Tasks and Numerical Algorithms for Optimization of Reliability of the Hardware-Redundant Technical Systems in a Conflict Situation under Different Strategies for Protection Against Enemy Attacks

Abstract

The subject of the article is the situation when a side in a conflict, defending itself from the enemy attacks, is a hardware-redundant technical system, containing the main and standby units, which can be involved for recovery of its functionality in the process of a conflict in accordance with the chosen protection strategy instead of the main unites, which failed under the impact of the enemy attacks. During a conflict the attacking side with its attack resources tries to weaken the targeted technical system by focusing its attacks on the functional units, increasing their failure rate during the period of the conflict and thus reducing the faultless operation and average uptime of the targeted technical system. Given the probabilistic character of the process, the behavior of the considered technical system involved in a conflict situation is approximated by Markov process and is described by Kolmogorov system of differential equations with variable coefficients. For solving of these equations the method of discretization and integer programming is used. The essence of this method, applied to the considered problem, is that the system of differential equations describing the behavior of a technical system in a conflict situation, the coefficients of which are functions of time, should be replaced by a system of discrete analogues, the coefficients of which can be considered constant with a predetermined degree of accuracy at discrete time intervals during the conflict. In order to optimize the reliability function and average time before a failure of the defender hardware-redundant technical systems in the process of the conflict, the author in this work proposes mathematical models for solving of these problems under different strategies for the use of the reserve units instead of the faulty ones. These strategies boil down to a targeted redundant power distribution between the main units of the technical system prior to the beginning of a conflict and dynamic reallocation of them in the process of conflict for achievement of the tasks, set before the technical system in a confrontation with the enemy. For implementation of these strategies the author proposes a method for computing of the corresponding vectors of redundancy and sequence of moments of redistribution of the reserve units between the main ones in the process of a conflict. Numerical algorithms were developed for solving of four problems of optimization of reliability of the considered technical system in the process of the conflict by selection of an appropriate backup strategy, convenient for implementation with the help of modern personal computers.