Non-skip-free M/G/1 and G/M/1 type Markov chains

被引：32

作者：

Gail, HR ^{[1
]}

Hantler, SL ^{[1
]}

Taylor, BA ^{[1
]}

机构：

[1] UNIV MICHIGAN,ANN ARBOR,MI 48109

来源：

ADVANCES IN APPLIED PROBABILITY | 1997年 / 29卷 / 03期

关键词：

matrix analytic methods; Markov chains;

D O I：

10.2307/1428084

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 [统计学]; 070103 [概率论与数理统计]; 0714 [统计学];

摘要：

For Markov chains of M/G/1 type that are not skip-free to the left, the corresponding G matrix is shown to have special structure and be determined by its first block row. An algorithm that takes advantage of this structure is developed for computing G. For non-skip-free M/G/1 type Markov chains, the algorithm sig nificantly reduces the computational complexity of calculating the G matrix, when compared with reblocking to a system that is skip-free to the left and then applying usual iteration schemes to find G. A similar algorithm to calculate the R matrix for G/M/1 type Markov chains that are not skip-free to the right is also described.

引用

页码：733 / 758

页数：26

共 20 条

[1]

Bini D, 1995, COMPUTATIONS WITH MARKOV CHAINS, P21

[2]

On the solution of a nonlinear matrix equation arising in queueing problems [J].