COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE AND SYSTEMS ANALYSIS

Singularly Perturbed Markov Models of Recovery Processes of Human–Machine–Environmental Systems with a Protection Subsystem

Authors

I. H. Yaloveha ORCID 0000-0002-2486-1812
Kharkiv National University of Radio Electronics ROR
A. O. Fedosieienko
Kharkiv National University of Radio Electronics ROR
DOI https://doi.org/10.31649/1997-9266-2026-187-4-108-118

Keywords

singularly perturbed systems continuous-time Markov processes human-machine-environmental systems technical systems recovery processes multiscale stochastic models mathematical modeling of complex systems differential equations neural sets fuzzy sets

Abstract

The relevance of the study is due to the need to increase the efficiency of mathematical modeling of the recovery processes of complex human-machine-environmental systems operating in post-accident modes and is characterized by the presence of fast-acting protection subsystems, different time scales of the course of degradation and recovery processes. Traditional Markov models of continuous time do not always enable to adequately take into account the multi-scale structure of the dynamics of such systems, which necessitates the use of singularly perturbed stochastic models.

The aim of the article is to develop a singularly perturbed Markov model of the recovery processes of a human-machine-environmental system with a protection subsystem and to study its asymptotic properties taking into account different time scales of the subsystems’ functioning.

The methodological basis of the study is the apparatus of Markov processes of continuous time, methods of asymptotic analysis of singularly perturbed systems, Kolmogorov equations and approaches to the aggregation of states of multi-scale stochastic models. The paper proposes the representation of the transition intensity matrix as the sum of fast and slow components with the introduction of a small parameter characterizing the ratio of time scales of the functioning of the protection subsystems and the technical system.

A generalized singularly perturbed Markov model of the post-accident recovery processes of the human-machine-environmental system has been developed, which allows taking into account the interaction of the technical subsystem, the operator and the protection subsystem in a single stochastic state space. An aggregated transition matrix of the reduced model has been obtained and the possibility of determining the stationary characteristics of the system functioning, in particular the readiness coefficient, the average recovery time and the probability of the system being in a critical state, has been shown.

The scientific novelty of the obtained results lies in the construction of a singularly perturbed Markov model of the recovery processes of human-machine-environmental systems with a protection subsystem, which allows taking into account the multi-scale structure of the functioning processes and performing a reduction of the state space without losing the accuracy of the description of the post-accident dynamics of the system.

The practical significance of the results obtained lies in the possibility of using the proposed model to assess the reliability and readiness indicators of complex technical systems of critical infrastructure, as well as to analyze the efficiency    of protection subsystems functioning in emergency modes.

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How to Cite

[1]
“Singularly Perturbed Markov Models of Recovery Processes of Human–Machine–Environmental Systems with a Protection Subsystem”, Вісник ВПІ, no. 4, pp. 108–118, Oct. 2026, doi: 10.31649/1997-9266-2026-187-4-108-118.

Author Biographies

I. H. Yaloveha, Kharkiv National University of Radio Electronics

Cand. Sc. (Eng.), Associate Professor, Associate Professor of the Chair of Applied Mathematics of Kharkiv National University of Radio Electronics; Associate Professor of the Chair of Economic and Mathematical Modeling of Simon Kuznets Kharkiv National University of Economics 

A. O. Fedosieienko, Kharkiv National University of Radio Electronics

 Post-Graduate Student of the Chair of Applied Math

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