×

Frequentist inference on traffic intensity of \(M/M/1\) queuing system. (English) Zbl 1519.90056

MSC:

90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)

References:

[1] Almeida, M. A. C., and Cruz, F. R. B. A note on Bayesian estimation of traffic intensity in single-server Markovian queues. Communications in Statistics-Simulation and Computation 47, 9 (2018), 2577-2586. · Zbl 07550153
[2] Armero, C., and Bayarri, M. J. Bayesian prediction in M/M/1 queues. Queueing Systems 15, 1-4 (1994), 401-417. · Zbl 0789.60072
[3] Armero, C., and Bayarri, M. J. Prior assessments for prediction in queues. Journal of the Royal Statistical Society: Series D (The Statistician) 43, 1 (1994), 139-153.
[4] Armero, C., and Bayarri, M. J. Dealing with uncertainties in queues and networks of queues: A Bayesian approach. In Multivariate analysis, design of experiments, and survey sampling, S. Ghosh, Ed., CRC Press, 1999, pp. 603-632.
[5] Basak, A., and Choudhury, A. Bayesian inference and prediction in single server M/M/1 queuing model based on queue length. Communications in Statistics -Simulation and Computation 50, 6 (2021), 1576-1588. · Zbl 1497.62222
[6] Basawa, I. V., Lund, R., and Bhat, U. N. Estimating function methods of inference for queueing parameters. Lecture Notes-Monograph Series 32 (1997), 269-284. · Zbl 0905.62081
[7] Basawa, I. V., and Prabhu, N. U. Estimation in single server queues. Naval Research Logistics Quarterly 28, 3 (1981), 475-487. · Zbl 0468.60092
[8] Basawa, I. V., and Prabhu, N. U. Large sample inference from single server queues. Queueing Systems 3, 4 (1988), 289-304. · Zbl 0669.60086
[9] Bhat, U. U., and Rao, S. S. A statistical technique for the control of traffic intensity in the queuing systems M/G/1 and GI/M/1. Operations Research 20, 5 (1972), 955-966. · Zbl 0258.62060
[10] Brown, M., and Forsythe, A. Robust tests for the equality of variances. Journal of the American Statistical Association 69, 346 (1974), 364-367. · Zbl 0291.62063
[11] Choudhury, A., and Basak, A. Statistical inference on traffic intensity in an M/M/1 queueing system. International Journal of Management Science and Engineering Management 13, 4 (2018), 274-279.
[12] Choudhury, A., and Borthakur, A. C. Bayesian inference and prediction in the single server Markovian queue. Metrika 67, 3 (2008), 371-383. · Zbl 1433.90045
[13] Choudhury, A., and Medhi, P. Performance evaluation of a finite buffer system with varying rates of impatience.İstatistik -Journal of The Turkish Statistical Association 6, 1 (2013), 42-55. · Zbl 1420.60120
[14] Chowdhury, S., and Mukherjee, S. P. Estimation of waiting time distribution in an M/M/1 queue. Opsearch 48, 4 (2011), 306-317. · Zbl 1353.90037
[15] Chowdhury, S., and Mukherjee, S. P. Estimation of traffic intensity based on queue length in a single M/M/1 queue. Communications in Statistics -Theory and Methods 42, 13 (2013), 2376-2390. · Zbl 1284.60160
[16] Chowdhury, S., and Mukherjee, S. P. Bayes estimation in M/M/1 queues with bivariate prior. Journal of Statistics and Management Systems 19, 5 (2016), 681-699.
[17] Clarke, A. B. Maximum likelihood estimates in a simple queue. The Annals of Mathematical Statistics 28, 4 (1957), 1036-1040. · Zbl 0078.33602
[18] Cruz, F. R. B, Almeida, M. A. C., D’Angelo, M. F. S. V., and Woensel, T. Traffic intensity estimation in finite Markovian queueing systems. Mathematical Problems in Engineering 2018 (2018), 018758. · Zbl 1426.90067
[19] Cruz, F. R. B., Quinino, R. C., and Ho, L. L. 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 (2017), 7319-7331. · Zbl 1390.60322
[20] Dave, U., and Shah, Y. K. Maximum likelihood estimates in a M/M/2 queue with heterogeneous servers. Journal of the Operational Research Society 31, 5 (1980), 423-426. · Zbl 0447.62078
[21] Deepthi, V., and Jose, J. K. Bayesian estimation of an M/M/R queue with heterogeneous servers using Markov chain Monte Carlo method. Stochastics and Quality Control 35, 2 (2020), 57-66. · Zbl 1454.62245
[22] Deepthi, V., and Jose, J. K. Bayesian estimation of M/Ek/1 queueing model using bivariate prior. American Journal of Mathematical and Management Sciences 40, 1 (2021), 88-105.
[23] Dutta, K., and Choudhury, A. Estimation of performance measures of M/M/1 queues -a simulation-based approach. Inter-national Journal of Applied Management Science 12, 4 (2020), 265-279.
[24] Jose, J. K., and Manoharan, M. Bayesian estimation of rate parameters of queueing models. Journal of Probability and Statistical Science 12, 1 (2014), 69-76.
[25] Lilliefors, H. W. Some confidence intervals for queues. Operations Research 14, 4 (1966), 723-727.
[26] Medhi, P. Modelling customers’ impatience with discouraged arrival and retention of reneging. Operations Research and Decisions 31, 3 (2021), 67-88. · Zbl 1485.90024
[27] Ogbonna, C. J., Idochi, O., and Sylvia, I. O. Effect of sample sizes on the empirical power of some tests of homogeneity of variances. International Journal of Mathematics Trends and Technology 65, 6 (2019), 119-134.
[28] Rohatgi, V. K., and Ehsanes Saleh, A. K. Md. An introduction to probability and statistics, 3rd ed., John Wiley & Sons, 2015. · Zbl 1321.62003
[29] Rusticus, S. A., and Lovato, C. Y. Impact of sample size and variability on the power and type I error rates of equivalence tests: A simulation study. Practical Assessment, Research, and Evaluation 19, (2014), 11.
[30] Schruben, L., and Kulkarni, R. Some consequences of estimating parameters for the M/M/1 queue. Operations Research Letters 1, 2 (1982), 75-78. · Zbl 0492.60090
[31] Shortle, J. F., Thompson, J. M., Gross, D., and Harris, C. M. Fundamentals of qeueing theory, 5th ed., vol. 399, John Wiley & Sons, 2018. · Zbl 1387.60001
[32] Srinivas, V., and Kale, B. K. ML and UMVU estimation in the M/D/1 queuing system. Communications in Statistics -Theory and Methods 45, 19 (2016), 5826-5834. · Zbl 1348.60133
[33] Srinivas, V., Rao, S. S., and Kale, B. K. Estimation of measures in M/M/1 queue. Communications in Statistics -Theory and Methods 40, 18 (2011), 3327-3336. · Zbl 1225.62119
[34] Srinivas, V., and Udupa, H. J. Best unbiased estimation and can property in the stable M/M/1 queue. Communications in Statistics -Theory and Methods 43, 2 (2014), 321-327. · Zbl 06599052
[35] Suyama, E., Quinino, R. C., and Cruz, F. R. B. Simple and yet efficient estimators for Markovian multiserver queues. Mathematical Problems in Engineering 2018 (2018), 3280846. · Zbl 1427.90100
[36] Sztrik, J. Basic queueing theory: Foundations of system performance modeling. GlobeEdit, 2016.
[37] Taha, H. A. Simulation modeling and SIMNET. Prentice Hall international series in industrial and systems engineering. Prentice Hall, Englewood Cliffs, N.J, 1988.
[38] Zheng, S., and Seila, A. F. Some well-behaved estimators for the M/M/1 queue. Operations Research Letters 26, 5 (2000), 231-235. · Zbl 0973.90024
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.