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

Table 1

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

0	0.003264	0.000634	0.000693	0.000751	0.000808	0.000864	0.000918	0.000970	0.001021	0.001070	0.001118	0.012112
1	0.003127	0.000606	0.000659	0.000712	0.000763	0.000812	0.000860	0.000906	0.000950	0.000992	0.002146	0.012531
2	0.002997	0.000578	0.000627	0.000674	0.000720	0.000763	0.000805	0.000845	0.000883	0.000919	0.003090	0.012903
3	0.002871	0.000552	0.000596	0.000639	0.000679	0.000718	0.000754	0.000789	0.000821	0.000851	0.003956	0.013228
4	0.002751	0.000527	0.000567	0.000605	0.000641	0.000675	0.000707	0.000736	0.000764	0.000789	0.004749	0.013511
5	0.002636	0.000503	0.000539	0.000573	0.000605	0.000635	0.000662	0.000687	0.000710	0.000731	0.005472	0.013754
10	0.002129	0.000398	0.000419	0.000437	0.000453	0.000467	0.000478	0.000487	0.000494	0.000499	0.008205	0.014465
50	0.000385	0.000062	0.000056	0.000050	0.000045	0.000040	0.000035	0.000031	0.000027	0.000024	0.008117	0.008872
100	0.000045	0.000006	0.000004	0.000003	0.000002	0.000002	0.000001	0.000000	0.000000	0.000000	0.002615	0.002678
200	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000170	0.000170
300	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000010	0.000010
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
	0.078040	0.013960	0.014132	0.014272	0.014383	0.014465	0.014522	0.014556	0.014567	0.014558	0.792539	1.000000