Markov model of unsteady flow elimination of accidents in restrictions on the performance of the operator

Authors

  • Ігор Володимирович Наумейко Kharkiv National University of Radio Electronics Lenina 14, Kharkov, Ukraine, 61166, Ukraine
  • Разі Джабур Аль-Азаві Kharkiv National University of Radio Electronics Lenina 14, Kharkov, Ukraine, 61166, Ukraine
  • Валід Ахмед Альрефаі Kharkiv National University of Radio Electronics Lenina 14, Kharkov, Ukraine, 61166, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.14748

Keywords:

Markov chain, Kolmogorov differential equations, the maximum entropy, ergodic, disasters, Erlang

Abstract

The actual problem of simulating the operation of the "Man-Machine-Environment" system, that is the process of the object recovery after the environmental disaster is considered, provided the recovery is made by one of its sub-systems, that include humans. The model differs significantly from the classical theory of reliability. The work is devoted to modeling of multi-step restoration process of an arbitrary nature object with non-stationary Poisson stream of events (accidents) and exponential intensity of recovery process. It passes a fixed finite sequence of phases - the states and is described by the Kolmogorov probabilities for these states. The cases of ergodic and absorbing chains with continuous time are considered. Some of the states in the chain indicate the efficiency of the operator in elimination the accident. It is assumed that the efficiency of the operator can not recover during the process of eliminating accidents. According to the verbal descriptions of the object, graphs of states are drawn, and in accordance to them – the Kolmogorov equations and their stationary solutions. The resulting figures of numerical solutions allow us to determine the time of the process stabilization. For actual input data the following resulting probabilities are obtained: for trouble-free operation of the facility, for a fatal accident and for disaster recovery

Author Biographies

Ігор Володимирович Наумейко, Kharkiv National University of Radio Electronics Lenina 14, Kharkov, Ukraine, 61166

PhD, Associate Professor

Department of Applied Mathematics

 

Разі Джабур Аль-Азаві, Kharkiv National University of Radio Electronics Lenina 14, Kharkov, Ukraine, 61166

Postgraduate

Department of Applied Mathematics

Валід Ахмед Альрефаі, Kharkiv National University of Radio Electronics Lenina 14, Kharkov, Ukraine, 61166

Postgraduate

Department of Applied Mathematics

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Published

2013-06-20

How to Cite

Наумейко, І. В., Аль-Азаві, Р. Д., & Альрефаі, В. А. (2013). Markov model of unsteady flow elimination of accidents in restrictions on the performance of the operator. Eastern-European Journal of Enterprise Technologies, 3(4(63), 20–23. https://doi.org/10.15587/1729-4061.2013.14748

Issue

Vol. 3 No. 4(63) (2013): Mathematics and cybernetics - fundamental ans applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2014 Ігор Володимирович Наумейко, Разі Джабур Аль-Азаві, Валід Ахмед Альрефаі

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