Bayesian estimation for the M/G/1 queue using a phase-type approximation

TL;DR: In this article, a semi-parametric approach based on Erlang mixture distributions is used to model the general inter-arrival time distribution and Bayesian Markov Chain Monte Carlo methods are used to estimate the system parameters and the predictive distributions of the usual performance measures.

TL;DR: In this paper, a broad literature survey of parameter and state estimation for queueing systems is presented, based on various inference activities, queueing models, observations schemes, and statistical methods.

TL;DR: In this paper, an improved expectation-maximization (EM) algorithm for phase-type (PH) distributions with grouped and truncated data was proposed, and the time complexity of the algorithm was reduced to the square of the number of phases.

TL;DR: In this paper, a flexible model based on mixtures of Erlang distributions is proposed to approximate the special features frequently observed in insurance claim sizes, such as long tails and heterogeneity, and a Bayesian density estimation approach for the claim sizes is implemented using reversible jump Markov chain Monte Carlo methods.

TL;DR: A generalization of the sampling method introduced by Metropolis et al. as mentioned in this paper is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates.

TL;DR: The Markov Chain Monte Carlo Implementation Results Summary and Discussion MEDICAL MONITORING Introduction Modelling Medical Monitoring Computing Posterior Distributions Forecasting Model Criticism Illustrative Application Discussion MCMC for NONLINEAR HIERARCHICAL MODELS.

TL;DR: In this article, the authors propose a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of differing dimensionality, which is flexible and entirely constructive.