Bayesian Estimation of M/Ek/1 Queueing Model using Bivariate Prior

References

• Abou-El-Ata, M., O., & Hariri, A., M., A. (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. https://doi.org/10.1080/01966324.1995.10737386
   Google Scholar
• Armero, C., & Bayarri, M. J. (1994a). Bayesian prediction in M/M/1 queues. Queueing Systems, 15(1-4), 401–417. https://doi.org/10.1007/BF01189248
   Google Scholar
• Armero, C., & Bayarri, M. J. (1994b). Prior assessments for prediction in queues. The Statistician, 43(1), 139–153. https://doi.org/10.2307/2348939
   Google Scholar
• Armero, C., & Conesa, D. (1998). Inference and prediction in bulk arrival queues and queues with service in stages. Applied Stochastic Models and Data Analysis, 14(1), 35–46. https://doi.org/10.1002/(SICI)1099-0747(199803)14:1<35::AID-ASM305>3.0.CO;2-O
   Google Scholar
• Basawa, I. V., Bhat, U. N., & Lund, R. (1996). Maximum likelihood estimation for single server queues from waiting time data. Queueing Systems, 24(1-4), 155–167. https://doi.org/10.1007/BF01149084
   Web of Science ®Google Scholar
• Basawa, I. V., & Prabhu, N. U. (1988). Large sample inference from single server queues. Queueing Systems, 3(4), 289–304. https://doi.org/10.1007/BF01157852
   Google Scholar
• Calabria, R., & Pulcini, G. (1996). Point estimation under asymmetric loss function for left truncated exponential samples. Communications in Statistics - Theory and Methods, 25(3), 585–600. https://doi.org/10.1080/03610929608831715
   Web of Science ®Google Scholar
• Choudhury, A., & Basak, A. (2018). Statistical inference on traffic intensity in an M/M/1 queueing system. International Journal of Management Science and Engineering Management, 3, 1–6. https://doi.org/10.1080/17509653.2018.1436010
   Google Scholar
• Choudhury, C., & Borthakur, A. C. (2008). Bayesian inference and prediction in the single server Markovian queue. Metrika, 67(3), 371–383. https://doi.org/10.1007/s00184-007-0138-3
   Web of Science ®Google Scholar
• Chowdhury, S., & Maiti, S. (2014). Bayesian estimation of traffic intensity in an M/Er/1 queueing model. Research & Reviews: Journal of Statistics, Special Issue on Recent Statistical Methodologies and Applications, 1, 99–106.
   Google Scholar
• Chowdhury, S., & Mukherjee, S. P. (2016). Bayes estimation in M/M/1 queues with bivariate prior. Journal of Statistics and Management Systems, 19(5), 681–699. https://doi.org/10.1080/09720510.2015.1130905
   Web of Science ®Google Scholar
• Clarke, A. B. (1957). Maximum likelihood estimates in a simple queue. The Annals of Mathematical Statistics, 28(4), 1036–1040. https://doi.org/10.1214/aoms/1177706808
   Google Scholar
• Cruz, F. R. B., Quinino, R. C., & Ho, L. L. (2016). 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), 7319–7331.
   Web of Science ®Google Scholar
• David, R. I., Michael, W., & Fabrizio, R. (1998). Bayesian analysis of M/Er/1 and M/Hk/1 queues. Queuing Syst, 30, 289–308.
   Web of Science ®Google Scholar
• Ghahramani, M. H., Badamchi Zadeh, A., & Salehi Rad, M., R. (2019). Two M/M/1 queues with incongruent arrivals and services with random feedback. American Journal of Mathematical and Management Sciences, 38(4), 386–394. https://doi.org/10.1080/01966324.2019.1597794
   Google Scholar
• Gross, D., & Harris, P. (1998). Fundamentals of queueing theory. 3rd ed. Wiley.
   Google Scholar
• Jose, J. K., & Manoharan, M. (2014). Bayesian estimation of rate parameters of queueing models. Journal of Probability and Statistical Science, 12, 69–76.
   Google Scholar
• Jose, J., K., & Manoharan, M. (2018). Bayesian estimation of queue parameters by bivariate prior distributions with order restrictions. Journal of Indian Statistical Association, 56(1 & 2), 29–46.
   Google Scholar
• Jose, J. K., & Deepthi, V. (2020). Bayesian inference of Markovian queueing model with two heterogeneous servers. Stochastic Modelling and Applications, 24(1), 1–14.
   Google Scholar
• McGrath, M. F., Gross, D., & Singpurwalla, N. D. (1987). A subjective bayesian approach to the theory of queues I - modelling. Queueing Systems, 1(4), 317–333. https://doi.org/10.1007/BF01150668
   Google Scholar
• McGrath, M. F., & Singpurwalla, N. D. (1987). A subjective bayesian approach to the theory of queues II - inference and information in M/M/1 queues. Queueing Systems, 1(4), 335–353. https://doi.org/10.1007/BF01150669
   Google Scholar
• Metropolis, N., Rosenbluth, A., W., Rosenbluth, M., N., Teller, A., H., & Teller, E. (1953). Equations of state calculations by fast computing machine. The Journal of Chemical Physics, 21(6), 1087–1091. https://doi.org/10.1063/1.1699114
   Web of Science ®Google Scholar
• Mohammadi, A., & Salehi-Rad, M. R. (2012). Bayesian inference and prediction in an M/G/1 with optional second service. Communications in Statistics-Simulation and Computation, 41(3), 419–435.
   Google Scholar
• Mohammadi, A., Salehi-Rad, M. R., & Wit, E. C. (2013). Using mixtute of gamma distributions for Bayesian analysis in an M/G/1 queue with optional second service. Computational Statistics, 28, 683–700.
   Google Scholar
• Mukherjee, S. P., & Chowdhury, S. (2010). Bayes estimation of measures of effectiveness in an M/M/1 queueing model. Calcutta Statistical Association Bulletin, 62(1-2), 97–108. https://doi.org/10.1177/0008068320100107
   Google Scholar
• Prudnikov, A. P., Brychkov, Y. A., & Marichev, O. I. (1986). Integrals and series. Gordon and Breach Science Publishers.
   Google Scholar
• Wang, T.-Y., Ke, J.-C., Wang, K.-H., & Ho, S.-C. (2006). Maximum likelihood estimates and confidence intervals of an M/M/R queue with heterogeneous servers. Mathematical Methods of Operations Research, 63(2), 371–384. https://doi.org/10.1007/s00186-005-0047-z
   Web of Science ®Google Scholar
• Wiper, M., P. (1998). Bayesian analysis of Er/M/1 and Er/M/c queues. Journal of Statistical Planning and Inference, 69(1), 65–79.
   Web of Science ®Google Scholar