V. A. Bogatyrev, A. V. Bogatyrev, S. V. Bogatyryev

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 A Markov model is suggested for secure information systems, functioning under conditions of destructive impacts, which aftereffects are found by on-line and test control. It is assumed that on-line control, in contrast to the test one, is char- acterized by the limited control completeness, but does not require the stopping of computational process. The aim of re- search is to create models that optimize intervals of test control initialization by the criterion of probability maximization for system stay in the ready state to secure fulfillment of the functional requests and minimization of the dangerous system states in view of the uncertainty and intensity variance of the destructive impacts. Variants of testing intervals optimization are con- sidered depending on the intensity of destructive impacts by the criterion of the maximum system availability for the safe execution of queries. Optimization is carried out with and without adaptation to the actual intensity change of destructive impacts.  The efficiency of adaptive change for testing periods is shown depending on the observed activity of destructive impacts. The solution of optimization problem is obtained by built-in tools of computer mathematics Mathcad 15, including symbolic mathematics for solution of systems of algebraic equations. The proposed models and methods of determining the optimal testing intervals can find their application in the system design of computer systems and networks of critical applications, working under conditions of destabilizing actions with the increased requirements for their safety.

Keywords:   Markov model, control, dangerous states, destructive impacts, optimization

Acknowledgements. The work is done within the framework of S&R “Methods and Models for Integrated Security and Operation Stability of Computer Systems”.

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