Bernoulli

  • Bernoulli
  • Volume 24, Number 4A (2018), 2531-2568.

The $M/G/\infty$ estimation problem revisited

Alexander Goldenshluger

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Abstract

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.

Article information

Source
Bernoulli, Volume 24, Number 4A (2018), 2531-2568.

Dates
Received: June 2016
Revised: December 2016
First available in Project Euclid: 26 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.bj/1522051217

Digital Object Identifier
doi:10.3150/17-BEJ936

Mathematical Reviews number (MathSciNet)
MR3779694

Zentralblatt MATH identifier
06853257

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

Citation

Goldenshluger, Alexander. The $M/G/\infty$ estimation problem revisited. Bernoulli 24 (2018), no. 4A, 2531--2568. doi:10.3150/17-BEJ936. https://projecteuclid.org/euclid.bj/1522051217


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