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Nonparametric inference for networks of queues

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Joint Statistics Seminar

Stochastic networks are systems of nodes which interact due to moving customers. Typical application fields are telecommunication systems, the internet as well as systems of neurons and population models. For applications statistical inference of the service time distributions based on incomplete observations of the systems is of great importance in order to classify the performance behavior. For example, a unimodal service time density shows a homogeneous service behavior whereas a bimodal density may indicate that there are two distinct customer populations or breakdowns of the server. In the statistical literature there are up to now only results for single node systems and moreover, for the most part the analysis is done in case of exponential distributed arrival times only. With this talk we try to close this gap and present two different approaches for a statistical analysis study of general open networks of queues. We assume that at each node we observe the external input process and the external departure process of customers. Our aim is to estimate the service time distributions at the nodes as well as the routing probabilities according to which customers move in the network. In the first approach the arrival processes are general point processes and the analysis is based on spectral analysis methods for multivariate point processes. We show consistency and asymptotic normality for our estimators. In the second approach we deal with Poisson processes as arrival processes and construct estimators for the service time distribution functions which converge uniformly. The talk is based on joint work with Susan Pitts and Michael Schmälzle.

This talk is part of the Optimization and Incentives Seminar series.

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