Advances in Operations Research / 2015 / Article / Tab 2

Research Article

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

Table 2

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


00.0008920.0055070.0009810.0009890.0009960.0010000.0010020.0010020.0010010.0009980.0009930.0009880.016350
10.0018150.0052770.0009370.0009410.0009430.0009430.0009420.0009390.0009340.0009280.0009200.0018970.017417
20.0027650.0050560.0008940.0008950.0008930.0008910.0008860.0008790.0008720.0008620.0008530.0027310.018480
30.0037400.0048450.0008530.0008510.0008460.0008400.0008330.0008240.0008130.0008020.0007900.0034970.019537
40.0047350.0046420.0008140.0008090.0008020.0007930.0007830.0007720.0007590.0007460.0007320.0041970.020587
50.0044480.0007780.0007700.0007600.0007490.0007360.0007230.0007090.0006940.0006780.0048370.015881
100.0035930.0006160.0005980.0005800.0005610.0005410.0005220.0005010.0004820.0004630.0072520.015710
500.0006500.0000960.0000800.0000670.0000550.0000460.0000380.0000320.0000260.0000210.0071750.008288
1000.0000770.0000090.0000060.0000040.0000030.0000020.0000010.0000010.0000000.0000000.0023110.002417
2000.0000010.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0001510.000152
3000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000090.000009
3700.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000010.000001
3800.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.000000

Total 0.013947 0.131681 0.021593 0.020178 0.018923 0.017798 0.016781 0.015856 0.015010 0.014231 0.013511 0.700489 1.000000

, , and
, , and