Algorithms for Determination of Sample Sizes for Bayesian Estimations in Single-Server Markovian Queues

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.

Keywords:

• Bayesian inference
• credible region
• Markovian queues
• sample size

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.

Additional information

Funding

ESG acknowledges CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nìvel Superior, grant 88887.823719/2023-00 under Programa de Demanda Social at UFMG). FRBC acknowledges FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais, grant CEX-PPM-00564-17) and CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico, grant 305442/2022-8) for partial financial support. SKS acknowledges OSHEC (Odisha State Higher Education Council) for financial support under OURIIP Seed Fund, Govt. of Odisha, India with reference no. 22SF/ST/116 (Sanction Order Number 174/144/OSHEC).