Nonparametric estimation of the service time distribution in the M/G/∞ queue

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The subject of this paper is the problem of estimating the service time distribution of the M/G/∞ queue from incomplete data on the queue. The goal is to estimate G from observations of the queue-length process at the points of the regular grid on a fixed time interval. We propose an estimator and analyze its accuracy over a family of target service time distributions. An upper bound on the maximal risk is derived. The problem of estimating the arrival rate is considered as well.

Original languageEnglish
Pages (from-to)1117-1138
Number of pages22
JournalAdvances in Applied Probability
Issue number4
StatePublished - 1 Dec 2016

Bibliographical note

Publisher Copyright:
© Copyright 2017 Applied Probability Trust.


  • M/G/∞ queue
  • covariance function
  • minimax risk
  • nonparametric estimation
  • rates of convergence
  • stationary process

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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