Research Article
Queue Length and Server Content Distribution in an Infinite-Buffer Batch-Service Queue with Batch-Size-Dependent Service
Table 2
Joint distribution of queue and server content at arbitrary epoch (
) of an
queue with
.
| | | | | | | | | | | | | | |
| 0 | 0.000892 | 0.005507 | 0.000981 | 0.000989 | 0.000996 | 0.001000 | 0.001002 | 0.001002 | 0.001001 | 0.000998 | 0.000993 | 0.000988 | 0.016350 | 1 | 0.001815 | 0.005277 | 0.000937 | 0.000941 | 0.000943 | 0.000943 | 0.000942 | 0.000939 | 0.000934 | 0.000928 | 0.000920 | 0.001897 | 0.017417 | 2 | 0.002765 | 0.005056 | 0.000894 | 0.000895 | 0.000893 | 0.000891 | 0.000886 | 0.000879 | 0.000872 | 0.000862 | 0.000853 | 0.002731 | 0.018480 | 3 | 0.003740 | 0.004845 | 0.000853 | 0.000851 | 0.000846 | 0.000840 | 0.000833 | 0.000824 | 0.000813 | 0.000802 | 0.000790 | 0.003497 | 0.019537 | 4 | 0.004735 | 0.004642 | 0.000814 | 0.000809 | 0.000802 | 0.000793 | 0.000783 | 0.000772 | 0.000759 | 0.000746 | 0.000732 | 0.004197 | 0.020587 | 5 | | 0.004448 | 0.000778 | 0.000770 | 0.000760 | 0.000749 | 0.000736 | 0.000723 | 0.000709 | 0.000694 | 0.000678 | 0.004837 | 0.015881 | 10 | | 0.003593 | 0.000616 | 0.000598 | 0.000580 | 0.000561 | 0.000541 | 0.000522 | 0.000501 | 0.000482 | 0.000463 | 0.007252 | 0.015710 | 50 | | 0.000650 | 0.000096 | 0.000080 | 0.000067 | 0.000055 | 0.000046 | 0.000038 | 0.000032 | 0.000026 | 0.000021 | 0.007175 | 0.008288 | 100 | | 0.000077 | 0.000009 | 0.000006 | 0.000004 | 0.000003 | 0.000002 | 0.000001 | 0.000001 | 0.000000 | 0.000000 | 0.002311 | 0.002417 | 200 | | 0.000001 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000151 | 0.000152 | 300 | | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000009 | 0.000009 | 370 | | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000001 | 0.000001 | 380 | | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| Total | 0.013947 | 0.131681 | 0.021593 | 0.020178 | 0.018923 | 0.017798 | 0.016781 | 0.015856 | 0.015010 | 0.014231 | 0.013511 | 0.700489 | 1.000000 |
| , , and | , , and |
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