Bayesian analysis of single server Markovian queueing model with balking under asymmetric loss functions

References

• Abou-El-Ata, M., and A. Hariri. 1995. Point estimation and confidence intervals of the M/M/2/N queue with balking and heterogeneity. American Journal of Mathematical and Management Sciences 15 (1–2):35–55. doi:10.1080/01966324.1995.10737386.
   Google Scholar
• Almeida, M. A., and F. R. Cruz. 2018. A note on Bayesian estimation of traffic intensity in single-server Markovian queues. Communications in Statistics - Simulation and Computation 47 (9):2577–86. doi:10.1080/03610918.2017.1353614.
   Web of Science ®Google Scholar
• Almeida, M. A., F. R. Cruz, F. L. Oliveira, and G. de Souza. 2020. Bias correction for estimation of performance measures of a Markovian queue. Operational Research 20 (2):943–58. doi:10.1007/s12351-017-0351-4.
   Web of Science ®Google Scholar
• Armero, C., and M. Bayarri. 1994a. Prior assessments for prediction in queues. The Statistician 43 (1):139–53. doi:10.2307/2348939.
   Google Scholar
• Armero, C., and M. J. Bayarri. 1994b. Bayesian prediction in M/M/1 queues. Queueing Systems 15 (1–4):401–17. doi:10.1007/BF01189248.
   Google Scholar
• Basak, A., and A. Choudhury. 2019. Bayesian inference and prediction in single server M/M/1 queuing model based on queue length. Communications in Statistics - Simulation and Computation 50 (6):1576–88. doi:10.1080/03610918.2019.1586924.
   Google Scholar
• Basawa, I., and N. Prabhu. 1981. Estimation in single server queues. Naval Research Logistics Quarterly 28 (3):475–87. doi:10.1002/nav.3800280311.
   Google Scholar
• Calabria, R., and G. Pulcini. 1994. An engineering approach to Bayes estimation for the Weibull distribution. Microelectronics Reliability 34 (5):789–802. doi:10.1016/0026-2714(94)90004-3.
   Web of Science ®Google Scholar
• Chapman, D. G. 1956. Estimating the parameters of a truncated gamma distribution. The Annals of Mathematical Statistics 27 (2):498–506. doi:10.1214/aoms/1177728272.
   Google Scholar
• Choudhury, A., and A. Basak. 2018. Statistical inference on traffic intensity in an M/M/1 queueing system. International Journal of Management Science and Engineering Management 13 (4):1–6. doi:10.1080/17509653.2018.1436010.
   Web of Science ®Google Scholar
• Choudhury, A., and A. C. Borthakur. 2007. Statistical inference in M/M/1 Queues: A Bayesian Approach. American Journal of Mathematical and Management Sciences 27 (1–2):25–41. doi:10.1080/01966324.2007.10737686.
   Google Scholar
• Choudhury, A., and A. C. Borthakur. 2008. Bayesian inference and prediction in the single server Markovian queue. Metrika 67 (3):371–83. doi:10.1007/s00184-007-0138-3.
   Web of Science ®Google Scholar
• Clarke, A. B. 1957. Maximum likelihood estimates in a simple queue. The Annals of Mathematical Statistics 28 (4):1036–40. doi:10.1214/aoms/1177706808.
   Google Scholar
• Cruz, F. R., M. A. Almeida, M. F. D’Angelo, and T. van Woensel. 2018. Traffic intensity estimation in finite Markovian queueing systems. Mathematical Problems in Engineering 2018 (2):1–15. doi:10.1155/2018/3018758.
   Google Scholar
• Cruz, F. R., R. Quinino, and L. L. Ho. 2017. Bayesian estimation of traffic intensity based on queue length in a multi-server M/M/S queue. Communications in Statistics - Simulation and Computation 46 (9):7319–31. doi:10.1080/03610918.2016.1236953.
   Web of Science ®Google Scholar
• Dave, U., and Y. Shah. 1980. Maximum likelihood estimates in a M/M/2 queue with heterogeneous servers. Journal of the Operational Research Society 31 (5):423–6. doi:10.1057/jors.1980.75.
   Web of Science ®Google Scholar
• Deepthi, V., and S. P. Annie. 2022. Bayesian inference on M/M/1 queue using bivariate gamma prior. Journal of Applied Probability and Statistics 17 (2):49–68.
   Google Scholar
• Deepthi, V., and J. K. Jose. 2020a. Bayesian estimation of an M/M/R queue with heterogeneous servers using Markov Chain Monte Carlo Method. Stochastics and Quality Control 35 (2):57–66. doi:10.1515/eqc-2020-0010.
   Google Scholar
• Deepthi, V., and J. K. Jose. 2020b. Bayesian estimation of M/E k/1 queueing model using bivariate prior. American Journal of Mathematical and Management Sciences 40 (1):88–105. doi:10.1080/01966324.2020.1835589.
   Google Scholar
• Deepthi, V., and J. K. Jose. 2021. Bayesian inference on M/M/1 queue under asymmetric loss function using Markov Chain Monte Carlo method. Journal of Statistics and Management Systems 24 (5):1003–23. doi:10.1080/09720510.2020.1794529.
   Web of Science ®Google Scholar
• DeGroot, M. H. 1970. Optimal statistical decisions. Technical Report.
   Google Scholar
• Gross, D. 2008. Fundamentals of queueing theory. New Jersey: John Wiley & Sons.
   Google Scholar
• Harishchandra, K., and S. S. Rao. 1988. A note on statistical inference about the traffic intensity parameter in M/E K /1 queue. Sankhyā: The Indian Journal of Statistics, Series B 50 (1):144–8.
   Google Scholar
• Jabarali, A., and K. S. Kannan. 2016. Single server queueing model with Gumbel distribution using Bayesian approach. Hacettepe Journal of Mathematics and Statistics 45 (4):1275–96.
   Web of Science ®Google Scholar
• Jain, S., and J. Templeton. 1991. Confidence interval for M/M/2 queue with heterogeneous servers. Operations Research Letters 10 (2):99–101. doi:10.1016/0167-6377(91)90094-6.
   Web of Science ®Google Scholar
• Lilliefors, H. W. 1966. Letter to the editor-some confidence intervals for queues. Operations Research 14 (4):723–7. doi:10.1287/opre.14.4.723.
   Web of Science ®Google Scholar
• McGrath, M. F., and N. D. Singpurwalla. 1987. A subjective Bayesian approach to the theory of queues 2—inference and information in M/M/1 queues. Queueing Systems 1 (4):335–53. doi:10.1007/BF01150669.
   Google Scholar
• Mcgrath, M. F., D. Gross, and N. D. Singpurwalla. 1987. A subjective Bayesian approach to the theory of queues1—Modeling. Queueing Systems 1 (4):317–33. doi:10.1007/BF01150668.
   Google Scholar
• Muddapur, M. 1972. Bayesian estimates of parameters in some queueing models. Annals of the Institute of Statistical Mathematics 24 (1):327–31. doi:10.1007/BF02479762.
   Web of Science ®Google Scholar
• Mukherjee, S., and S. Chowdhury. 2005. Bayesian estimation of traffic intensity. IAPQR Transactions 30 (2):89.
   Google Scholar
• Mukherjee, S., and S. Chowdhury. 2010. Bayes estimation of measures of effectiveness in an M/M/1 queueing model. Calcutta Statistical Association Bulletin 62 (1–2):97–108. doi:10.1177/0008068320100107.
   Google Scholar
• Rizzo, M. L. 2019. Statistical computing with R. New York, USA: CRC Press.
   Google Scholar
• Shortle, J. F., J. M. Thompson, D. Gross, and C. M. Harris. 2018. Fundamentals of queueing theory, volume 399. New Jersey: John Wiley & Sons.
   Google Scholar
• Sohn, S. Y. 1996. Empirical Bayesian analysis for traffic intensity: M/M/1 queues with covariates. Queueing Systems 22 (3–4):383–401. doi:10.1007/BF01149180.
   Web of Science ®Google Scholar
• Wang, K.-H., S.-C. Chen, and J.-C. Ke. 2004. Maximum likelihood estimates and confidence intervals of an M/M/R/N queue with balking and heterogeneous servers. RAIRO - Operations Research 38 (3):227–41. doi:10.1051/ro:2004021.
   Web of Science ®Google Scholar
• Zeller, A. 1986. Bayesian estimation and prediction using asymmetric loss function. Journal of the American Statistical Association 81:446–51.
   Web of Science ®Google Scholar