Using Semi-Markov Chains to Solve Semi-Markov Processes

Bei Wu (), Brenda Ivette Garcia Maya and Nikolaos Limnios
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Bei Wu: Beijing Institute of Technology
Brenda Ivette Garcia Maya: Sorbonne University
Nikolaos Limnios: Sorbonne University

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 4, 1419-1431

Abstract: Abstract 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.

Keywords: Semi-Markov processes; Numerical methods; Markov renewal equations; System availabilities; Sequential cyber-attacks (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s11009-020-09820-y

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