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

• Published in: Sankhya. Series. A Vol. 86; no. 1; pp. 494 - 529
• Main Authors: Quinino, V. B., Cruz, F. R. B., Quinino, R. C.
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.02.2024
• Subjects: Mathematics and Statistics; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; 90B22; Multi-server queues; Markovian queues; Traffic intensity; Maximum likelihood estimators; Bootstrap; General queues; Nonparametric estimator; 68M20; 60K25
• ISSN: 0976-836X; 0976-8378
• DOI: 10.1007/s13171-023-00331-9

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.