LADDER HEIGHTS AND THE MARKOV-MODULATED M/G/1 QUEUE

被引：36

作者：

ASMUSSEN, S ^{[1
]}

机构：

[1] GOTHENBURG UNIV,S-41296 GOTHENBURG,SWEDEN

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1991年 / 37卷 / 02期

关键词：

M/G/1; QUEUE; MARKOV-MODULATION; WAITING TIME; POLLACZEK-KHINCHINE FORMULA; LADDER HEIGHTS; WIENER-HOPF FACTORIZATION; TIME REVERSAL; OCCUPATION MEASURE; PHASE-TYPE DISTRIBUTIONS; NONLINEAR MATRIX ITERATION;

D O I：

10.1016/0304-4149(91)90050-M

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：

The waiting time distribution is studied for the Markov-modulated M/G/1 queue with both the arrival rate beta-i and the distribution beta-i of the service time of the arriving customer depending on the state i of the environmental process. The analysis is based on ladder heights and occupation measure identities, and the fundamental step is to compute the intensity matrix Q of a certain Markov jump process as the solution of a non-linear matrix equation. The results come out as close matrix parallels of the Pollaczek-Khinchine formula without using transforms or complex variables. Further it is shown that if the B(i) are all phase-type, then the waiting time distribution is so as well.

引用

页码：313 / 326

页数：14

共 18 条

[11] NONLINEAR MATRIX EQUATIONS IN APPLIED PROBABILITY - SOLUTION TECHNIQUES AND OPEN PROBLEMS [J].