The M/G/∞ estimation problem revisited

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Abstract

The subject of this paper is the M/G/∞ estimation problem: the goal is to estimate the service time distribution G of the M/G/∞ 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.

Original languageEnglish
Pages (from-to)2429-2460
Number of pages32
JournalBernoulli
Volume24
Issue number4A
DOIs
StatePublished - Nov 2018

Bibliographical note

Funding Information:
The research was supported by the grants BSF 2010466 and ISF 361/15. The author is grateful to Rui Castro for useful discussions and valuable remarks.

Publisher Copyright:
© 2018 ISI/BS.

Keywords

  • M/G/∞ queue
  • Nonparametric estimation
  • Poisson point process
  • Rates of convergence

ASJC Scopus subject areas

  • Statistics and Probability

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