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 3
Distribution of the number of customers served during a busy period.
| n | Matrix exponential distribution | Chi-square distribution | , , | , , | | | | | | | | | | | | |
| 3 | 0.339685 | | | 0.220001 | | | 4 | 0.222371 | | | 0.170756 | | | 5 | 0.139825 | | | 0.125171 | | | 6 | 0.090430 | | | 0.093132 | | | 7 | 0.060262 | 0.080509 | | 0.070848 | 0.029218 | | 8 | 0.041179 | 0.122977 | | 0.055009 | 0.052916 | | 9 | 0.028722 | 0.130997 | 0.039195 | 0.043465 | 0.066170 | 0.010648 | 10 | 0.020371 | 0.121409 | 0.076975 | 0.034852 | 0.071365 | 0.024794 | 20 | 0.001091 | 0.014350 | 0.033872 | 0.006110 | 0.031203 | 0.044522 | 50 | 0.000001 | 0.000016 | 0.000054 | 0.000167 | 0.001229 | 0.002577 | 100 | 0.000000 | 0.000000 | 0.000000 | 0.000001 | 0.000011 | 0.000026 | | | | | | | | | 5.1703 | 12.0640 | 15.5109 | 7.5000 | 17.5000 | 22.5000 | | 35.5201 | 166.047 | 266.953 | 95.625 | 398.125 | 118.125 | | 8.7880 | 20.5054 | 26.3641 | 39.375 | 91.875 | 624.375 |
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