Tail asymptotics for the queue length in an M/G/1 retrial queue

Weixin SHANG, Liming LIU, Quan Lin LI

Research output: Journal PublicationsJournal Article (refereed)

19 Citations (Scopus)

Abstract

In this paper, we study the tail behavior of the stationary queue length of an M/G/1 retrial queue. We show that the subexponential tail of the stationary queue length of an M/G/1 retrial queue is determined by that of the corresponding M/G/1 queue, and hence the stationary queue length in an M/G/1 retrial queue is subexponential if the stationary queue length in the corresponding M/G/1 queue is subexponential. Our results for subexponential tails also apply to regularly varying tails, and we provide the regularly varying tail asymptotics for the stationary queue length of the M/G/1 retrial queue.
Original languageEnglish
Pages (from-to)193-198
Number of pages6
JournalQueueing Systems
Volume52
Issue number3
DOIs
Publication statusPublished - 1 Mar 2006
Externally publishedYes

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Queue
Tail behavior

Keywords

  • M/G/1 retrial queue; Queue length; Subexponentiality; Regular variation; Tail asymptotics

Cite this

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title = "Tail asymptotics for the queue length in an M/G/1 retrial queue",
abstract = "In this paper, we study the tail behavior of the stationary queue length of an M/G/1 retrial queue. We show that the subexponential tail of the stationary queue length of an M/G/1 retrial queue is determined by that of the corresponding M/G/1 queue, and hence the stationary queue length in an M/G/1 retrial queue is subexponential if the stationary queue length in the corresponding M/G/1 queue is subexponential. Our results for subexponential tails also apply to regularly varying tails, and we provide the regularly varying tail asymptotics for the stationary queue length of the M/G/1 retrial queue.",
keywords = "M/G/1 retrial queue; Queue length; Subexponentiality; Regular variation; Tail asymptotics",
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Tail asymptotics for the queue length in an M/G/1 retrial queue. / SHANG, Weixin; LIU, Liming; LI, Quan Lin.

In: Queueing Systems, Vol. 52, No. 3, 01.03.2006, p. 193-198.

Research output: Journal PublicationsJournal Article (refereed)

TY - JOUR

T1 - Tail asymptotics for the queue length in an M/G/1 retrial queue

AU - SHANG, Weixin

AU - LIU, Liming

AU - LI, Quan Lin

PY - 2006/3/1

Y1 - 2006/3/1

N2 - In this paper, we study the tail behavior of the stationary queue length of an M/G/1 retrial queue. We show that the subexponential tail of the stationary queue length of an M/G/1 retrial queue is determined by that of the corresponding M/G/1 queue, and hence the stationary queue length in an M/G/1 retrial queue is subexponential if the stationary queue length in the corresponding M/G/1 queue is subexponential. Our results for subexponential tails also apply to regularly varying tails, and we provide the regularly varying tail asymptotics for the stationary queue length of the M/G/1 retrial queue.

AB - In this paper, we study the tail behavior of the stationary queue length of an M/G/1 retrial queue. We show that the subexponential tail of the stationary queue length of an M/G/1 retrial queue is determined by that of the corresponding M/G/1 queue, and hence the stationary queue length in an M/G/1 retrial queue is subexponential if the stationary queue length in the corresponding M/G/1 queue is subexponential. Our results for subexponential tails also apply to regularly varying tails, and we provide the regularly varying tail asymptotics for the stationary queue length of the M/G/1 retrial queue.

KW - M/G/1 retrial queue; Queue length; Subexponentiality; Regular variation; Tail asymptotics

UR - http://commons.ln.edu.hk/sw_master/4074

U2 - 10.1007/s11134-006-5223-1

DO - 10.1007/s11134-006-5223-1

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SP - 193

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JO - Queueing Systems

JF - Queueing Systems

SN - 0257-0130

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