This study solves the task to redistribute the load on a geographically distributed foggy environment in order to achieve a load balance of virtual clusters. The necessity and possibility of developing a universal and at the same time scientifically based approach to load balancing has been determined. Object of study: the process of redistribution of load in a foggy environment between virtual, geographically distributed clusters. A load balancing method makes it possible to reduce delays and decrease the time for completing tasks on foggy nodes, which brings task processing closer to real time. To solve the task, a mathematical model of the functioning of a separate cluster in a foggy environment has been built. As a result of modeling, the problem of finding the optimal distribution of tasks across the nodes of the virtual cluster was obtained. The limitations of the problem take into account the characteristics of the physical nodes of support for the virtual cluster. The process of distributing the additional load was also simulated through the graph representation of tasks entering virtual clusters. The task to devise a method for load transfer between virtual clusters within a foggy environment is solved using the proposed iterative algorithm for finding a suitable cluster and placing the load. The simulation results showed that the balance of the foggy environment when using the proposed method increases significantly provided the network load is small. The scope of application of the results includes geographically distributed foggy systems, in particular the foggy layer of the industrial Internet of Things. A necessary practical condition for using the proposed results is the non-exceeding the specified limit of the total load on the foggy medium, usually 70 %
The object of this study was the process of detecting anomalies in computer systems. The task to timely detect anomalies in computer systems was solved, based on a mathematical model underlying which is the criteria for uniformity of samples of input data. The necessity and possibility to devise a universal and at the same time scientifically based approach to tracking the states of the system were determined. Therefore, the purpose of this work was to develop a methodology for determining the general criterion of anomaly in the behavior of a computer system depending on the input data. This will increase the reliability of identifying the anomaly in the behavior of the system, which, in turn, should increase its safety. To solve the problem, a mathematical model for detecting anomalies in the behavior of a computer system has been built. The mathematical model differs from the well-known ones in the possibility of isolating a series of observations, the results of which show the anomaly in the behavior of the computer system. This made it possible to ensure the necessary level of reliability of the results of monitoring and research. In the process of modeling, the criteria for uniformity of samples of input data have been investigated and improved. The expediency of using the improved criterion of uniformity of samples of input data in the case of a significantly unequal distribution of values from the sensors of computer systems has been proved. An algorithm for the functioning of the software test tool has been developed. The results of the study showed that the confidence probability that the value of the statistical values of the shift in a certain criterion does not deviate from the mathematical expectation by more than 0.05 is approximately equal to 0.94. The scope of the obtained results is systems for detecting anomalies of computer systems. A necessary condition for the use of the proposed results is the presence of a series of observations of the state of the computer system
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