### Development of algorithms for accounting for the impact of page failures on the time characteristics of processing applications in computing complexes

#### Abstract

Multilevel analytical models of accounting for page failures in assessing the efficiency of solving problems in computing complexes (VC) are considered. To determine the frequency of page failures, a semi-Markov model with an algorithm for replacing the "most used page" (NDI) is proposed. The effect of page failures on the time of continuous counting of programs is determined on the basis of approximation of the time of continuous counting for two moments by an Erlang or hyperexponential distribution and solving the problem of combining two recurrent flows. The calculated ratios obtained serve as the basis for the development of an algorithm for accounting for page failures in multilevel hierarchical models for estimating probabilistic-temporal characteristics of VC with a page memory organization. Based on the proposed approach, a software package has been implemented that allows for a multivariate analysis of various modes of operation of computing complexes with a multivirtual operating system.

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