7434
Number of servers (s) 6 Average number of customers in the system (L) 4.9101
10.0573 0.0711
30.1658 0.3562
50.1439 0.6729
90.0335 0.9239
10 0.0232 0.9472
11 0.0161 0.9633
12 0.0112 0.9745
Problem 9-21 (2 p.m. – 5 p.m.)
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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
14.16666667 1-1.315789474 -3.1667 4.166667 -5.48246 -1.31579 -0.2193 -0.05263
312.0563272 13.847222 -31.00198413 -0.0583 1.388889 -6.45426 -2.2876 -0.25817 -0.0915
510.4655618 38.462224 62.79337063 0.0099 0.833333 3.100736 7.267403 0.124029 0.290696
91.04312365 62.774726 1.942368175 0.0155 0.462963 0.025873 4.19254 0.001035 0.167702
10 0.43463485 63.81785 0.745088321 0.0155 0.416667 0.008243 4.17491 0.00033 0.166996
11 0.16463441 64.252484 0.265021252 0.0155 0.378788 0.002505 4.169171 0.0001 0.166767
12 0.05716473 64.417119 0.087571497 0.0155 0.347222 0.000722 4.167389 2.89E-05 0.166696
13 0.01832203 64.474284 0.026964494 0.0155 0.320513 0.000197 4.166864 7.89E-06 0.166675