Asymptotic analysis for loss probability of queues with finite GI/M/1 type structure

Jeongsim Kim, Bara Kim

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

This paper discusses the asymptotic behavior of the loss probability for general queues with finite GI/M/1 type structure such as GI/M/c/K, SM/M/1/K and GI/MSP/1/K queues. We find an explicit expression for the asymptotic behavior of the loss probability as K tends to infinity. With the result, it is shown that the loss probability tends to 0 at a geometric rate.

Original languageEnglish
Pages (from-to)47-55
Number of pages9
JournalQueueing Systems
Volume57
Issue number1
DOIs
Publication statusPublished - 2007 Sept

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).

Keywords

  • GI/M/1 type Markov chain
  • Loss probability
  • Matrix-valued function
  • Maximal eigenvalue
  • Stationary distribution

ASJC Scopus subject areas

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

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