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

被引：9

作者：

Choi, BD ^{[1
]}

Kim, B ^{[1
]}

机构：

[1] Korea Univ, Dept Math, Seoul 136701, South Korea

来源：

JOURNAL OF APPLIED PROBABILITY | 2000年 / 37卷 / 04期

关键词：

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

D O I：

10.1239/jap/1014843080

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we investigate how fast the stationary distribution pi ((K)) of an embedded Markov chain (time-stationary distribution q((K))) of the GI/M/1/K queue converges to the stationary distribution pi 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-->infinity) sigma (-K)parallel to pi ((K))-pi parallel to and lim(K-->infinity) sigma (-K)parallel toq((K))-q parallel to explicitly.

引用

页码：1010 / 1019

页数：10

共 8 条

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[2]

CHOI BD, 2000, UNPUB EXACT CONVERGE

[3]

CHOI BD, 2000, IN PRESS QUEUEING SY

[4] COMPLEMENTARY GENERATING-FUNCTIONS FOR THE MX/GI/1/K AND GI/MY/1/K QUEUES AND THEIR APPLICATION TO THE COMPARISON OF LOSS PROBABILITIES [J].