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

Table 3

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

0	0.000258	0.000099	0.000153	0.000219	0.000292	0.000370	0.000448	0.000524	0.000594	0.002957
1	0.000842	0.000315	0.000473	0.000655	0.000850	0.001048	0.001237	0.001410	0.002109	0.008939
2	0.001719	0.000624	0.000910	0.001225	0.001546	0.001854	0.002133	0.002369	0.004502	0.016882
3	0.002806	0.000989	0.001401	0.001832	0.002249	0.002626	0.002942	0.003185	0.007498	0.025528
4	0.004009	0.001371	0.001886	0.002397	0.002862	0.003253	0.003551	0.003748	0.010738	0.033815
5	0.005237	0.001737	0.002321	0.002867	0.003331	0.003685	0.003918	0.004031	0.013887	0.041014
6	0.006412	0.002064	0.002678	0.003216	0.003634	0.003913	0.004053	0.004065	0.016684	0.046719
7	0.007477	0.002335	0.002943	0.003434	0.003775	0.003957	0.003993	0.003904	0.018962	0.050780
8	0.008393	0.002544	0.003113	0.003531	0.003775	0.003853	0.003787	0.003609	0.020643	0.053248
9	0.009135	0.002687	0.003193	0.003520	0.003661	0.003637	0.003482	0.003235	0.021717	0.054267
10	0.009695	0.002767	0.003193	0.003421	0.003461	0.003347	0.003122	0.002827	0.022220	0.054053
20	0.007889	0.001665	0.001434	0.001156	0.000887	0.000656	0.000470	0.000330	0.012376	0.026862
30	0.003194	0.000499	0.000320	0.000194	0.000113	0.000064	0.000035	0.000019	0.003808	0.008246
40	0.000949	0.000110	0.000052	0.000024	0.000010	0.000004	0.000002	0.000000	0.000961	0.002112
60	0.000053	0.000003	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000046	0.000102
80	0.000002	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000002	0.000004
85	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
	0.226652	0.053249	0.054267	0.054053	0.052844	0.050871	0.048344	0.045446	0.414272	1.000000