arXiv subjects

Cornelia Wichelhaus

Publications and source records attributed to Cornelia Wichelhaus.

3 recordsLinked to original sources

arXiv2017

Bayesian nonparametric inference for the M/G/1 queueing systems based on the marked departure process

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.

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arXiv2017

Bayesian Nonparametric Inference for M/G/1 Queueing Systems

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.

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arXiv2014

Nonparametric Estimation of the Service Time Distribution in the Discrete-Time $GI/G/\infty$ Queue with Partial Information

Estimation of the service time distribution in the discrete-time $GI/G/\infty$-queue based solely on information on the arrival and departure processes is considered. The focus is put on the estimation approach via the so called "sequence of differences". Existing results for this approach are substantially extended by proving a functional central limit theorem for the resultant estimator. Here, the underlying function space is taken to be the space of sequences converging to zero. The moving block bootstrap technique is considered for the estimation of the resultant covariance kernel and is shown to be applicable under mild additional conditions.

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