  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.
