Adaptive minimax estimation of service time distribution in the Mt/G/∞ queue from departure data

Wenwen Li; Alexander Goldenshluger

doi:10.1007/s11134-024-09921-2

Adaptive minimax estimation of service time distribution in the Mt/G/∞ queue from departure data

Wenwen Li, Alexander Goldenshluger

Department of Statistics

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

Abstract

This article deals with the problem of estimating the service time distribution of the M_t/G/∞ queue from observation of the departure epochs. We develop minimax optimal estimators of G and study behavior of the minimax pointwise risk over a suitable family of service time distribution functions. In addition, we address the problem of adaptive estimation and propose a data–driven estimation procedure that adapts to unknown smoothness of the service time distribution function G. Lastly, a numerical study is presented to illustrate practical performance of the developed adaptive procedure.

Original language	English
Pages (from-to)	81-123
Number of pages	43
Journal	Queueing Systems
Volume	108
Issue number	1
DOIs	https://doi.org/10.1007/s11134-024-09921-2
State	Published - Oct 2024

Bibliographical note

Publisher Copyright:
© The Author(s) 2024.

Keywords

60K25
62G05
Adaptive estimation
Deconvolution
Laplace transform
M/G/∞ queue
Minimax risk
Poisson process

ASJC Scopus subject areas

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

Access to Document

10.1007/s11134-024-09921-2

Cite this

@article{c6d397a64d944f15a9d5d783e6ff5a4d,

title = "Adaptive minimax estimation of service time distribution in the Mt/G/∞ queue from departure data",

abstract = "This article deals with the problem of estimating the service time distribution of the Mt/G/∞ queue from observation of the departure epochs. We develop minimax optimal estimators of G and study behavior of the minimax pointwise risk over a suitable family of service time distribution functions. In addition, we address the problem of adaptive estimation and propose a data–driven estimation procedure that adapts to unknown smoothness of the service time distribution function G. Lastly, a numerical study is presented to illustrate practical performance of the developed adaptive procedure.",

keywords = "60K25, 62G05, Adaptive estimation, Deconvolution, Laplace transform, M/G/∞ queue, Minimax risk, Poisson process",

author = "Wenwen Li and Alexander Goldenshluger",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2024.",

year = "2024",

month = oct,

doi = "10.1007/s11134-024-09921-2",

language = "English",

volume = "108",

pages = "81--123",

journal = "Queueing Systems",

issn = "0257-0130",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Adaptive minimax estimation of service time distribution in the Mt/G/∞ queue from departure data

AU - Li, Wenwen

AU - Goldenshluger, Alexander

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/10

Y1 - 2024/10

N2 - This article deals with the problem of estimating the service time distribution of the Mt/G/∞ queue from observation of the departure epochs. We develop minimax optimal estimators of G and study behavior of the minimax pointwise risk over a suitable family of service time distribution functions. In addition, we address the problem of adaptive estimation and propose a data–driven estimation procedure that adapts to unknown smoothness of the service time distribution function G. Lastly, a numerical study is presented to illustrate practical performance of the developed adaptive procedure.

AB - This article deals with the problem of estimating the service time distribution of the Mt/G/∞ queue from observation of the departure epochs. We develop minimax optimal estimators of G and study behavior of the minimax pointwise risk over a suitable family of service time distribution functions. In addition, we address the problem of adaptive estimation and propose a data–driven estimation procedure that adapts to unknown smoothness of the service time distribution function G. Lastly, a numerical study is presented to illustrate practical performance of the developed adaptive procedure.

KW - 60K25

KW - 62G05

KW - Adaptive estimation

KW - Deconvolution

KW - Laplace transform

KW - M/G/∞ queue

KW - Minimax risk

KW - Poisson process

UR - http://www.scopus.com/inward/record.url?scp=85200030909&partnerID=8YFLogxK

U2 - 10.1007/s11134-024-09921-2

DO - 10.1007/s11134-024-09921-2

M3 - Article

AN - SCOPUS:85200030909

SN - 0257-0130

VL - 108

SP - 81

EP - 123

JO - Queueing Systems

JF - Queueing Systems

IS - 1

ER -

Adaptive minimax estimation of service time distribution in the Mt/G/∞ queue from departure data

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this