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Bias correction for estimation of performance measures of a Markovian queue

Author

Listed:
  • M. A. C. Almeida

    (Universidade Federal do Pará)

  • F. R. B. Cruz

    (Universidade Federal de Minas Gerais)

  • F. L. P. Oliveira

    (Universidade Federal de Ouro Preto)

  • G. Souza

    (Universidade Federal de Ouro Preto)

Abstract

There are several situations in our daily lives in which queues are present, such as cafeterias, supermarkets, banks, gas stations, and so forth. The performance of such queues can be described by several measures. In this article, the focus is on estimates of traffic intensity ($$\rho$$ρ), also called the utilization factor of the service station, the expected number of customers in the system (L), and the average queue size ($${L_{q}}$$Lq ) for infinite single-serve queues with Poisson arrivals and exponential (Markovian) service times. The computational experiments show that the maximum likelihood estimators (MLEs) of the performance measures are biased for small and moderate samples ($$n

Suggested Citation

  • M. A. C. Almeida & F. R. B. Cruz & F. L. P. Oliveira & G. Souza, 2020. "Bias correction for estimation of performance measures of a Markovian queue," Operational Research, Springer, vol. 20(2), pages 943-958, June.
    • Handle: RePEc:spr:operea:v:20:y:2020:i:2:d:10.1007_s12351-017-0351-4
    DOI: 10.1007/s12351-017-0351-4
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    References listed on IDEAS

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    1. Armero, Carmen & Conesa, David, 2004. "Statistical performance of a multiclass bulk production queueing system," European Journal of Operational Research, Elsevier, vol. 158(3), pages 649-661, November.
    2. John D. C. Little, 1961. "A Proof for the Queuing Formula: L = (lambda) W," Operations Research, INFORMS, vol. 9(3), pages 383-387, June.
    3. Jau-Chuan Ke & Yunn-Kuang Chu, 2009. "Comparison on five estimation approaches of intensity for a queueing system with short run," Computational Statistics, Springer, vol. 24(4), pages 567-582, December.
    4. C. Armero & D. Conesa, 1998. "Inference and prediction in bulk arrival queues and queues with service in stages," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 14(1), pages 35-46, March.
    5. Laoucine Kerbache & G. M. Gontijo & G. S. Atuncar & F.R.B. Cruz, 2011. "Performance Evaluation and Dimensioning of GIX/M/c/N Systems Through Kernel Estimation," Post-Print hal-00796342, HAL.
    6. Amit Choudhury & Arun Borthakur, 2008. "Bayesian inference and prediction in the single server Markovian queue," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 371-383, April.
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    Cited by:

    1. Arpita Basak & Amit Choudhury, 2024. "Bayesian estimation of finite buffer size in single server Markovian queuing system," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(6), pages 2366-2373, June.
    2. Singh, Saroja Kumar & Acharya, Sarat Kumar & Cruz, F.R.B. & Cançado, André L.F., 2023. "Change point estimation in an M/M/2 queue with heterogeneous servers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 182-194.

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