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 5
Distribution of the number of customers served during a busy period.
| n | Markov-modulated Poisson process | Interrupted Poisson process | , , | , , | , , | , , | | | | | | | | | | | | |
| 3 | 0.580690 | | | 0.416275 | | | 4 | 0.225374 | | | 0.230894 | | | 5 | 0.097992 | | | 0.130911 | | | 6 | 0.046357 | | | 0.077951 | | | 7 | 0.023164 | 0.281322 | | 0.048328 | 0.129386 | | 8 | 0.012020 | 0.254765 | | 0.030916 | 0.167454 | | 9 | 0.006413 | 0.176690 | 0.195809 | 0.020268 | 0.156863 | 0.072134 | 10 | 0.003494 | 0.112568 | 0.227989 | 0.013549 | 0.130565 | 0.120031 | 20 | 0.000015 | 0.000724 | 0.003611 | 0.000426 | 0.007541 | 0.021595 | 50 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000002 | 0.000007 | | | | | | | | | 3.81818 | 8.9091 | 11.4545 | 4.6154 | 10.7692 | 13.8462 | | 16.4254 | 83.681 | 136.747 | 26.7911 | 128.785 | 208.184 | | 1.8469 | 4.3095 | 5.5407 | 5.4893 | 12.8084 | 16.4679 |
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