Portal de Periódicos da CAPES

Artigo Produção Nacional Revisado por pares

BIBTEX RIS

Classical and Bayesian estimations of performance measures in a single server Markovian queueing system based on arrivals during service times

2023; Taylor & Francis; Volume: 53; Issue: 10 Linguagem: Inglês

10.1080/03610926.2022.2155789

1532-415X

Saroja Kumar Singh, F.R.B. Cruz, Eriky S. Gomes, A. D. Banik,

Transportation Planning and Optimization

AbstractAbstractThe present study considers a single-server Markovian queueing system by observing the number of customer arrivals during the service time of a customer. We estimate the traffic intensity in this queueing system along with the average queue length and the expected number of customers in the system. We propose classical and Bayesian frameworks to estimate the parameters of interest. In the Bayesian setup, three forms of prior distributions for ρ and two loss functions are considered. Furthermore, the predictive distribution of the number of customer arrivals during the service time of a customer and the equal-tailed credible region of ρ are obtained. The aforementioned approaches are illustrated with numerical examples based on simulation studies.Keywords: QueueingM/M/1 queuemaximum likelihood estimationBayesian estimationpredictive distributioncredible intervalMATHEMATICS SUBJECT CLASSIFICATION (2010): 60K2568M2090B22 AcknowledgmentsWe would like to thank Mr. Gabriel Mariz for his insightful comments on an earlier version of this manuscript and the Editor in Chief and the two referees for their detailed and insightful comments, which has resulted in this improved and revised manuscript. FRBC dedicates this study to the memory of Prof. Borges, always an encourager.Authors' contributionsAll authors, SKS, FRBC, ESG, and ADB contributed equally toward the design and implementation of the research, analysis of the results, and the final draft of the manuscript.Availability of data and materialsThe data used to support the findings of this study are included within the article.Code availabilityThe proposed algorithms can be encoded in the reader's favorite programming language. The R scripts can be obtained from the authors upon request.Conflicts of interest/competing interestsThe founder had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The authors declare that there are no conflicts of interest regarding the publication of this article.Additional informationFundingFRBC 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 305515/2018-7) for partial financial support. ADB was supported partially by DST, New Delhi, India, under research grant file number MTR/2021/000287.