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

Jerim Kim, Jeongsim Kim, Bara Kim

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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
Issue number14
StatePublished - Aug 2012


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


Dive into the research topics of 'Tail asymptotics of the queue size distribution in the MMm retrial queue'. Together they form a unique fingerprint.

Cite this