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September, 1994 Nonparametric Estimation of the Stationary Waiting Time Distribution Function for the $GI/G/1$ Queue
Susan M. Pitts
Ann. Statist. 22(3): 1428-1446 (September, 1994). DOI: 10.1214/aos/1176325635

Abstract

The $GI/G/1$ queueing model is regarded as a functional that maps the service and interarrival time distribution functions onto the stationary waiting time distribution function. By considering the output of the functional when it is applied to nonparametric estimators of the input distribution functions, we obtain a nonparametric estimator of the stationary waiting time distribution function. Using appropriate continuity and differentiability properties of the functional, we show that statistical properties of the input estimators carry over to corresponding properties for the stationary waiting time distribution function estimator.

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Susan M. Pitts. "Nonparametric Estimation of the Stationary Waiting Time Distribution Function for the $GI/G/1$ Queue." Ann. Statist. 22 (3) 1428 - 1446, September, 1994. https://doi.org/10.1214/aos/1176325635

Information

Published: September, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0824.60095
MathSciNet: MR1311982
Digital Object Identifier: 10.1214/aos/1176325635

Subjects:
Primary: 60K25
Secondary: 62G05

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 3 • September, 1994
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