Tail asymptotics of the queue size distribution in the MMm retrial queue

Jerim Kim, Jeongsim Kim, Bara Kim

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We consider an MMm retrial queue and investigate the tail asymptotics for the joint distribution of the queue size and the number of busy servers in the steady state. The stationary queue size distribution with the number of busy servers being fixed is asymptotically given by a geometric function multiplied by a power function. The decay rate of the geometric function is the offered load and independent of the number of busy servers, whereas the exponent of the power function depends on the number of busy servers. Numerical examples are presented to illustrate the result.

Original languageEnglish
Pages (from-to)3445-3460
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume236
Issue number14
DOIs
Publication statusPublished - 2012 Aug 1

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Keywords

  • Censored Markov process
  • Karamata Tauberian theorem
  • MMm retrial queue
  • Queue size distribution
  • Riemann-Lebesgue lemma
  • Tail asymptotics

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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