First passage times for Markov renewal processes and applications

被引：0

作者：

Xu, GH ^{[1
]}

Yuan, XM

Li, QL

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China

[2] Chinese Acad Sci, Asian Pacific Operat Res Ctr, Beijing 100080, Peoples R China

[3] APORS, Asian Pacific Operat Res Ctr, Beijing 100080, Peoples R China

[4] Chinese Acad Sci, Inst Automat, Natl Lab Pattern Recognit, Beijing 100080, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY | 2000年 / 43卷 / 12期

基金：

中国国家自然科学基金;

关键词：

Markov renewal process (MRP); joint transform; first passage time; busy period; busy cycle; uniform error;

D O I：

10.1007/BF02880061

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage number of steps for general Markov renewal processes with any initial state probability vector. The uniformly convergent algorithm with arbitrarily prescribed error can be efficiently applied to compute busy periods, busy cycles, waiting times, sojourn times, and relevant indices of various generic queueing systems and queueing networks. This paper also conducts a numerical experiment to implement the proposed algorithm.

引用

页码：1238 / 1249

页数：12

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