Title: Bayesian Nonparametric Inference for M/G/1 Queueing Systems,
Abstract: In this work, nonparametric statistical inference is provided for the
continuous-time M/G/1 queueing model from a Bayesian point of view. The
inference is based on observations of the inter-arrival and service times.
Beside other characteristics of the system, particular interest is in the
waiting time distribution which is not accessible in closed form. Thus, we use
an indirect statistical approach by exploiting the Pollaczek-Khinchine
transform formula for the Laplace transform of the waiting time distribution.
Due to this, an estimator is defined and its frequentist validation in terms of
posterior consistency and posterior normality is studied. It will turn out that
we can hereby make inference for the observables separately and compose the
results subsequently by suitable techniques.