Sharp results on convergence rates for the distribution of GI/M/1/K queues as K tends to infinity

Bong Dae Choi, Bara Kim

Research output: Contribution to journalArticle

Abstract

In this paper, we investigate how fast the stationary distribution π(K) of an embedded Markov chain (time-stationary distribution q(K)) of the GI/M/1/K queue converges to the stationary distribution π of the embedded Markov chain (time-stationary distribution q) of the GI/M/1 queue as K tends to infinity. Simonot (1997) proved certain equalities. We obtain sharper results than these by finding limit values lim K → ∞ σ-K ∥π(K) -π∥ and limK → ∞ σ -K ∥q(K) -q∥ explicitly.

Original languageEnglish
Pages (from-to)1010-1019
Number of pages10
JournalJournal of Applied Probability
Volume37
Issue number4
DOIs
Publication statusPublished - 2000 Jan 1

Keywords

  • GI/M/1/K queue; dual sequence; stationary measure; stationary distribution; convergence rate

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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