First-passage-time densities and avoiding probabilities for birth-and-death processes with symmetric sample paths

被引：9

作者：

Di Crescenzo, A ^{[1
]}

机构：

[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, I-80126 Naples, Italy

来源：

JOURNAL OF APPLIED PROBABILITY | 1998年 / 35卷 / 02期

关键词：

truncated processes; transition probabilities; spatial symmetry; absorption; reflection; first-passage time; avoiding transition probabilities; M/M/1 queueing system; busy period;

D O I：

10.1017/S0021900200015011

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：

For truncated birth-and-death processes with two absorbing or two reflecting boundaries, necessary and sufficient conditions on the transition rates are given such that the transition probabilities satisfy a suitable spatial symmetry relation. This allows one to obtain simple expressions for first-passage-time densities and for certain avoiding transition probabilities. An application to an M/M/1 queueing system with two finite sequential queueing rooms of equal sizes is finally provided.

引用

页码：383 / 394

页数：12

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