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Nonparametric Estimation for Multi-server Queues Based on the Number of Clients in the System

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  • V. B. Quinino

    (Universidade Federal de Minas Gerais)

  • F. R. B. Cruz

    (Universidade Federal de Minas Gerais)

  • R. C. Quinino

    (Universidade Federal de Minas Gerais)

Abstract

In this article, we introduce a nonparametric (or distribution-free) estimator for traffic intensity in multi-server queues, which has not yet been discussed in the literature. Because this is a very useful model with many potential practical applications, it is the main focus of this study. We compare the performance of a new nonparametric estimator for situations in which the use of Markovian multi-server queues (M/M/s queues in Kendall notation) is adequate or in which it is necessary to consider multi-server queues with general arrival and general service times. We show that, when the parametric Markovian assumptions of M/M/s queues are satisfied, the new estimator is not superior to the maximum likelihood estimator based on the Markovian assumption with respect to M/M/s queues. However, for situations in which the interarrival time distribution and/or the service time distribution cannot be considered exponential (that is, non-Markovian), the new nonparametric estimator is superior. All evaluations are carried out using Monte Carlo simulations. A detailed numerical example is presented to show the usefulness of the technique for practical applications.

Suggested Citation

  • V. B. Quinino & F. R. B. Cruz & R. C. Quinino, 2024. "Nonparametric Estimation for Multi-server Queues Based on the Number of Clients in the System," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 494-529, February.
    • Handle: RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00331-9
    DOI: 10.1007/s13171-023-00331-9
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    References listed on IDEAS

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    1. Ger Koole & Avishai Mandelbaum, 2002. "Queueing Models of Call Centers: An Introduction," Annals of Operations Research, Springer, vol. 113(1), pages 41-59, July.
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    3. 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.
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    5. Singh, Saroja Kumar & Acharya, Sarat Kumar & Cruz, Frederico R.B. & Quinino, Roberto C., 2021. "Bayesian sample size determination in a single-server deterministic queueing system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 17-29.
    6. F. R. B. Cruz & M. A. C. Santos & F. L. P. Oliveira & R. C. Quinino, 2021. "Estimation in a general bulk-arrival Markovian multi-server finite queue," Operational Research, Springer, vol. 21(1), pages 73-89, March.
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