Bayesian Estimation of an M/M/𝑅 Queue with Heterogeneous Servers Using Markov Chain Monte Carlo Method

Deepthi V. () and Jose Joby K. ()
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Deepthi V.: Department of Statistical Sciences, Kannur University, K.U. Campus, Mangattuparamba, Kannur, Kerala, India
Jose Joby K.: Department of Statistical Sciences, Kannur University, K.U. Campus, Mangattuparamba, Kannur, Kerala, India

Stochastics and Quality Control, 2020, vol. 35, issue 2, 57-66

Abstract: In this paper, we consider the Bayesian inference of M/M/𝑅 queue with 𝑅 heterogeneous servers with service rates μ1,μ2,…,μR\mu_{1},\mu_{2},\ldots,\mu_{R}, where μ1>μ2>⋯>μR\mu_{1}>\mu_{2}>\cdots>\mu_{R}. Assuming multivariate gamma prior distribution for service rates and gamma prior distribution for arrival rate 𝜆, we derive the conditional posterior densities of mean arrival rate and mean service rates. We apply the Markov chain Monte Carlo method and compute the Bayes estimates and credible interval for the M/M/3 queue, as a particular case of the M/M/𝑅 queue under squared error loss function, entropy loss function and linex loss function corresponding to a different set of hyperparameters.

Keywords: Multi-Server Queue; Bayes Estimates; Markov Chain Monte Carlo Method; Metropolis–Hastings Sampler; Gibbs Sampler (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1515/eqc-2020-0010

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