Exact Convergence Rate for the Distributions of GI/M/c/K Queue as K Tends to Infinity

Bong Dae Choi, Bara Kim, Jeongsim Kim, In-Suk Wee

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We obtain the exact convergence rate of the stationary distribution π(K) of the embedded Markov chain in GI/M/c/K queue to the stationary distribution π of the embedded Markov chain in GI/M/c queue as K → ∞. Similar result for the time-stationary distributions of queue size is also included. These generalize Choi and Kim's results of the case c = 1 by nontrivial ways. Our results also strengthen the Simonot's results [5].

Original languageEnglish
Pages (from-to)125-136
Number of pages12
JournalQueueing Systems
Volume44
Issue number2
DOIs
Publication statusPublished - 2003 Jun 1

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Markov processes
Stationary distribution
Queue
Convergence rate
Markov chain
Rate of convergence

Keywords

  • GI/M/c queue
  • GI/M/c/K queue
  • Stationary distribution

ASJC Scopus subject areas

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

Cite this

Exact Convergence Rate for the Distributions of GI/M/c/K Queue as K Tends to Infinity. / Choi, Bong Dae; Kim, Bara; Kim, Jeongsim; Wee, In-Suk.

In: Queueing Systems, Vol. 44, No. 2, 01.06.2003, p. 125-136.

Research output: Contribution to journalArticle

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