On Bayesian inference for the M/G/1 queue with efficient MCMC sampling

We introduce an efficient MCMC sampling scheme to perform Bayesian inference in the M/G/1 queueing model given only observations of interdeparture times. Our MCMC scheme uses a combination of Gibbs sampling and simple Metropolis updates together with three novel shift and scale updates. We show that our novel updates improve the speed of sampling considerably, by factors of about 60 to about 180 on a variety of simulated data sets.