Bayesian inference and prediction in single server M/M/1 queuing model based on queue length

References

• Almeida, M. A., and F. R. Cruz. 2017. A note on Bayesian estimation of traffic intensity in single-server Markovian queues. Communications in Statistics-Simulation and Computation 47 (9):2577–2586.
   Web of Science ®Google Scholar
• Armero, C., and M. Bayarri. 1994. Prior assessments for prediction in queues. The Statistician 43 (1):139–53. doi:10.2307/2348939.
   Google Scholar
• Basawa, I. V., and N. U. Prabhu. 1988. Large sample inference from single server queues. Queueing Systems 3 (4):289–304. doi:10.1007/BF01157852.
   Google Scholar
• Box, G. E. 1980. Sampling and Bayes’ inference in scientific modelling and robustness. Journal of the Royal Statistical Society. Series A (General) 143 (4):383–430. doi:10.2307/2982063.
   Web of Science ®Google Scholar
• Chen, M.-H., Q.-M. Shao, and J. G. Ibrahim. 2012. Monte Carlo methods in Bayesian computation. Berlin: Springer Science & Business Media.
   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. 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
• Chowdhury, S., and S. Mukherjee. 2013. Estimation of traffic intensity based on queue length in a single M/M/1 queue. Communications in Statistics-Theory and Methods 42 (13):2376–90. doi:10.1080/03610926.2011.609320.
   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. Quinino, and 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
• Johnson, N. L., A. W. Kemp, and S. Kotz. 2005. Univariate discrete distributions. volume 444. Hoboken, NJ: John Wiley & Sons.
   Google Scholar
• Kass, R. E., and A. E. Raftery. 1995. Bayes factors. Journal of the American Statistical Association 90 (430):773–95. doi:10.1080/01621459.1995.10476572.
   Web of Science ®Google Scholar
• Mcgrath, M. F., D. Gross, and N. D. Singpurwalla. 1987. A subjective Bayesian approach to the theory of queues I—modeling. Queueing Systems 1 (4):317–33. doi:10.1007/BF01150668.
   Google Scholar
• McGrath, M. F., and N. D. Singpurwalla. 1987. A subjective Bayesian approach to the theory of queues II—inference and information in M/M/1 queues. Queueing Systems 1 (4):335–53. doi:10.1007/BF01150669.
   Google Scholar
• Medhi, J. 2002. Stochastic models in queueing theory. Amsterdam: Academic Press.
   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
• Rohatgi, V. K., and A. M. E. Saleh. 2015. An introduction to probability and statistics. New York: John Wiley & Sons.
   Google Scholar
• Schruben, L., and R. Kulkarni. 1982. Some consequences of estimating parameters for the M/M/1 queue. Operations Research Letters 1 (2):75–8. doi:10.1016/0167-6377(82)90051-7.
   Google Scholar
• Srinivas, V., S. Subba Rao, and B. Kale. 2011. Estimation of measures in M/M/1 queue. Communications in Statistics-Theory and Methods 40 (18):3327–36. doi:10.1080/03610926.2010.498653.
   Web of Science ®Google Scholar
• Srinivas, V., and H. J. Udupa. 2014. Best unbiased estimation and can property in the stable M/M/1 queue. Communications in Statistics-Theory and Methods 43 (2):321–7. doi:10.1080/03610926.2012.661502.
   Web of Science ®Google Scholar
• Zheng, S., and A. F. Seila. 2000. Some well-behaved estimators for the M/M/1 queue. Operations Research Letters 26 (5):231–5. doi:10.1016/S0167-6377(00)00030-4.
   Web of Science ®Google Scholar