Mathematical model for optimizing cloud IT infrastructure

Abstract

This research is dedicated to the formalization of a mathematical model for optimizing cloud IT infrastructure under conditions of rapidly growing demand for computing resources and increasing requirements for service performance and reliability. Cloud computing is a key paradigm of modern organizational IT infrastructure, as it provides scalability, flexibility, cost reduction, and rapid service deployment. At the same time, the growing complexity of infrastructure generates new challenges: the need to balance between resource costs and the quality of end-user service. The study analyzes the main metrics that determine the quality of cloud systems: response, latency, error rate, throughput, and availability. Particular attention is given to the “number of nines” approach in evaluating service availability. Service Level Objectives (SLOs) and Service Level Agreements (SLAs) play an important role, as they formalize system requirements and define the consequences of non-compliance. The paper explains how SLOs and SLAs can be integrated into mathematical optimization models to ensure controlled service quality while maintaining economic efficiency. The use of classical linear programming methods is proposed for solving resource allocation tasks. In the model, variables represent the quantity and types of resources (CPU, memory, bandwidth), while constraints correspond to SLO, SLA, and budget requirements. This approach makes it possible to find optimal infrastructure configurations that maximize the “performance-to-cost” ratio. Additionally, the scaling problem is considered, where optimization reduces to selecting combinations of cloud service providers’ virtual machines of different types within defined constraints. Attention is also given to modern research in the field of automatic scaling and the use of integer linear programming methods for virtual machine consolidation tasks. This extends the classical mathematical model and makes it applicable to solving real-world problems faced by cloud service providers. The results of the study demonstrate that formalizing the cloud infrastructure optimization problem through a system of metrics, SLOs, and SLAs creates a foundation for building efficient algorithms for automated resource management. The proposed approach can be applied both in scientific research and in the practical activities of companies striving to achieve a balance between cost and reliability in high-load cloud environments.