The subject of the research is models and methods for optimizing resource and task management in the fog computing environment of the Internet of Things (IoT). The increasing number of connected devices and the volumes of data collected in IoT networks make it essential to improve management systems that ensure the optimal distribution of tasks and resources. Fog computing addresses this challenge by distributing computational tasks closer to data sources and end-users. The goal of this work is to enhance the efficiency of fog computing technologies to achieve optimal task and resource allocation in IoT networks. The main tasks of this work are as follows. Firstly, considering the diverse requirements of computational resources and tasks in IoT, reviewing existing methods and developments in the field is necessary. Secondly, it is essential to investigate and compare clustering methods, particularly DBSCAN and C-Means, for effective resource management. The DBSCAN clustering method enables efficient task distribution based on their location, while the C-Means method allows grouping resources based on their characteristics. The final task involves developing a mathematical model that considers input parameters such as system response, cluster resource requirements, data proximity to processing, etc. This model will enable the analysis of potential scenarios and decision-making regarding the optimal distribution of tasks and resources in the IoT environment. Conclusion. This research aims to solve the urgent problem of managing resources and tasks in the fog IoT environment. A review of existing methods and developments in resource and task management in IoT is conducted. DBSCAN and C-Means clustering methods are compared to determine their effectiveness in resource management. A set-theoretic model is developed that considers various parameters for making optimal decisions on the distribution of tasks and resources. It is established that the use of clustering methods and the developed model help to improve system performance and ensure more efficient use of fog computing resources in the IoT environment.
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