Title: Bayesian nonparametric inference for the M/G/1 queueing systems based on the marked departure process,
Abstract: In the present work we study Bayesian nonparametric inference for the
continuous-time M/G/1 queueing system. In the focus of the study is the
unobservable service time distribution. We assume that the only available data
of the system are the marked departure process of customers with the marks
being the queue lengths just after departure instants. These marks constitute
an embedded Markov chain whose distribution may be parametrized by stochastic
matrices of a special delta form. We develop the theory in order to obtain
integral mixtures of Markov measures with respect to suitable prior
distributions. We have found a sufficient statistic with a distribution of a
so-called S-structure sheding some new light on the inner statistical structure
of the M/G/1 queue. Moreover, it allows to update suitable prior distributions
to the posterior. Our inference methods are validated by large sample results
as posterior consistency and posterior normality.