Tail asymptotics for the fundamental period in the MAP/G/1 queue

Bara Kim; Jisu Lee; In Suk Wee

doi:10.1007/s11134-007-9042-9

Tail asymptotics for the fundamental period in the MAP/G/1 queue

Bara Kim, Jisu Lee, In Suk Wee

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

4 Citations (Scopus)

Abstract

This paper studies the tail behavior of the fundamental period in the MAP/G/1 queue. We prove that if the service time distribution has a regularly varying tail, then the fundamental period distribution in the MAP/G/1 queue has also regularly varying tail, and vice versa, by finding an explicit expression for the asymptotics of the tail of the fundamental period in terms of the tail of the service time distribution. Our main result with the matrix analytic proof is a natural extension of the result in (de Meyer and Teugels, J. Appl. Probab. 17: 802-813, 1980) on the M/G/1 queue where techniques rely heavily on analytic expressions of relevant functions.

Original language	English
Pages (from-to)	1-18
Number of pages	18
Journal	Queueing Systems
Volume	57
Issue number	1
DOIs	https://doi.org/10.1007/s11134-007-9042-9
Publication status	Published - 2007 Sept

Bibliographical note

Funding Information:
B. Kim’s research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).

Funding Information:
I.-S. Wee’s research was supported by the Korea Research Foundation Grant KRF 2003-070-00008.

Keywords

Abelian-Tauberian theorem
Fundamental period
MAP/G/1 queue
Regular variation

ASJC Scopus subject areas

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

Access to Document

10.1007/s11134-007-9042-9

Cite this

@article{dbe5fd4f4f654ba79b40868ecca2652d,

title = "Tail asymptotics for the fundamental period in the MAP/G/1 queue",

abstract = "This paper studies the tail behavior of the fundamental period in the MAP/G/1 queue. We prove that if the service time distribution has a regularly varying tail, then the fundamental period distribution in the MAP/G/1 queue has also regularly varying tail, and vice versa, by finding an explicit expression for the asymptotics of the tail of the fundamental period in terms of the tail of the service time distribution. Our main result with the matrix analytic proof is a natural extension of the result in (de Meyer and Teugels, J. Appl. Probab. 17: 802-813, 1980) on the M/G/1 queue where techniques rely heavily on analytic expressions of relevant functions.",

keywords = "Abelian-Tauberian theorem, Fundamental period, MAP/G/1 queue, Regular variation",

author = "Bara Kim and Jisu Lee and Wee, {In Suk}",

note = "Funding Information: B. Kim{\textquoteright}s research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment). Funding Information: I.-S. Wee{\textquoteright}s research was supported by the Korea Research Foundation Grant KRF 2003-070-00008.",

year = "2007",

month = sep,

doi = "10.1007/s11134-007-9042-9",

language = "English",

volume = "57",

pages = "1--18",

journal = "Queueing Systems",

issn = "0257-0130",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Tail asymptotics for the fundamental period in the MAP/G/1 queue

AU - Kim, Bara

AU - Lee, Jisu

AU - Wee, In Suk

N1 - Funding Information: B. Kim’s research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment). Funding Information: I.-S. Wee’s research was supported by the Korea Research Foundation Grant KRF 2003-070-00008.

PY - 2007/9

Y1 - 2007/9

N2 - This paper studies the tail behavior of the fundamental period in the MAP/G/1 queue. We prove that if the service time distribution has a regularly varying tail, then the fundamental period distribution in the MAP/G/1 queue has also regularly varying tail, and vice versa, by finding an explicit expression for the asymptotics of the tail of the fundamental period in terms of the tail of the service time distribution. Our main result with the matrix analytic proof is a natural extension of the result in (de Meyer and Teugels, J. Appl. Probab. 17: 802-813, 1980) on the M/G/1 queue where techniques rely heavily on analytic expressions of relevant functions.

AB - This paper studies the tail behavior of the fundamental period in the MAP/G/1 queue. We prove that if the service time distribution has a regularly varying tail, then the fundamental period distribution in the MAP/G/1 queue has also regularly varying tail, and vice versa, by finding an explicit expression for the asymptotics of the tail of the fundamental period in terms of the tail of the service time distribution. Our main result with the matrix analytic proof is a natural extension of the result in (de Meyer and Teugels, J. Appl. Probab. 17: 802-813, 1980) on the M/G/1 queue where techniques rely heavily on analytic expressions of relevant functions.

KW - Abelian-Tauberian theorem

KW - Fundamental period

KW - MAP/G/1 queue

KW - Regular variation

UR - http://www.scopus.com/inward/record.url?scp=35549010209&partnerID=8YFLogxK

U2 - 10.1007/s11134-007-9042-9

DO - 10.1007/s11134-007-9042-9

M3 - Article

AN - SCOPUS:35549010209

SN - 0257-0130

VL - 57

SP - 1

EP - 18

JO - Queueing Systems

JF - Queueing Systems

IS - 1

ER -

Tail asymptotics for the fundamental period in the MAP/G/1 queue

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this