A note on the subexponential asymptotics of the stationary distribution of M/G/1 type Markov chains

Bara Kim; Jeongsim Kim

doi:10.1016/j.ejor.2012.01.016

A note on the subexponential asymptotics of the stationary distribution of M/G/1 type Markov chains

Bara Kim, Jeongsim Kim

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

4 Citations (Scopus)

Abstract

Masuyama (2011) obtained the subexponential asymptotics of the stationary distribution of an M/G/1 type Markov chain under the assumption related to the periodic structure of G-matrix. In this note, we improve Masuyama's result by showing that the subexponential asymptotics holds without the assumption related to the periodic structure of G-matrix.

Original language	English
Pages (from-to)	132-134
Number of pages	3
Journal	European Journal of Operational Research
Volume	220
Issue number	1
DOIs	https://doi.org/10.1016/j.ejor.2012.01.016
Publication status	Published - 2012 Jul 1

Bibliographical note

Funding Information:
B. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2011-0004133 ). J. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2011-0011887 ).

Keywords

M/G/1 type Markov chain
Queueing
Stationary distribution
Subexponential asymptotics

ASJC Scopus subject areas

General Computer Science
Modelling and Simulation
Management Science and Operations Research
Information Systems and Management

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10.1016/j.ejor.2012.01.016

Cite this

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title = "A note on the subexponential asymptotics of the stationary distribution of M/G/1 type Markov chains",

abstract = "Masuyama (2011) obtained the subexponential asymptotics of the stationary distribution of an M/G/1 type Markov chain under the assumption related to the periodic structure of G-matrix. In this note, we improve Masuyama's result by showing that the subexponential asymptotics holds without the assumption related to the periodic structure of G-matrix.",

keywords = "M/G/1 type Markov chain, Queueing, Stationary distribution, Subexponential asymptotics",

author = "Bara Kim and Jeongsim Kim",

note = "Funding Information: B. Kim{\textquoteright}s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2011-0004133 ). J. Kim{\textquoteright}s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2011-0011887 ).",

year = "2012",

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doi = "10.1016/j.ejor.2012.01.016",

language = "English",

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journal = "European Journal of Operational Research",

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T1 - A note on the subexponential asymptotics of the stationary distribution of M/G/1 type Markov chains

AU - Kim, Bara

AU - Kim, Jeongsim

N1 - Funding Information: B. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2011-0004133 ). J. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2011-0011887 ).

PY - 2012/7/1

Y1 - 2012/7/1

N2 - Masuyama (2011) obtained the subexponential asymptotics of the stationary distribution of an M/G/1 type Markov chain under the assumption related to the periodic structure of G-matrix. In this note, we improve Masuyama's result by showing that the subexponential asymptotics holds without the assumption related to the periodic structure of G-matrix.

AB - Masuyama (2011) obtained the subexponential asymptotics of the stationary distribution of an M/G/1 type Markov chain under the assumption related to the periodic structure of G-matrix. In this note, we improve Masuyama's result by showing that the subexponential asymptotics holds without the assumption related to the periodic structure of G-matrix.

KW - M/G/1 type Markov chain

KW - Queueing

KW - Stationary distribution

KW - Subexponential asymptotics

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DO - 10.1016/j.ejor.2012.01.016

M3 - Article

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SN - 0377-2217

VL - 220

SP - 132

EP - 134

JO - European Journal of Operational Research

JF - European Journal of Operational Research

IS - 1

ER -

A note on the subexponential asymptotics of the stationary distribution of M/G/1 type Markov chains

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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