The subject of this study is various types of network traffic in modern computer networks with a complex structure and a certain degree of self-similarity. Efficient use of network resources and ensuring the quality of service to subscribers are important tasks of computer networks. The probability of losing a message due to buffer storage device overflow is an important parameter in determining the quality of service (QoS). The mathematical model should be used to estimate this parameter. Recent advancements have resulted in many different models of packet loss probability in a router buffer. However, many models do not consider the traffic characteristics of various modern applications and protocols. The traffic in modern computer networks has a complex structure and often has a certain degree of self-similarity. Currently, a large number of models are available for estimating the probability of packet loss due to buffer overflow. The goal of this work is to perform a comparative analysis of such models and provide recommendations for their use and to estimate the influence of network traffic fractality on the probability of packet loss in a router due to buffer overflow. The tasks to be solved are as follows: 1) to conduct an analysis of analytical models that describe the packet loss probability in a router considering the influence of fractality and without it; 2) to construct the dependencies of the packet loss probability in the router on the data transmission channel load for different buffer capacity values, the Hurst exponent, and traffic deviation; and 3) to describe the dependences of the packet loss probability on the buffer capacity for different channel load values. Comparative analysis of various methods of fractal traffic modeling and simulation with different storage capacity, Hurst exponent, deviation coefficients, and channel load factor values is used. The following results were obtained: 1) The M/M/1 queuing system model gives the most optimistic estimate. This estimate can be used as a lower bound for the message loss probability for a given buffer capacity and a channel load factor; 2) the highest message loss probability was observed when using queuing systems with a Hurst exponent of 0.95; 3) the packet loss probability also increased with an increasing traffic fractality and deviation coefficient; 4) the influence of fractality decreased with an increase in the buffer capacity was found; 5) an objective estimation of the message loss probability due to a router buffer overflow can only be made by considering the nature of the traffic. Conclusions. The main contribution of this research is that various types of network traffic have a fractal nature, and the traditional methods of route service specification, such as traffic using the M/M/1 queuing model, give more errors. Because of the research conducted to reduce the impact of traffic fractality, increasing the capacity of buffer storage devices is necessary.
The subject are mathematical models of decision-making under uncertainty in a production environment with human presence. The research objectives: is to form a safe and effective policy for controlling the motion of a three-link collaborative robot-manipulator, by developing a mathematical model of a partially observable Markov decision process (POMDP). Methods: methodology of partially observable Markov processes (POMDP), numerical modeling, approximation of the expected reward, comparative analysis of scenarios with different risk parameters. Results: the implemented model is able to form an adaptive policy for the manipulator's behavior taking into account incomplete information about the person's position; the dependence of optimal actions on the probability distribution of the human position and the intensity of the risk penalty is demonstrated; the influence of the difference in rewards between the fast movement and stop modes on the choice of actions is shown. Conclusions: the developed POMDP model can be used as a basis for building high-level adaptive control of a collaborative manipulator in a shared workspace with a human. The proposed approach has the prospect of being implemented in flexible production systems and cyber-physical complexes, in particular, taking into account dynamic risk reassessment and integration with computer vision algorithms.
The subject matter of the article is the efficiency analysis of greedy optimization algorithms for subset selection in distributed systems under delta-matroid constraints. The goal is to compare the performance of the classical unconstrained greedy algorithm and the GREEDI algorithm with delta-matroid constraints in terms of solution quality, computational characteristics, and scalability. The tasks to be solved are: to implement both algorithms; to perform simulations on synthetic graph datasets with sizes ranging from 10 to 100 nodes; to benchmark computational efficiency and approximation quality; to analyze the impact of delta-matroid constraints on benefit maximization and distributed execution. The methods used are: graph-based modeling, combinatorial optimization under matroid-type constraints, approximation algorithms, and distributed processing frameworks. The following results were obtained: GREEDI consistently provided higher-benefit subsets compared to the unconstrained greedy algorithm, achieving better trade-offs between execution time and solution quality; the distributed processing framework demonstrated scalability for large datasets and supported real-time responsiveness; performance advantages were more pronounced for larger graphs and higher constraint densities. Conclusions. The scientific novelty of the results obtained is as follows: 1) an experimental validation of the GREEDI algorithm under delta-matroid constraints for distributed subset selection was carried out; 2) the influence of such constraints on approximation quality and computational characteristics was quantified; 3) a scalable real-time processing approach for large graph-structured data was proposed, enabling potential applications in sensor deployment, recommendation systems, feature selection, and cache optimization.
The subject of this study is the digital transformation of the occupational safety management system in civil aviation. Owing to the country’s unique geopolitical position in the centre of Eurasia, the Republic of Kazakhstan’s rapid growth in cargo and passenger traffic is associated with increasing employee risks, making it critically necessary to review existing occupational safety management systems. Traditional approaches to occupational safety management, which often focus on reactive elimination of consequences, are insufficiently effective in the context of the dynamic development of a high-tech industry, where every incident has serious economic, reputational, and social repercussions. It is possible to improve occupational safety by applying advanced digital technologies, in particular digital twin and AI agent technologies, which are capable of continuously accumulating, processing, and transmitting vast amounts of data in real time through self-learning, creating a comprehensive picture of an aviation enterprise’s entire occupational safety management system’s functioning. This study aims to justify the feasibility of modifying the occupational safety management system in civil aviation in the Republic of Kazakhstan by integrating digital twin and AI agent technologies into key functional processes. Results. The proposed algorithm for the developed AI agent, which is explicitly designed for integration into the occupational safety management systems of aviation enterprises in Kazakhstan, is the key contribution of this study. Its architecture, operating principles, and algorithms for interacting with big data received from digital twins of various elements of the aviation system are described in detail, ranging from the condition of aircraft and ground equipment to the personnel’s psychophysiological indicators and the working environment’s characteristics. This algorithm enables the AI agent to detect anomalies and build predictive models, signalling potential threats in advance. The results of the AI agent’s risk assessment in the civil aviation occupational safety system have been visualised, demonstrating its high efficiency in identifying vulnerabilities, predicting critical situations and forming informed, personalised recommendations for their prevention. The research results demonstrate how proactive monitoring and analysis performed by an AI agent based on digital twin data can significantly reduce the likelihood of injuries and occupational diseases. Conclusions. The proposed approach to modifying the occupational safety management system at civil aviation enterprises is based on the synergistic integration of digital twins and AI agents, whereby risk management shifts from reactive elimination to preventive modelling and mitigation of potential threats. The creation of an occupational safety management system at the country’s aviation enterprises, based on the use of digital twins and AI agents, will significantly increase the competitiveness of civil aviation in the Republic of Kazakhstan on the world market, positioning it as a leader in the application of high-tech solutions for ensuring occupational safety and sustainable development.
The object of the study is a formalized model of requirements traceability in project documentation for hardware-software systems. The subject matter of the research encompasses the application of mathematical modeling and tool-based approaches to automate the traceability process, focusing on the design and functionality of the TraceTrend software tool. The primary goal of the study is to improve the quality and integrity of requirements management by implementing traceability mechanisms that ensure logical consistency, hierarchical correctness, and complete test coverage across all project documentation stages. The research tasks include: identifying challenges related to manual requirements tracing in safety-critical domains; constructing a formal mathematical model based on set theory, binary relations, and directed graphs; defining binary matrices for requirement inheritance and test coverage; developing automated analysis techniques for traceability conditions; integrating the model into the TraceTrend tool; and demonstrating its applicability through a real-world case study. The study employed the following methods: mathematical modeling of binary relations, model-based testing, static analysis of documentation structures, and the use of Boolean matrix operations for verifying coverage and consistency. As a result of the research, a formal model of requirements traceability was created and implemented in the TraceTrend tool. The tool enables automated extraction of requirement identifiers, construction of traceability matrices, and verification of coverage and logical completeness. The application of TraceTrend has shown its effectiveness in identifying undocumented requirements, broken dependencies, and gaps in test coverage early in the project lifecycle. Conclusions. The integration of formal models and traceability tools significantly strengthens the reliability and auditability of requirements management processes in engineering projects. TraceTrend has proven to be a valuable instrument for improving documentation quality and supporting compliance with standards such as IEC 61508 and ISO/IEC/IEEE 29148. Although the tool requires initial configuration for requirement markup, its benefits in enhancing visibility, consistency, and verification readiness justify its adoption in high-assurance development environments. The study confirms the necessity of embedding formal traceability analysis into standard project workflows to ensure both structural rigor and regulatory compliance.
