NONPARAMETRIC ESTIMATION OF THE SERVICE TIME DISTRIBUTION IN THE M/G/∞ QUEUE

Alexander Goldenshluger

doi:10.1017/apr.2016.67

NONPARAMETRIC ESTIMATION OF THE SERVICE TIME DISTRIBUTION IN THE M/G/∞ QUEUE

Alexander Goldenshluger

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	1117-1138
Number of pages	22
Journal	Annals of Applied Probability
Volume	48
Issue number	4
DOIs	https://doi.org/10.1017/apr.2016.67
State	Published - 2025

Bibliographical note

Publisher Copyright:
© Applied Probability Trust 2017.

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1017/apr.2016.67

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abstract = "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.",

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KW - covariance function

KW - minimax risk

KW - nonparametric estimation

KW - rates of convergence

KW - stationary process

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ER -

NONPARAMETRIC ESTIMATION OF THE SERVICE TIME DISTRIBUTION IN THE M/G/∞ QUEUE

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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