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A B C D E F G H I J
Problem 9-19
Queuing Model M/M/s (Exponential Service Times)
1 0.1875 0.4375
2 0.1406 0.5781
3 0.1055 0.6836
13 0.0059 0.9822
14 0.0045 0.9866
15 0.0033 0.9900
16 0.0025 0.9925
17 0.0019 0.9944
(d) (2.25 customers) x (4 queues) = 9 customers total
(f) Single M/M/4 system is more efficient than 4 parallel
independent M/M/1 systems. The latter may have idle
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4 0.013184 2.1015625 0.016225962 0.4722 0.1875 0.001768 0.751768 0.000589 0.250589
5 0.001978 2.1147461 0.002326517 0.4724 0.15 0.000194 0.750194 6.46E-05 0.250065
6 0.000247 2.1167236 0.000282506 0.4724 0.125 1.91E-05 0.750019 6.35E-06 0.250006
7 2.65E-05 2.1169708 2.96631E-05 0.4724 0.107143 1.68E-06 0.750002 5.6E-07 0.250001
8 2.48E-06 2.1169973 2.73982E-06 0.4724 0.09375 1.34E-07 0.75 4.46E-08 0.25
19 3.48E-20 2.117 3.61876E-20 0.4724 0.039474 7.02E-22 0.75 2.34E-22 0.25
20 1.3E-21 2.117 1.35425E-21 0.4724 0.0375 2.49E-23 0.75 8.31E-24 0.25
21 4.66E-23 2.117 4.82766E-23 0.4724 0.035714 8.45E-25 0.75 2.82E-25 0.25
22 1.59E-24 2.117 1.64303E-24 0.4724 0.034091 2.74E-26 0.75 9.13E-27 0.25
23 5.18E-26 2.117 5.34949E-26 0.4724 0.032609 8.52E-28 0.75 2.84E-28 0.25