Mathematical Problems in Engineering

Research Article

Traffic Intensity Estimation in Finite Markovian Queueing Systems

Table 3

Mean estimates for and the mean squared error (MSE, in parentheses) for .
Estimate
102050100200
MLE0.010.00928 (0.00084)0.00960 (0.00045)0.01000 (0.00019)0.01003 (0.00010)0.01007 (0.00005)
0.100.09158 (0.00710)0.09609 (0.00383)0.09844 (0.00159)0.09906 (0.00081)0.09964 (0.00041)
0.200.18345 (0.01178)0.19186 (0.00631)0.19684 (0.00255)0.19827 (0.00128)0.19919 (0.00064)
0.500.47366 (0.01422)0.48783 (0.00666)0.49543 (0.00255)0.49750 (0.00127)0.49885 (0.00062)
0.900.89001 (0.00144)0.89551 (0.00057)0.89835 (0.00020)0.89915 (0.00010)0.89960 (0.00005)
0.990.98737 (0.00016)0.98903 (0.00008)0.98982 (0.00003)0.98995 (0.00002)0.98998 (0.00001)
Beta0.010.09009 (0.00692)0.05374 (0.00226)0.02864 (0.00052)0.01953 (0.00018)0.01487 (0.00007)
0.100.15477 (0.00743)0.12978 (0.00388)0.11242 (0.00159)0.10616 (0.00080)0.10320 (0.00041)
0.200.22892 (0.00850)0.21530 (0.00529)0.20632 (0.00237)0.20304 (0.00124)0.20157 (0.00063)
0.500.47779 (0.01125)0.48892 (0.00597)0.49556 (0.00245)0.49753 (0.00125)0.49885 (0.00062)
0.900.88221 (0.00180)0.89167 (0.00065)0.89680 (0.00021)0.89837 (0.00010)0.89921 (0.00005)
0.990.98149 (0.00017)0.98570 (0.00007)0.98856 (0.00003)0.98953 (0.00002)0.98990 (0.00001)
Jeffreys0,010,05225 (0,00231)0,03334 (0,00089)0,01998 (0,00027)0,01506 (0,00011)0,01253 (0,00005)
0,100,11744 (0,00482)0,11002 (0,00316)0,10425 (0,00149)0,10203 (0,00078)0,10113 (0,00040)
0,200,19224 (0,00794)0,19572 (0,00502)0,19866 (0,00233)0,19927 (0,00123)0,19970 (0,00063)
0,500,46147 (0,01532)0,48167 (0,00767)0,49430 (0,00302)0,49826 (0,00151)0,50064 (0,00074)
0,900,88217 (0,00180)0,89165 (0,00065)0,89680 (0,00021)0,89837 (0,00010)0,89921 (0,00005)
0,990,98148 (0,00017)0,98570 (0,00007)0,98856 (0,00003)0,98953 (0,00002)0,98990 (0,00001)
Bootstrap0.010.00993 (0.00096)0.01000 (0.00049)0.01018 (0.00020)0.01013 (0.00010)0.01012 (0.00005)
0.100.09763 (0.00795)0.09976 (0.00409)0.10010 (0.00164)0.09994 (0.00082)0.10007 (0.00041)
0.200.19462 (0.01281)0.19846 (0.00661)0.19982 (0.00260)0.19982 (0.00130)0.19997 (0.00065)
0.500.49390 (0.01405)0.49897 (0.00659)0.50019 (0.00254)0.49995 (0.00127)0.50008 (0.00062)
0.900.89910 (0.00118)0.89987 (0.00051)0.90008 (0.00019)0.90002 (0.00009)0.90003 (0.00005)
0.990.99000 (0.00016)0.99042 (0.00009)0.99031 (0.00004)0.99012 (0.00002)0.99002 (0.00001)