Advances in Operations Research / 2015 / Article / Tab 6

Research Article

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

Table 6

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


00.0009290.0714000.0210360.0182600.0144030.0103970.0069020.0042310.147558
10.0050220.0710160.0207230.0177080.0136750.0096210.0062040.0061220.150090
20.0144700.0696330.0197820.0162890.0120370.0080690.0049480.0062220.151450
30.0298190.0663140.0179000.0138570.0095800.0060000.0034400.0052210.152130
40.0496630.0603410.0150770.0107300.0068150.0039310.0020830.0038120.152452
50.0517390.0116900.0075140.0043270.0022760.0011060.0024890.081141
60.0414170.0083030.0047570.0024610.0011720.0005200.0014820.060112
70.0308000.0053990.0027310.0012610.0005410.0002180.0008160.041766
80.0212450.0032210.0014290.0005860.0002260.0000830.0004210.027211
90.0136010.0017700.0006850.0002490.0000860.0000280.0002050.016624
100.0080970.0008990.0003020.0000970.0000300.0000090.0000940.009528
120.0023330.0001860.0000470.0000120.0000030.0000000.0000180.002599
140.0005200.0000290.0000050.0000010.0000000.0000000.0000030.000558
160.0000920.0000040.0000000.0000000.0000000.0000000.0000000.000096
180.0000130.0000000.0000000.0000000.0000000.0000000.0000000.000013
200.0000010.0000000.0000000.0000000.0000000.0000000.0000000.000001
230.0000000.0000000.0000000.0000000.0000000.0000000.0000000.000000

Total
0.099903
0.514462
0.126533
0.094459
0.065544
0.042364
0.025546
0.031189
1.000000

, , and
, , and