Bayesian Inference and Prediction in an M/G/1 with Optional Second Service

Abstract

In this article, we exploit the Bayesian inference and prediction for an M/G/1 queuing model with optional second re-service. In this model, a service unit attends customers arriving following a Poisson process and demanding service according to a general distribution and some of customers need to re-service with probability “p”. First, we introduce a mixture of truncated Normal distributions on interval (− ∞, 0) to approximate the service and re-service time densities. Then, given observations of the system, we propose a Bayesian procedure based on birth-death MCMC methodology to estimate some performance measures. Finally, we apply the theories in practice by providing a numerical example based on real data which have been obtained from a hospital.

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