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]
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Database:	Engineering Source

Description
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]
ISSN:	19322321
DOI:	10.24412/1932-2321-2026-190-309-323