The Annals of Statistics

Large sample Bayesian analysis for ${\rm Geo}/G/1$ discrete-time queueing models

Pier Luigi Conti

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In this paper, a nonparametric Bayesian analysis of queueing models with geometric input and general service time is performed. In particular, statistical inference for the probability generating function p.g.f. of the equilibrium waiting time distribution is considered. The consistency of the posterior distribution for such a p.g.f., as well as the weak convergence to a Gaussian process of a suitable rescaling, are proved. As by-products, results on statistical inference for queueing characteristics are also obtained. Finally, the problem of estimating the probability of a long delay is considered.

Article information

Ann. Statist., Volume 27, Number 6 (1999), 1785-1807.

First available in Project Euclid: 4 April 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G15: Tolerance and confidence regions
Secondary: 62N99: None of the above, but in this section

Queues consistency asymptotics Bernstein-von Mises theorem teletraffic


Conti, Pier Luigi. Large sample Bayesian analysis for ${\rm Geo}/G/1$ discrete-time queueing models. Ann. Statist. 27 (1999), no. 6, 1785--1807. doi:10.1214/aos/1017939239.

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