Heavy-tailed asymptotics for a fluid model driven by an M/G/1 queue

Quan Lin LI; Liming LIU; Weixin SHANG

doi:10.1016/j.peva.2007.06.022

Heavy-tailed asymptotics for a fluid model driven by an M/G/1 queue

Quan Lin LI, Liming LIU, Weixin SHANG

Research output: Journal Publications › Journal Article (refereed) › peer-review

17 Citations (Scopus)

Abstract

In this paper, an infinite-buffer fluid queue driven by an M/G/1 queue is discussed. The Laplace transform of the distribution of the stationary buffer content is expressed through the minimal positive solution to a crucial equation, similar to the fundamental equation satisfied by the busy period of an M/G/1 queue. Furthermore, the distribution of the stationary buffer content is shown to be regularly varying with index −α+1 if the distribution of the service times is regularly varying with index −α

Original language	English
Pages (from-to)	227-240
Number of pages	14
Journal	Performance Evaluation
Volume	65
Issue number	3-4
DOIs	https://doi.org/10.1016/j.peva.2007.06.022
Publication status	Published - Mar 2008
Externally published	Yes

Keywords

Buffer content
Busy period
Fluid queue
M/G/1
Regularly varying function
queue

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10.1016/j.peva.2007.06.022

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AB - In this paper, an infinite-buffer fluid queue driven by an M/G/1 queue is discussed. The Laplace transform of the distribution of the stationary buffer content is expressed through the minimal positive solution to a crucial equation, similar to the fundamental equation satisfied by the busy period of an M/G/1 queue. Furthermore, the distribution of the stationary buffer content is shown to be regularly varying with index −α+1 if the distribution of the service times is regularly varying with index −α

KW - Buffer content

KW - Busy period

KW - Fluid queue

KW - M/G/1

KW - Regularly varying function

KW - queue

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EP - 240

JO - Performance Evaluation

JF - Performance Evaluation

IS - 3-4

ER -

Heavy-tailed asymptotics for a fluid model driven by an M/G/1 queue

Abstract

Keywords

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