Advances in Operations Research / 2015 / Article / Tab 5

Research Article

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 .


00.0003490.0003420.0007030.0010600.0012700.0012700.0010920.006084
10.0025150.0020540.0036130.0047690.0050820.0045710.0042020.026806
20.0090560.0061620.0092910.0107290.0101630.0082280.0082410.061869
30.0217340.0123250.0159280.0160940.0135510.0098740.0110170.100523
40.0391200.0184870.0204790.0181060.0135510.0088870.0113300.129959
50.0563330.0221840.0210640.0162950.0108410.0063980.0095920.142707
60.0676000.0221840.0180550.0122210.0072270.0038390.0069870.138113
70.0695320.0190150.0132650.0078570.0041300.0019740.0045160.120289
80.0625780.0142610.0085270.0044190.0020650.0008880.0026500.095388
90.0500630.0095070.0048730.0022100.0009180.0003550.0014360.069362
100.0360450.0057040.0025060.0009940.0003670.0001280.0007280.046472
120.0141560.0015560.0005020.0001520.0000440.0000130.0001580.016581
140.0040320.0003080.0000730.0000170.0000040.0000000.0000290.004463
160.0008710.0000460.0000080.0000010.0000000.0000000.0000040.000930
180.0001470.0000050.0000000.0000000.0000000.0000000.0000000.000152
200.0000200.0000000.0000000.0000000.0000000.0000000.0000000.000020
230.0000000.0000000.0000000.0000000.0000000.0000000.0000000.000000

0.4679580.1381140.1202890.0953900.0693620.0464730.0624141.000000