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On Transient Analysis of $$\Delta _N$$ Δ N -Markov Chains

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  • Stephanie Reed

    (California State University, Fullerton)

  • Elia Ziadé

    (Palomar College)

Abstract

Consider a cyber-physical system which has the purpose of maintaining the security of some physical asset. A particularly relevant scenario is one in which the system must perform its functions while at the same time enduring malicious attacks for an extended amount of time without energy renewal. We will study a theoretical model analogous to this cyber-physical system with an arbitrary number of nodes. The nodes in this system are able to communicate with one another and have the task of maintaining the security of the system. Initially all nodes comprising this system are in working order, however, due to attacks they can eventually become corrupted and then work against the security of the system. Of particular interest is the calculation of a number of metrics related to reliability of the system including the reliability function and the mean-time to failure. A particular case of this model has been examined by many researchers in the past, mostly using numerical methods. The contribution of this paper is the presentation of explicit expressions for the transient-state transition probabilities, reliability function, and the mean-time to failure along with rigorous proofs for the validity of these expressions. A result such as this is stronger than previous results via numerical methods and is an extension of previous analytical results where additional constraints on the model were imposed.

Suggested Citation

  • Stephanie Reed & Elia Ziadé, 2023. "On Transient Analysis of $$\Delta _N$$ Δ N -Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-28, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10002-9
    DOI: 10.1007/s11009-023-10002-9
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    References listed on IDEAS

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    1. Ashish Kumar & Monika Saini & Dinesh Kumar Saini & Nikhilesh Badiwal, 2021. "Cyber physical systems-reliability modelling: critical perspective and its impact," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(6), pages 1334-1347, December.
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