Research Article
Analytically Explicit Results for the Distribution of the Number of Customers Served during a Busy Period for Special Cases of the M/G/1 Queue
Table 2
Distribution of the number of customers served during a busy period.
| n | Generalized Erlang distribution | Hyperexponential distribution | , , , | , , , , , | | | | | | | | | | | | |
| 3 | 0.151704 | | | 0.373248 | | | 4 | 0.129454 | | | 0.220963 | | | 5 | 0.101837 | | | 0.133358 | | | 6 | 0.080573 | | | 0.084303 | | | 7 | 0.064895 | 0.012274 | | 0.055373 | 0.100306 | | 8 | 0.053219 | 0.024439 | | 0.037470 | 0.138556 | | 9 | 0.044348 | 0.033129 | 0.003491 | 0.025955 | 0.138307 | 0.051999 | 10 | 0.037468 | 0.038404 | 0.008938 | 0.018318 | 0.122466 | 0.092350 | 20 | 0.010875 | 0.029860 | 0.030692 | 0.000971 | 0.012428 | 0.029950 | 50 | 0.001310 | 0.005343 | 0.008297 | 0.000001 | 0.000014 | 0.000044 | 100 | 0.000129 | 0.000588 | 0.001014 | 0.000000 | 0.000000 | 0.000000 | 200 | 0.000003 | 0.000017 | 0.000030 | 0.000000 | 0.000000 | 0.000000 | | | | | | | | | 12.000 | 28.000 | 36.000 | 5.000 | 11.667 | 15.000 | | 348.00 | 1260.00 | 1908.00 | 33.194 | 155.231 | 249.583 | | 204.00 | 476.000 | 612.00 | 8.1944 | 19.1204 | 24.5833 |
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