Advances in Operations Research / 2015 / Article / Tab 3

Research Article

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

Table 3

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


00.0002580.0000990.0001530.0002190.0002920.0003700.0004480.0005240.0005940.002957
10.0008420.0003150.0004730.0006550.0008500.0010480.0012370.0014100.0021090.008939
20.0017190.0006240.0009100.0012250.0015460.0018540.0021330.0023690.0045020.016882
30.0028060.0009890.0014010.0018320.0022490.0026260.0029420.0031850.0074980.025528
40.0040090.0013710.0018860.0023970.0028620.0032530.0035510.0037480.0107380.033815
50.0052370.0017370.0023210.0028670.0033310.0036850.0039180.0040310.0138870.041014
60.0064120.0020640.0026780.0032160.0036340.0039130.0040530.0040650.0166840.046719
70.0074770.0023350.0029430.0034340.0037750.0039570.0039930.0039040.0189620.050780
80.0083930.0025440.0031130.0035310.0037750.0038530.0037870.0036090.0206430.053248
90.0091350.0026870.0031930.0035200.0036610.0036370.0034820.0032350.0217170.054267
100.0096950.0027670.0031930.0034210.0034610.0033470.0031220.0028270.0222200.054053
200.0078890.0016650.0014340.0011560.0008870.0006560.0004700.0003300.0123760.026862
300.0031940.0004990.0003200.0001940.0001130.0000640.0000350.0000190.0038080.008246
400.0009490.0001100.0000520.0000240.0000100.0000040.0000020.0000000.0009610.002112
600.0000530.0000030.0000000.0000000.0000000.0000000.0000000.0000000.0000460.000102
800.0000020.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000020.000004
850.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.000000

0.2266520.0532490.0542670.0540530.0528440.0508710.0483440.0454460.4142721.000000