On Bayesian estimation for an M/G/1 queue with optional second service

In this article, we exploit the Bayesian inference and prediction for an M/G/1 queueing system with optional second reservice. 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 reservice with probability "p" after taking the service. First, we approximate the service and reservice time densities with a class of Erlang mixture distributions. Then, given observations of the system, we propose a Bayesian procedure based on birth-death MCMC method to estimate some performance measures. Finally, we have applied the theories in practice by providing a numerical example based on the data which have been obtained from a hospital.