In this paper, a nonparametric Bayesian analysis of queueing models
with geometric input and general service time is performed. In particular,
statistical inference for the probability generating function p.g.f. of the
equilibrium waiting time distribution is considered. The consistency of the
posterior distribution for such a p.g.f., as well as the weak convergence to a
Gaussian process of a suitable rescaling, are proved. As by-products, results
on statistical inference for queueing characteristics are also obtained.
Finally, the problem of estimating the probability of a long delay is
considered.