TRANSIENT AND BUSY PERIOD ANALYSIS OF THE GI/G/1 QUEUE AS A HILBERT FACTORIZATION PROBLEM

被引：6

作者：

BERTSIMAS, DJ ^{[1
]}

KEILSON, J ^{[1
]}

NAKAZATO, D ^{[1
]}

ZHANG, HT ^{[1
]}

机构：

[1] MIT,OPERAT RES CTR,CAMBRIDGE,MA 02139

来源：

JOURNAL OF APPLIED PROBABILITY | 1991年 / 28卷 / 04期

关键词：

TRANSIENT ANALYSIS; BUSY PERIOD; LINDLEY EQUATION;

D O I：

10.2307/3214690

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 find the waiting time distribution in the transient domain and the busy period distribution of the GI/G/1 queue. We formulate the problem as a two-dimensional Lindley process and then transform it to a Hilbert factorization problem. We achieve the solution of the factorization problem for the GI/R/1, R/G/1 queues, where R is the class of distributions with rational Laplace transforms. We obtain simple closed-form expressions for the Laplace transforms of the waiting time distribution and the busy period distribution. Furthermore, we find closed-form formulae for the first two moments of the distributions involved.

引用

页码：873 / 885

页数：13