Abstract
This paper is concerned with the Bayesian analysis of general queues with Poisson input and exponential service times. Joint posterior distribution of the arrival rate and the individual service rate is obtained from a sample consisting inn observations of the interarrival process andm complete service times. Posterior distribution of traffic intensity inM/M/c is also obtained and the statistical analysis of the ergodic condition from a decision point of view is discussed.
References
D.J. Aigner, Parameter estimation from crosssectional observations on an elementary queueing system, Oper. Res. 22 (1975) 422.
C. Armero, Bayesian Analysis ofM/M/1/∞/FIFO queues, Bayesian Statistics 2, eds. Bernardo et al. (North-Holland, Amsterdam, 1985) p. 613.
C. Armero, Análisis bayesiano de colasM/M (in Spanish), Doctoral dissertation, University of Valencia (1988).
C. Armero and M.J. Bayarri, Bayesian prediction inM/M/1 queues, Queueing Systems 15 (1994) 401–417.
C. Armero and M.J. Bayarri, Prior assessments for prediction in queues, The Statistician (1994), in press.
L.J. Bain,Statistical Analysis of Reliability and Life-Testing Models (Marcel Dekker, New York, 1978).
I.V. Basawa and B.L.S. Prakasa Rao,Statistical Inference for Stochastic Processes (Academic Press, New York, 1980).
I.V. Basawa and N.U. Prabhu, Estimation in single server queues, Naval Res. Logist. Quart. 28 (1981) 475.
I.V. Basawa and N.U. Prabhu, Large sample inference from single server queues, Queueing Systems 3 (1988) 289.
V.E. Benes, A sufficient set of statistics for a simple telephone exchange model, Bell Syst. Tech. J. 36 (1957) 939.
J. Berger,Statistical Decision Theory and Bayesian Analysis, 2nd ed. (Wiley, New York, 1985).
U.N. Bhat, A sequential technique for the control of traffic intensity in Markovian queues, Ann. Oper. Res. 8 (1987) 151.
U.N. Bhat and S.S. Rao, Statistical analysis of queueing systems, Queueing Systems 1 (1987) 217.
U.N. Bhat and S.S. Rao, A statistical technique for the control of traffic intensity in queueing systemsM/G/1 and GI/M/1, Oper. Res. 20 (1972) 955.
A.B. Clarke, Maximum likelihood estimates in a simple queue, Ann. Math. Statist. 28 (1957) 1036.
D.R. Cox, Some problems of statistical analysis connected with congestion,Proc. Symp. on Congestion Theory, University of North Carolina Press, Chapel Hill, North Carolina (1965) p. 289.
M.H. DeGroot,Optimal Statistical Decision (McGraw-Hill, New York, 1970).
D.P. Gaver and P.A. Jacobs, On inference concerning time-dependent queue performance: TheM/G/1 example, Queueing Systems 6 (1990) 261.
K. Harischandraand S.S. Rao, A note on statistical inference about the traffic intensity parameter in M/Ek/1 queues, Sankhya B 50 (1988) 144.
D.G. Kendall, Stochastic processes occurring in the theory of queues and their analysis by the method of imbedded Markov chains, Ann. Math. Statist. 24 (1953) 338.
N. Keiding, Maximum likelihood estimation in the birth- and-death process, Ann. Stat. 3 (1975) 363.
H.W. Lilliefors, Some confidence intervals for queue, Oper. Res. 14 (1966) 723.
M.F. McGrath, D. Gross and N.D. Singpurwalla, A subjective bayesian approach to the theory of queues I-Modeling, Queueing Systems 1 (1987) 317.
M.F. McGrath and N.D. Singpurwalla, A subjective bayesian approach to the theory of queues II-Inference and information inM/M/1 queues, Queueing Systems 1 (1987) 335.
M.F. Neuts and Y. Chandramouli, Statistical group testing with queueing involved, Queueing Systems 2 (1987) 19.
S.S. Rao, U.N. Bhat and K. Harischandra, Control of traffic intensity in a queue — A method based on SPRT, Opsearch 21 (1984) 63.
J.F. Reynolds, On estimating the parameters in some queueing models, Austral. J. Stat. 15 (1973) 35.
G. Rubin and D.S. Robson, A single server queue with random arrivals and balking confidence interval estimation, Queueing Systems 7 (1990) 283.
J.E. Samaan and D.S. Tracy, On the parameter estimation in queueing theory, P. Comp. Sci. St. 13 (1981) 324.
L. Schruben and R. Kulkarni, Some consequences of estimating parameters for theM/M/1 queue, Oper. Res. Lett. 1 (1982) 75.
D. Thiruvaiyaru and I.V. Basawa, Empirical Bayes estimation for queueing systems and networks, Queueing Systems 11 (1992) 179.
D. Thiruvaiyaru, I.V. Basawa and U.N. Bhat, Estimation for a class of simple queueing networks, Queueing Systems 9 (1991) 301.
R.W. Wolf, Problems of statistical inference for birth- and-death queueing models, Oper. Res. 13(1965)343.
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Armero, C. Bayesian inference in Markovian queues. Queueing Syst 15, 419–426 (1994). https://doi.org/10.1007/BF01189249
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DOI: https://doi.org/10.1007/BF01189249