Using Semi-Markov Chains to Solve Semi-Markov Processes

被引：20

作者：

Wu, Bei ^{[1
]}

Maya, Brenda Ivette Garcia ^{[2
]}

Limnios, Nikolaos ^{[2
]}

机构：

[1] Beijing Inst Technol, Sch Management & Econ, Beijing 100081, Peoples R China

[2] Sorbonne Univ, Univ Technol Compiegne, Paris, France

来源：

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2021年 / 23卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Semi-Markov processes; Numerical methods; Markov renewal equations; System availabilities; Sequential cyber-attacks; RELIABILITY; MODEL;

D O I：

10.1007/s11009-020-09820-y

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：

This article provides a novel method to solve continuous-time semi-Markov processes by algorithms from discrete-time case, based on the fact that the Markov renewal function in discrete-time case is a finite series. Bounds of approximate errors due to discretization for the transition function matrix of the continuous-time semi-Markov process are investigated. This method is applied to a reliability problem which refers to the availability analysis of the system subject to sequential cyber-attacks. Two cases where sojourn times follow exponential and Weibull distributions are considered and computed in order to verify and illustrate the proposed method.

引用

页码：1419 / 1431

页数：13

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