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

Bara Kim, Jeongsim Kim, Jerim Kim

Research output: Contribution to journalArticlepeer-review

16 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

Bibliographical note

Funding Information:
This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment) and the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2008-314-C00031).

Keywords

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

ASJC Scopus subject areas

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

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