## The Annals of Statistics

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

Pier Luigi Conti

#### Abstract

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

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

Dates
First available in Project Euclid: 4 April 2002

https://projecteuclid.org/euclid.aos/1017939239

Digital Object Identifier
doi:10.1214/aos/1017939239

Mathematical Reviews number (MathSciNet)
MR1765617

Zentralblatt MATH identifier
0963.62092

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

#### Citation

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. https://projecteuclid.org/euclid.aos/1017939239

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• VIA DELLE BELLE ARTI, 41 BOLOGNA 40126 ITALY E-MAIL: conti@stat.unibo.it