DINAMICS OF CONNECTIVITY PROBABILITY OF DISTRIBUTED INFORMATION SYSTEM CHANGE OVER TIME CONSIDERING RANDOM INFLUENCE ON ELEMENTS

Abstract

The design, subsequent implementation, and operation of information systems are integral elements in solving many applied problems today. Particularly relevant and interesting in several situations in the case where conditions dictate that the developed information system will operate autonomously—that is, without human intervention or with only negligible human involvement. Against this backdrop, studying the functional reliability of an information system becomes especially important.

Numerous methods have been developed to quantitatively assess a system's functional reliability. These methods are often referred to as functional reliability indicators and include, for example, connectivity probability, edge and vertex connectivity degree, and many others. However, their primary drawback is that they only allow an assessment of functional reliability at specific moments of operation. Meanwhile, during the design phase, it may be critically necessary to represent them as functions of time. Such a necessity often arises, for example, when studying the degradation dynamics of a designed information system.

Currently, there are mathematically grounded attempts to represent some functional reliability indicators as time-dependent functions. However, these attempts generally do not account for possible random influences on individual elements of the information system or on the system as a whole. This paper attempts to generalize the representation of connectivity probability as a time function to the case where the load on each element is not a strictly deterministic variable changing over time but rather a random process with a normal distribution at each moment in time. The study considers a scenario where it is known that the mean and standard deviation of element loads in the information system are periodic functions with a predetermined period, and their values are known at specific moments throughout the period.