Queue Length and Server Content Distribution in an Infinite-Buffer Batch-Service Queue with Batch-Size-Dependent Service

Table 5

Joint distribution of queue and server content at departure epoch () of an queue with , , , , and .

0	0.000349	0.000342	0.000703	0.001060	0.001270	0.001270	0.001092	0.006084
1	0.002515	0.002054	0.003613	0.004769	0.005082	0.004571	0.004202	0.026806
2	0.009056	0.006162	0.009291	0.010729	0.010163	0.008228	0.008241	0.061869
3	0.021734	0.012325	0.015928	0.016094	0.013551	0.009874	0.011017	0.100523
4	0.039120	0.018487	0.020479	0.018106	0.013551	0.008887	0.011330	0.129959
5	0.056333	0.022184	0.021064	0.016295	0.010841	0.006398	0.009592	0.142707
6	0.067600	0.022184	0.018055	0.012221	0.007227	0.003839	0.006987	0.138113
7	0.069532	0.019015	0.013265	0.007857	0.004130	0.001974	0.004516	0.120289
8	0.062578	0.014261	0.008527	0.004419	0.002065	0.000888	0.002650	0.095388
9	0.050063	0.009507	0.004873	0.002210	0.000918	0.000355	0.001436	0.069362
10	0.036045	0.005704	0.002506	0.000994	0.000367	0.000128	0.000728	0.046472
12	0.014156	0.001556	0.000502	0.000152	0.000044	0.000013	0.000158	0.016581
14	0.004032	0.000308	0.000073	0.000017	0.000004	0.000000	0.000029	0.004463
16	0.000871	0.000046	0.000008	0.000001	0.000000	0.000000	0.000004	0.000930
18	0.000147	0.000005	0.000000	0.000000	0.000000	0.000000	0.000000	0.000152
20	0.000020	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000020
23	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
	0.467958	0.138114	0.120289	0.095390	0.069362	0.046473	0.062414	1.000000