Advances in Operations Research / 2015 / Article / Tab 4

Research Article

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

Table 4

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


00.0002530.0193300.0045380.0046200.0045960.0044870.0043110.0040890.0038350.0035630.053622
10.0010160.0192580.0045110.0045800.0045400.0044140.0042220.0039830.0037150.0067230.056962
20.0024580.0191110.0044580.0045020.0044360.0042820.0040640.0038020.0035130.0094040.060030
30.0046370.0188720.0043730.0043820.0042790.0040900.0038400.0035500.0032410.0115600.062824
40.0075250.0185290.0042560.0042210.0040750.0038460.0035620.0032470.0029210.0131820.065364
50.0110270.0180820.0041080.0040230.0038300.0035610.0032470.0029130.0025760.0142900.067657
60.0150160.0175350.0039320.0037950.0035550.0032510.0029130.0025670.0022290.0149300.069723
70.0168960.0037320.0035430.0032620.0029290.0025750.0022260.0018960.0151620.052221
80.0161800.0035150.0032770.0029610.0026060.0022460.0019020.0015880.0150540.049329
90.0154000.0032860.0030050.0026600.0022940.0019360.0016050.0013120.0146740.046172
100.0145720.0030490.0027320.0023680.0019980.0016500.0013380.0010700.0140880.042865
200.0064450.0010640.0007480.0005080.0003360.0002180.0001390.0000880.0058240.015370
300.0020520.0002580.0001380.0000720.0000360.0000180.0000090.0000040.0016420.004229
400.0005370.0000510.0000200.0000080.0000030.0000010.0000000.0000000.0003970.001017
600.0000260.0000010.0000000.0000000.0000000.0000000.0000000.0000000.0000180.000045
750.0000020.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000010.000003
850.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.000000

Total 0.041932 0.344036 0.069281 0.061779 0.054699 0.048127 0.042119 0.036691 0.031838 0.269497 1.000000

, , and
, , and