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Subject of Research. The existing approaches to the automatic scaling of non-stationary operating cloud systems are analyzed. The drawbacks of the existing approaches to workload prediction are revealed due to the insufficient performance of the algorithms being used. The analysis of the properties of periodic non-stationary processes and automatic length estimation of their period are performed on the basis of measured data. The accuracy of the developed analytical models was confirmed in the course of numerous simulation experiments in the AnyLogic Professional modeling environment. Method. The basis of the developed method of automatic length estimation of the non-stationary processes period is the consistent approximation of the intermediate result to the desired value. The proposed method ranks the expected results in accordance with the probability of their compliance with the determined period of the non-stationary process. Main Results. The possibility is provided toestimate the period length for an adequate time. The testing was carried out on a system with an AMD FX 8120 CPU with a clock frequency of 3.1 GHz in one thread. The original signal was generated with amplitude 1. The waveform, the period value, the amplitude multiplier and the magnitude of the superimposed random noise were varied. According to the data from the largest transport network hub of Russia, Joint-Stock Company Center for Interaction of Computer Networks MSK-IX, the period of total transit traffic has been successfully determined, and also the periods of non-stationary processes for the cloud system model have been successfully determined. Practical Relevance. The developed method can be used as part of the services of cloud systems automatic scaling and provides more efficient management of the infrastructure resources of cloud computing systems.

In queuing systems modeling it is traditionally assumed that the distribution of the inter-arrival time between requests entering the system is unimodal. At the same time, in practice, systems with a multimodal inter-arrival time distribution having two or more modes are encountered. The multimodal distribution is usually replaced by a unimodal one with appropriate numerical moments, which simplifies the modeling process, but introduces a methodical error in the obtained results. The subject of the study is the analysis of properties of multimodal flows and the estimation of such an error. Simulation modeling in the AnyLogic environment is used as a re-search method provided to discover the error dependence on the system load. It was revealed that in the high-load systems the error introduced by the replacement is not higher than 15%, but with a decrease in the system load, the error increases and can reach hundreds of percent. In the course of extensive experiments, it was found out that with an increase in the inter-arrival time the value of the variation coefficient between incoming queries in a polymodal flow tends to a constant value not greater than unity. The practical importance of the work lies in simplification of design process for high-load computing systems with the use of simulation and analytical models by replacing the polymodal flows with unimodal providing required accuracy of calculations.