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

Bara Kim, Jisu Lee, In-Suk Wee

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3 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 languageEnglish
Pages (from-to)1-18
Number of pages18
JournalQueueing Systems
Volume57
Issue number1
DOIs
Publication statusPublished - 2007 Sep 1

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Keywords

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

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Management Science and Operations Research

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