Tail asymptotics for the queue size distribution in a discrete-time Geo/G/1 retrial queue

Bara Kim; Jeongsim Kim

doi:10.1007/s11134-009-9106-0

Tail asymptotics for the queue size distribution in a discrete-time Geo/G/1 retrial queue

Bara Kim, Jeongsim Kim

Department of Mathematics

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

8 Citations (Scopus)

Abstract

We consider a discrete-time Geo/G/1 retrial queue where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically geometric. Remarkably, the result is inconsistent with the corresponding result in the continuous-time counterpart, the M/G/1 retrial queue, where the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function.

Original language	English
Pages (from-to)	243-254
Number of pages	12
Journal	Queueing Systems
Volume	61
Issue number	2-3
DOIs	https://doi.org/10.1007/s11134-009-9106-0
Publication status	Published - 2009 Mar

Keywords

Geo/G/1 retrial queue
Queue size distribution
Tail asymptotics

ASJC Scopus subject areas

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

Access to Document

10.1007/s11134-009-9106-0

Cite this

@article{612f03611d2e443a8faa5e2e07dee398,

title = "Tail asymptotics for the queue size distribution in a discrete-time Geo/G/1 retrial queue",

abstract = "We consider a discrete-time Geo/G/1 retrial queue where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically geometric. Remarkably, the result is inconsistent with the corresponding result in the continuous-time counterpart, the M/G/1 retrial queue, where the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function.",

keywords = "Geo/G/1 retrial queue, Queue size distribution, Tail asymptotics",

author = "Bara Kim and Jeongsim Kim",

note = "Funding Information: This 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) and the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2008-314-C00031).",

year = "2009",

month = mar,

doi = "10.1007/s11134-009-9106-0",

language = "English",

volume = "61",

pages = "243--254",

journal = "Queueing Systems",

issn = "0257-0130",

publisher = "Springer Netherlands",

number = "2-3",

}

TY - JOUR

T1 - Tail asymptotics for the queue size distribution in a discrete-time Geo/G/1 retrial queue

AU - Kim, Bara

AU - Kim, Jeongsim

N1 - Funding Information: This 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) and the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2008-314-C00031).

PY - 2009/3

Y1 - 2009/3

N2 - We consider a discrete-time Geo/G/1 retrial queue where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically geometric. Remarkably, the result is inconsistent with the corresponding result in the continuous-time counterpart, the M/G/1 retrial queue, where the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function.

AB - We consider a discrete-time Geo/G/1 retrial queue where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically geometric. Remarkably, the result is inconsistent with the corresponding result in the continuous-time counterpart, the M/G/1 retrial queue, where the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function.

KW - Geo/G/1 retrial queue

KW - Queue size distribution

KW - Tail asymptotics

UR - http://www.scopus.com/inward/record.url?scp=62349139447&partnerID=8YFLogxK

U2 - 10.1007/s11134-009-9106-0

DO - 10.1007/s11134-009-9106-0

M3 - Article

AN - SCOPUS:62349139447

SN - 0257-0130

VL - 61

SP - 243

EP - 254

JO - Queueing Systems

JF - Queueing Systems

IS - 2-3

ER -

Tail asymptotics for the queue size distribution in a discrete-time Geo/G/1 retrial queue

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this