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

  • Authors:

  • Bara Kim;Jisu Lee;In-Suk Wee

  • Affiliations:

  • Department of Mathematics, Korea University, Seoul, South Korea 136-701;Department of Mathematics, Korea University, Seoul, South Korea 136-701;Department of Mathematics, Korea University, Seoul, South Korea 136-701

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2007

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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.