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Statistical inference for unreliable queueing systems

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Cornelia Wichelhaus, Technical University of Darmstadt

In practical applications of queueing systems there are typically processes or parameters which are unknown and cannot be observed. Thus, there is great interest in statistical inference for system characteristics depending on incomplete information of the stochastic components. Further, real service regimes are never completely reliable, the service is interrupted from time to time due to human or technical failures. In this talk we will present the statistical analysis for a queueing system with Poisson arrivals, a general service time distribution and parallel servers which are unreliable; the servers interrupt the service process from time to time and take a random repair period. Based only on observations of the arrival and departure epochs of the customers (without the possibility of their correct matching) we want to obtain information about the unknown repair time distributions and the breakdown rates of the servers. Explicit constructions of the estimators are presented as well as their analytic performance. Decompounding techniques for random sums play a major role in the proofs. By simulation results we illustrate the practicability of our analysis.