Dispersion of the cost of restoration and optimization problems in the recovery processes of technical and information systems

In work, for the simple and general recovery process, formulas for the variance of the recovery cost are obtained that depend on the recovery functions (average number of failures) of the models under consideration. The presence of formulas for the average number of failures, the average cost of recovery and the corresponding dispersion formulas makes it possible to consider new optimization problems in terms of price, quality, risk when organizing recovery processes. Dispersion is given a sense of risk. The wording problems that arise here remind Markowitz’s well-known tasks of forming a portfolio of securities, where the mean is given the meaning of income, dispersion is the meaning of risk. The task of minimizing the variance of the cost of recovery with the set limits on the average number of failures, the average cost of recovery and the duration of the recovery process in a simple process with exponential distribution of the operating time of the replacement elements is considered. It is noted that optimization tasks in terms of price, quality, risk can be expanded by including questions about the choice of recovery strategies, when, along with emergency recovery, preventive minimum scans are carried out intensity of cost or maximum of such importance in the operation of information systems the size of the readiness factor. In the exponential distribution of a simple recovery process, Chebyshev's inequalities and variation coefficients for the number of failures and the cost of recovery have been written. The developed mathematical apparatus is intended for use in setting and solving various optimization problems of information and computer security, as well as in the operation of technical and information systems, software and software-hardware tools of information protection when there are failures, threats of attacks, and security threats of a random nature occur.

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