3. Mathematical models of periodic monitoring and backup

As noted earlier, the basic mechanism for providing functional stability to information systems (ISs) is systematic monitoring and backup against possible failures. There are two key approaches to arranging monitoring in IS. The first one relates to the occurrence of a certain event of the computation process (message processing, initiating an exchange among processes, system program call, etc.) [6]. This approach's drawbacks are the difficulty in identifying a set of controlled events of the computation process and the potential for unlimited growth of control points. The latter makes the approach hard to apply during IS normal operation, given the specified resource and task-time restrictions.

The second approach involves a periodic check of the system at predetermined intervals [7–10]. This is consistent with time schedules and allows the existing resource restrictions to be taken into consideration, but fails to fully reflect the stochastic nature of the occurrence of various errors and irregularities. Furthermore, a number of subjective factors make it impossible, in the first place, to organize periodic control in ergatic systems at strictly specified intervals. There is another approach, however, that takes into account the stochastic external factors of IS functional stability, given the specified time and economic constraints.

Under ISO/IEC 15408–1:2009,<sup>1</sup> monitoring covers not only SW (assessment object) but also the operational environment. Let us consider stochastic and deterministic models of the earlier procedures.
