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 1
Distribution of the number of customers served during a busy period.
| n | Exponential distribution | Deterministic distribution | , , | , , | | | | | | | | | | | | |
| 3 | 0.512000 | | | 0.301194 | | | 4 | 0.245760 | | | 0.242276 | | | 5 | 0.117965 | | | 0.162402 | | | 6 | 0.058720 | | | 0.104507 | | | 7 | 0.030199 | 0.209715 | | 0.066745 | 0.060810 | | 8 | 0.015945 | 0.234881 | | 0.042742 | 0.114134 | | 9 | 0.008599 | 0.187905 | 0.134218 | 0.027536 | 0.137712 | 0.027324 | 10 | 0.004717 | 0.132285 | 0.193274 | 0.017862 | 0.136757 | 0.065936 | 20 | 0.000019 | 0.001148 | 0.005804 | 0.000319 | 0.010366 | 0.032485 | 30 | 0.000000 | 0.000009 | 0.000052 | 0.000008 | 0.000367 | 0.001660 | | | | | | | | | 4.000 | 9.3333 | 12.000 | 5.000 | 11.6667 | 15.000 | | 18.222 | 92.296 | 150.67 | 30.556 | 149.074 | 241.667 | | 2.2222 | 5.1852 | 6.6667 | 5.5556 | 12.963 | 16.6667 |
|
|