Abstract
For operating any new finite capacity (say K) queuing system in which customers arrive according to a Poisson process and are served by a single server under exponential service time (in Kendall’s notation M/M/1/K system), the assumption of fixing K and estimating the parameter traffic intensity \(\rho\), is quite practical. But in situation of any pre-existing M/M/1/K queuing system, it is essential to determine an estimator of K to increase system efficiency for fixed value of \(\rho\). This paper therefore considered the problem of estimating the parameter finite buffer (K). A Bayes estimator of K is proposed and compared it with classical estimator based on maximum likelihood principal, under the assumption that \(\rho\) is known. A simulation study is carried out to establish the efficacy and effectiveness of the proposed approaches. A real life situation is analyzed to illustrate the applicability of the developed algorithms.
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References
Aksoy HK, Gupta SM (2010) Near optimal buffer allocation in remanufacturing systems with N-policy. Comput Ind Eng 59(4):496–508
Almeida MA, Cruz FR (2018) A note on Bayesian estimation of traffic intensity in single-server Markovian queues. Commun Stat-Simul Comput 47(9):2577–2586
Almeida MA, Cruz FR, Oliveira FL, de Souza G (2020) Bias correction for estimation of performance measures of a Markovian queue. Oper Res Int J 20(2):943–958
Amjath M, Kerbache L, Smith JM, Elomri A (2023) Optimisation of buffer allocations in manufacturing systems: a study on intra and outbound logistics systems using finite queueing networks. Appl Sci 13(17):9525
Armero C, Bayarri MJ (1994) Prior assessments for prediction in queues. J R Stat Soc Ser D Statistician 43(1):139–153
Armero C, Bayarri M (1997) A bayesian analysis of a queueing system with unlimited service. J Stat Plann Inference 58(2):241–261
Armero C, Bayarri M (1999) Dealing with uncertainties in queues and networks of queues: a Bayesian approach. Multivariate analysis, design of experiments, and survey sampling. CRC Press, Boca Raton, pp 603–632
Armero C, Bayarri MJ (1994) Bayesian prediction in m/m/1 queues. Queue Syst 15(1):401–417
Armero C, Conesa D (1998) Inference and prediction in bulk arrival queues and queues with service in stages. Appl Stochast Models Data Anal 14(1):35–46
Armero C, Conesa D (2000) Prediction in markovian bulk arrival queues. Queue Syst 34(1):327–350
Armero C, Conesa D (2006) Bayesian hierarchical models in manufacturing bulk service queues. J Stat Plan Inference 136(2):335–354
Basak A, Choudhury A (2021) Bayesian inference and prediction in single server m/m/1 queuing model based on queue length. Commun Stat Simul Comput 50(6):1576–1588
Basak A, Choudhury A (2023) Classical and Bayesian inference on traffic intensity of multiserver Markovian queuing system. Commun Stat Simul Comput 52(5):2044–2057
Basawa IV, Prabhu NU (1988) Large sample inference from single server queues. Queue Syst 3(4):289–304
Chan SC, Chan KM, Liu K, Lee JY (2013) On queue length and link buffer size estimation in 3G/4G mobile data networks. IEEE Trans Mob Comput 13(6):1298–1311
Choudhury A, Basak A (2018) Statistical inference on traffic intensity in an m/m/1 queueing system. Int J Manag Sci Eng Manag 13(4):274–279
Choudhury A, Borthakur AC (2008) Bayesian inference and pre- diction in the single server markovian queue. Metrika 67(3):371–383
Chowdhury S, Mukherjee S (2013) Estimation of traffic intensity based on queue length in a single m/m/1 queue. Commun Stat Theory Methods 42(13):2376–2390
Su C, Xu A (2014) Buffer allocation for hybrid manufacturing/remanufacturing system considering quality grading. Int J Prod Res 52(5):1269–1284
Clarke AB (1957) Maximum likelihood estimates in a simple queue. Ann Math Stat 28(4):1036–1040
Cruz FR, Almeida MA, D’Angelo MF, van Woensel T (2018) Traffic intensity estimation in finite markovian queueing systems. Math Probl Eng
Cruz FR, Quinino R, Ho LL (2017) Bayesian estimation of traffic intensity based on queue length in a multi-server m/m/s queue. Commun Stat Simul Comput 46(9):7319–7331
Mcgrath MF, Gross D, Singpurwalla ND (1987) A subjective bayesian approach to the theory of queues I-modeling. Queue Syst 1(4):317–333
McGrath MF, Singpurwalla ND (1987) A subjective bayesian approach to the theory of queues II-inference and information in M/M/1 queues. Queue Syst 1(4):335–353
Medhi J (2002) Stochastic models in queueing theory. Academic Press
Muddapur M (1972) Bayesian estimates of parameters in some queueing models. Ann Inst Stat Math 24(1):327–331
Rohatgi VK (2013) Statistical inference. Courier Corporation
Shi C, Gershwin SB (2009) An efficient buffer design algorithm for production line profit maximization. Int J Prod Econ 122(2):725–740
Singh SK, Acharya SK, Cruz FR, Quinino RC (2021) Estimation of traffic intensity from queue length data in a deterministic single server queueing system. J Comput Appl Math 398:113693
Singh SK, Acharya SK, Cruz FR, Quinino RC (2022) Bayesian inference and prediction in an M/D/1 queueing system. Commun Stat Theory Methods
Singh SK (2022) Change point problem for Markovian arrival queueing models: Bayes factor approach. Int J Syst Assur Eng Manag 13(6):2847–2854
Srinivas V, Subba Rao S, Kale B (2011) Estimation of measures in M/M/1 queue. Commun Stat Theory Methods 40(18):3327–3336
Srinivas V, Udupa HJ (2014) Best unbiased estimation and can property in the stable M/M/1 queue. Commun Stat Theory Methods 43(2):321–327
Suyama E, Quinino RC, Cruz FR (2018) Simple and yet efficient estimators for markovian multiserver queues. Math Probl Eng 2018:1–7
Zheng S, Seila AF (2000) Some well-behaved estimators for the M/M/1 queue. Oper Res Lett 26(5):231–235
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Basak, A., Choudhury, A. Bayesian estimation of finite buffer size in single server Markovian queuing system. Int J Syst Assur Eng Manag (2024). https://doi.org/10.1007/s13198-024-02250-w
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DOI: https://doi.org/10.1007/s13198-024-02250-w