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

Quan Lin LI, Liming LIU, Weixin SHANG

Research output: Journal PublicationsJournal 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 languageEnglish
Pages (from-to)227-240
Number of pages14
JournalPerformance Evaluation
Volume65
Issue number3-4
DOIs
Publication statusPublished - Mar 2008
Externally publishedYes

Funding

The authors thank three anonymous referees for their detailed comments and helpful suggestions. This research was supported in part by Hong Kong Research Grant Council through a grant PolyU6133/02E. The first author was also supported in part by the National Natural Science Foundation of China under Grant No. 10671107 and the National Fundamental Research 937 Program of China under Grant No. 2006CB805901.

Keywords

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

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