Open Access
November 2018 The $M/G/\infty$ estimation problem revisited
Alexander Goldenshluger
Bernoulli 24(4A): 2531-2568 (November 2018). DOI: 10.3150/17-BEJ936


The subject of this paper is the $M/G/\infty$ estimation problem: the goal is to estimate the service time distribution $G$ of the $M/G/\infty$ queue from the arrival–departure observations without identification of customers. We develop estimators of $G$ and derive exact non-asymptotic expressions for their mean squared errors. The problem of estimating the service time expectation is addressed as well. We present some numerical results on comparison of different estimators of the service time distribution.


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Alexander Goldenshluger. "The $M/G/\infty$ estimation problem revisited." Bernoulli 24 (4A) 2531 - 2568, November 2018.


Received: 1 June 2016; Revised: 1 December 2016; Published: November 2018
First available in Project Euclid: 26 March 2018

zbMATH: 06853257
MathSciNet: MR3779694
Digital Object Identifier: 10.3150/17-BEJ936

Keywords: $M/G/\infty$ queue , nonparametric estimation , Poisson point process , rates of convergence

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 4A • November 2018
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