Estimation of Traffic Intensity Based on Queue Length in a Single M/M/1 Queue

References

• Aigner , D. J. ( 1974 ). Parameter estimation from cross-sectional observations on an elementary queueing system . JSTOR 22 : 422 – 428 .
   Web of Science ®Google Scholar
• Armero , C. ( 1985 ). Bayesian analysis of M/M/1 queues . Bayesian Statist. 2 : 613 – 617 .
   Google Scholar
• Armero , C. ( 1994 ). Bayesian inference in Markovian queues . Que. Syst. 15 : 419 – 426 .
   Google Scholar
• Armero , C. , Bayarri , M. J. ( 1994 ). Bayesian prediction in M/M/1 queues . Que. Syst. 15 : 401 – 417 .
   Google Scholar
• Basawa , I. V. , Prabhu , N. U. ( 1981 ). Estimation in single server queues . Nav. Res. Logist. Quart. 28 : 475 – 487 .
   Google Scholar
• Basawa , I. V. , Bhat , U. N. , Lund , R. ( 1996 ). Maximum likelihood estimation for single server queues from waiting time data . Que. Syst. 24 : 155 – 167 .
   Web of Science ®Google Scholar
• Berger , J. O. ( 1985 ). Statistical Decision Theory and Bayesian Analysis . New York : Springer .
   Google Scholar
• Bhat , U. N. , Miller , G. K. , Rao , S. S. ( 1997 ). Statistical analysis of queueing systems . In: Dshalalow , J. H. , ed. Frontiers in Queueing . Boca Raton , FL : CRC Press .
   Google Scholar
• Bhat , U. N. , Basawa , I. V. ( 2002 ). Maximum likelihood estimation in queueing systems . In: Bala Krishnan , N. , ed. Advances on Methodological and Applied Aspects of Probability and Statistics . New York : Taylor & Francis .
   Google Scholar
• Clarke , A. B. ( 1957 ). Maximum likelihood estimates in a simple queue . Ann. Math. Statist. 28 : 1036 – 1040 .
   Google Scholar
• Cox , D. R. ( 1965 ). Some problems of statistical analysis connected with congestion . Proc. Symp. Congestion Theory .
   Google Scholar
• Gradshteyn , I. S. , Ryzhk , I. M. (2000). Table of Integrals, Series and Products . California : Academic Press.
   Google Scholar
• Gross , D. , Harris , P. ( 1998 ). Fundamentals of Queueing Theory. , 3rd ed. New York : Wiley .
   Google Scholar
• Harishchandra , K. , Rao , S. S. ( 1988 ). A note on statistical inference about the traffic intensity in M/E k /1 queue . Sankhya Ser. B 50 : 144 – 148 .
   Google Scholar
• McGrath , M. F. , Singpurwalla , N. D. ( 1987 ). A subjective Bayesian approach to the theory of queues, Part-1: Modelling . Queueing Syst. 1:317–333; Part-2: Inference and information in M/M/1 queues. Queueing Syst. 1 : 335 – 353 .
   Google Scholar
• Moran , P. A. P. ( 1951 ). The estimation of the parameters of a birth and death process . J. Roy. Statist. Soc. B 13 : 241 – 245 .
   Google Scholar
• Muddapur , M. V. ( 1972 ). Bayesian Estimates of parameters in some queueing models . Ann. Inst. Statist. Math. 24 : 327 – 331 .
   Web of Science ®Google Scholar
• Samaan , J. E. , Tracy , D. S. ( 1981 ). On the parameter estimation of queueing theory . Comput. Sci. Statist. 13 : 324 – 330 .
   Google Scholar
• Thiruvaiyaru , D. , Basawa , I. V. ( 1992 ). Empirical bayes estimation for queueing systems and networks . Queueing Sys. 11 : 179 – 202 .
   Google Scholar
• Wolff , R. W. ( 1965 ). Problems of statistical inference for birth and death queueing models . Operat. Res. 13 : 343 – 357 .
   Web of Science ®Google Scholar