Advances in Operations Research / 2015 / Article / Tab 1

Research Article

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 .


00.0032640.0006340.0006930.0007510.0008080.0008640.0009180.0009700.0010210.0010700.0011180.012112
10.0031270.0006060.0006590.0007120.0007630.0008120.0008600.0009060.0009500.0009920.0021460.012531
20.0029970.0005780.0006270.0006740.0007200.0007630.0008050.0008450.0008830.0009190.0030900.012903
30.0028710.0005520.0005960.0006390.0006790.0007180.0007540.0007890.0008210.0008510.0039560.013228
40.0027510.0005270.0005670.0006050.0006410.0006750.0007070.0007360.0007640.0007890.0047490.013511
50.0026360.0005030.0005390.0005730.0006050.0006350.0006620.0006870.0007100.0007310.0054720.013754
100.0021290.0003980.0004190.0004370.0004530.0004670.0004780.0004870.0004940.0004990.0082050.014465
500.0003850.0000620.0000560.0000500.0000450.0000400.0000350.0000310.0000270.0000240.0081170.008872
1000.0000450.0000060.0000040.0000030.0000020.0000020.0000010.0000000.0000000.0000000.0026150.002678
2000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0001700.000170
3000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000100.000010
3700.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000010.000001
380  0.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.000000

0.0780400.0139600.0141320.0142720.0143830.0144650.0145220.0145560.0145670.0145580.7925391.000000