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	Advances in Applied Probability
Volume	48
Issue number	4
DOIs	https://doi.org/10.1017/apr.2016.67
State	Published - 1 Dec 2016

Bibliographical note

Publisher Copyright:
© Copyright 2017 Applied Probability Trust.

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Applied Mathematics

Access to Document

10.1017/apr.2016.67

Cite this

@article{4bdaf758d39a4ba59661c10b90533930,

title = "Nonparametric estimation of the service time distribution in the M/G/∞ queue",

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.",

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

author = "Alexander Goldenshluger",

year = "2016",

month = dec,

day = "1",

doi = "10.1017/apr.2016.67",

language = "English",

volume = "48",

pages = "1117--1138",

journal = "Advances in Applied Probability",

issn = "0001-8678",

publisher = "Cambridge University Press",

number = "4",

}

TY - JOUR

T1 - Nonparametric estimation of the service time distribution in the M/G/∞ queue

AU - Goldenshluger, Alexander

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

AB - 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.

KW - M/G/∞ queue

KW - covariance function

KW - minimax risk

KW - nonparametric estimation

KW - rates of convergence

KW - stationary process

UR - http://www.scopus.com/inward/record.url?scp=85009231892&partnerID=8YFLogxK

U2 - 10.1017/apr.2016.67

DO - 10.1017/apr.2016.67

M3 - Article

AN - SCOPUS:85009231892

SN - 0001-8678

VL - 48

SP - 1117

EP - 1138

JO - Advances in Applied Probability

JF - Advances in Applied Probability

IS - 4

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this