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This paper presents the developed method for predicting the state of services in globally distributed computing systems (GRVK). The method is based on objective historical monitoring data by using the computational methods of Gauss-Jordan, Weierstrass, Durand-Kerner, and takes into account the Runge phenomenon to solve mathematical problems of interpolation of big data monitoring and to calculate the most accurate coefficients of predictive models of Newton, Lagrange, Bayes by the criterion of correlation R2 > 0,9. The analysis was carried out to determine the most suitable mathematical data model for predicting trends and faults using various mathematical models, criteria for assessing their effectiveness, an algorithm to be used in forecasting problems, identified main difficulties and ways to solve them arising when processing large data sets. Nonlinear mathematical models, criteria for evaluating their effectiveness, an algorithm for use in forecasting problems, the main difficulties arising in the processing of large data sets and ways to solve them are considered. Difficulties in using Lagrange polynomials with an increase in interpolation nodes because of unwanted oscillations at the ends of the interval, called the Runge phenomenon, are revealed, since a feature of big data is the choice of the parameters of the forecasting function. For example, when interpolating with high-order polynomials, the effect of unwanted oscillations at the ends of the interval, called the Runge phenomenon, appears, which degrades the correlation of the data. The use of the Chebyshev polynomial is proposed to simplify the calculation of the interpolation function to minimize the error estimate for the mathematical calculation of the approximating function. The main scientific results are mathematical models and a method for predicting the state of the computing resources of the GDVK, the essence of which is the use of objective monitoring data using original mathematical models on the example of Zabbix.
Keywords:monitoring, big data, modeling, forecasting function, monitoring metrics, status control, information systems, cloud technologies.
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