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

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

Alexander Goldenshluger

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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