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CLASSICAL AND BAYESIAN INFERENCE ON GEO/DPH/1 QUEUEING MODEL WITH DISCRETE PHASE-TYPE VACATION TIME.

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Title: CLASSICAL AND BAYESIAN INFERENCE ON GEO/DPH/1 QUEUEING MODEL WITH DISCRETE PHASE-TYPE VACATION TIME.
Authors: Salima, P.1 salimapacheeri@gmail.com, Manoharan, M.1 manumavila@gmail.com, Jose, Joby K.2 jobyk@kannuruniv.ac.in
Source: Reliability: Theory & Applications. Mar2026, Vol. 21 Issue 1, p309-323. 15p.
Subjects: Queuing theory, Expectation-maximization algorithms, Maximum likelihood statistics, Gibbs sampling, Bayesian analysis, Markov chain Monte Carlo
Abstract: This paper focuses on inference methods for the Geo/DPH/1 queueing model with phase-type vacation times. In this model, interarrival times follow a geometric distribution, while service and vacation times are represented using discrete phase-type distributions, allowing for flexible modeling of complex stochastic behaviors. Classical inference is addressed through Maximum Likelihood Estimation, with parameters estimated using the Expectation-Maximization algorithm, and key performance measures, including traffic intensity, the expected number of customers, waiting times, and busy periods, are evaluated. Building on this, a Bayesian framework is developed by specifying suitable prior distributions for all model parameters and obtaining posterior distributions via Markov Chain Monte Carlo methods, specifically using the Gibbs sampling algorithm. Bayesian estimates are computed under the squared error loss function, demonstrating the effectiveness of the approach in capturing system dynamics. Numerical illustrations are provided through two simulated examples, highlighting the practical applicability and robustness of the proposed methodologies. [ABSTRACT FROM AUTHOR]
Copyright of Reliability: Theory & Applications is the property of International Group on Reliability and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: CLASSICAL AND BAYESIAN INFERENCE ON GEO/DPH/1 QUEUEING MODEL WITH DISCRETE PHASE-TYPE VACATION TIME.
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  Data: <searchLink fieldCode="AR" term="%22Salima%2C+P%2E%22">Salima, P.</searchLink><relatesTo>1</relatesTo><i> salimapacheeri@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Manoharan%2C+M%2E%22">Manoharan, M.</searchLink><relatesTo>1</relatesTo><i> manumavila@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Jose%2C+Joby+K%2E%22">Jose, Joby K.</searchLink><relatesTo>2</relatesTo><i> jobyk@kannuruniv.ac.in</i>
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  Data: <searchLink fieldCode="JN" term="%22Reliability%3A+Theory+%26+Applications%22">Reliability: Theory & Applications</searchLink>. Mar2026, Vol. 21 Issue 1, p309-323. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Queuing+theory%22">Queuing theory</searchLink><br /><searchLink fieldCode="DE" term="%22Expectation-maximization+algorithms%22">Expectation-maximization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Maximum+likelihood+statistics%22">Maximum likelihood statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Gibbs+sampling%22">Gibbs sampling</searchLink><br /><searchLink fieldCode="DE" term="%22Bayesian+analysis%22">Bayesian analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Markov+chain+Monte+Carlo%22">Markov chain Monte Carlo</searchLink>
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  Data: This paper focuses on inference methods for the Geo/DPH/1 queueing model with phase-type vacation times. In this model, interarrival times follow a geometric distribution, while service and vacation times are represented using discrete phase-type distributions, allowing for flexible modeling of complex stochastic behaviors. Classical inference is addressed through Maximum Likelihood Estimation, with parameters estimated using the Expectation-Maximization algorithm, and key performance measures, including traffic intensity, the expected number of customers, waiting times, and busy periods, are evaluated. Building on this, a Bayesian framework is developed by specifying suitable prior distributions for all model parameters and obtaining posterior distributions via Markov Chain Monte Carlo methods, specifically using the Gibbs sampling algorithm. Bayesian estimates are computed under the squared error loss function, demonstrating the effectiveness of the approach in capturing system dynamics. Numerical illustrations are provided through two simulated examples, highlighting the practical applicability and robustness of the proposed methodologies. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Reliability: Theory & Applications is the property of International Group on Reliability and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.24412/1932-2321-2026-190-309-323
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        Text: English
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        Type: general
      – SubjectFull: Expectation-maximization algorithms
        Type: general
      – SubjectFull: Maximum likelihood statistics
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      – SubjectFull: Gibbs sampling
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      – SubjectFull: Bayesian analysis
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      – SubjectFull: Markov chain Monte Carlo
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      – TitleFull: CLASSICAL AND BAYESIAN INFERENCE ON GEO/DPH/1 QUEUEING MODEL WITH DISCRETE PHASE-TYPE VACATION TIME.
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              Text: Mar2026
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