Bayesian estimation for the M/G/1 queue using a phase-type approximation |
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| Institution: | 1. School of Risk and Actuarial Studies, UNSW Business School, University of New South Wales, Sydney, NSW 2052, Australia;2. Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA, USA;3. Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Canada |
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| Abstract: | This article deals with Bayesian inference and prediction for M/G/1 queueing systems. The general service time density is approximated with a class of Erlang mixtures which are phase-type distributions. Given this phase-type approximation, an explicit evaluation of measures such as the stationary queue size, waiting time and busy period distributions can be obtained. Given arrival and service data, a Bayesian procedure based on reversible jump Markov Chain Monte Carlo methods is proposed to estimate system parameters and predictive distributions. |
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