Tail asymptotics for the queue size distribution in the MAP/G/1 retrial queue

Bara Kim, Jeongsim Kim, Jerim Kim

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We consider a MAP/G/1 retrial queue where the service time distribution has a finite exponential moment. We derive matrix differential equations for the vector probability generating functions of the stationary queue size distributions. Using these equations, Perron-Frobenius theory, and the Karamata Tauberian theorem, we obtain the tail asymptotics of the queue size distribution. The main result on light-tailed asymptotics is an extension of the result in Kim et al. (J. Appl. Probab. 44:1111-1118, 2007) on the M/G/1 retrial queue.

Original languageEnglish
Pages (from-to)79-94
Number of pages16
JournalQueueing Systems
Volume66
Issue number1
DOIs
Publication statusPublished - 2010 Jun 4

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Differential equations
Queue
Generating function

Keywords

  • Karamata Tauberian theorem
  • MAP/G/1 retrial queue
  • Queue size distribution
  • Tail asymptotics

ASJC Scopus subject areas

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

Cite this

Tail asymptotics for the queue size distribution in the MAP/G/1 retrial queue. / Kim, Bara; Kim, Jeongsim; Kim, Jerim.

In: Queueing Systems, Vol. 66, No. 1, 04.06.2010, p. 79-94.

Research output: Contribution to journalArticle

Kim, Bara ; Kim, Jeongsim ; Kim, Jerim. / Tail asymptotics for the queue size distribution in the MAP/G/1 retrial queue. In: Queueing Systems. 2010 ; Vol. 66, No. 1. pp. 79-94.
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