Abstract
Although the single-server Markovian queues are one of the simplest models in Queue Theory, they have important practical applications. One of the initial steps for its application includes the determination of the necessary sample sizes for an interval estimation of its parameters. This includes the traffic intensity, which is defined as the ratio between the arrival rate and the service rate. In this article, we develop Bayesian algorithms to determine the size of samples that must be collected to guarantee a pre-specified mean amplitude or mean coverage for the traffic intensity. These samples are composed of the number of arrivals during service times, a practical way to collect data. Monte Carlo simulations attest to the efficiency and effectiveness of the algorithms proposed.
Acknowledgments
We would like to thank the referees and the Editor-in-Chief for their detailed and insightful comments, which led to a much-improved manuscript.
Authors’ Contributions
ESG, FRBC, and SKS contributed equally to the design and implementation of the research, to the analysis of the results, and to the final writing of the manuscript.
Disclosure Statement
No potential conflict of interest was reported by the author(s).
Data Availability Statement
The data used to support the findings of this study are included in the article.
Code Availability Statement
The proposed algorithms can be encoded in the reader’s favorite programming language. The R scripts can be obtained from the authors upon request.