Nonparametric estimation of the stationary waiting time distribution function for the $$GI/G/1$$ queue.(English)Zbl 0824.60095

The stochastic model in question is regarded as a functional that relates a quantity of interest, here the waiting time distribution in a (the) standard queueing model, to certain input distributions for which natural estimators exist. The statistical properties of these estimators, such as consistency, asymptotic normality, efficiency and functioning of the bootstrap, are well understood, and it is shown here that these properties carry over to the natural estimator for the quantity of interest that results if the functional is applied to the input estimators. In order to make this work certain local analytic properties of the functional are established, notably continuity and differentiability with respect to a suitable norm. The paper combines probabilistic, analytical and statistical ideas and techniques.

MSC:

 60K25 Queueing theory (aspects of probability theory) 62G05 Nonparametric estimation
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