Bayesian inference in Markovian queues

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.

[1]  J. Berger Statistical Decision Theory and Bayesian Analysis , 1988 .

[2]  U. Narayan Bhat A SEQUENTIAL TECHNIQUE FOR THE CONTROL OF TRAFFIC INTENSITY IN MARKOVIAN QUEUES , 1987 .

[3]  Hubert W. Lilliefors Letter to the Editor - Some Confidence Intervals for Queues , 1966, Oper. Res..

[4]  Dennis J. Aigner Technical Note - Parameter Estimation from Cross-Sectional Observations on an Elementary Queuing System , 1974, Oper. Res..

[5]  V. E. Benes A sufficient set of statistics for a simple telephone exchange model , 1957 .

[6]  Nozer D. Singpurwalla,et al.  A subjective Bayesian approach to the theory of queues II — Inference and information in M/M/1 queues , 1986, Queueing Syst. Theory Appl..

[7]  Ronald W. Wolff,et al.  Problems of Statistical Inference for Birth and Death Queuing Models , 1965 .

[8]  Nozer D. Singpurwalla,et al.  A subjective Bayesian approach to the theory of queues I — Modeling , 1987, Queueing Syst. Theory Appl..

[9]  Lee W. Schruben,et al.  Some consequences of estimating parameters for the M/M/1 queue , 1982, Oper. Res. Lett..

[10]  J. Reynolds,et al.  ON ESTIMATING THE PARAMETERS OF A BIRTH-DEATH PROCESS , 1973 .

[11]  D. S. Robson,et al.  A single server queue with random arrivals and balking: Confidence interval estimation , 1990, Queueing Syst. Theory Appl..

[12]  D. Kendall Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain , 1953 .

[13]  Ishwar V. Basawa,et al.  Introduction : Frequentist , Bayes and empirical Bayes approaches , 2005 .

[14]  Donald P. Gaver,et al.  On inference concerning time-dependent queue performance: The M/G/1 example , 1990, Queueing Syst. Theory Appl..

[15]  N. U. Prabhu,et al.  Large sample inference from single server queues , 1988, Queueing Syst. Theory Appl..

[16]  N. U. Prabhu,et al.  Estimation in single server queues , 1981 .

[17]  U. N. Bhat,et al.  9. Queues, storage and inventories : Control of traffic intensity in a queue—A method based on SPRT , 1984 .

[18]  Ishwar V. Basawa Statistical inference for stochastic processes , 1980 .

[19]  U. Narayan Bhat,et al.  Estimation for a class of simple queueing networks , 1991, Queueing Syst. Theory Appl..

[20]  Richard E. Barlow,et al.  Statistical Analysis of Reliability and Life Testing Models , 1975 .

[21]  U. Narayan Bhat,et al.  A Statistical Technique for the Control of Traffic Intensity in the Queuing Systems M/G/1 and GI/M/1 , 1972, Oper. Res..

[22]  M. J. Bayarri,et al.  Prior Assessments for Prediction in Queues , 1994 .

[23]  M. J. Bayarri,et al.  Bayesian prediction inM/M/1 queues , 1994, Queueing Syst. Theory Appl..

[24]  M. Degroot Optimal Statistical Decisions , 1970 .

[25]  A. Clarke Maximum Likelihood Estimates in a Simple Queue , 1957 .

[26]  Derrick S. Tracy,et al.  On the Parameter Estimation in Queueing Theory , 1981 .

[27]  F. Downton,et al.  Statistical analysis of reliability and life-testing models : theory and methods , 1992 .

[28]  Marcel F. Neuts,et al.  Statistical group testing with queueing involved , 1987, Queueing Syst. Theory Appl..

[29]  N. Keiding Maximum likelihood estimation in the birth-and-death process , 1974, Advances in Applied Probability.

[30]  U. Narayan Bhat,et al.  Statistical analysis of queueing systems , 1998, Queueing Syst. Theory Appl..