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

V. B. Quinino (), F. R. B. Cruz () and R. C. Quinino ()
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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

Sankhya A: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 15, 494-529

Abstract: 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.

Keywords: Multi-server queues; Markovian queues; General queues; Traffic intensity; Maximum likelihood estimators; Nonparametric estimator; Bootstrap; 60K25; 68M20; 90B22 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13171-023-00331-9

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