RADIOELECTRONIC AND COMPUTER SYSTEMS

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.

network; packet; packet loss probability; routing; buffer; traffic fractality; Hurst Exponent

Millán, G., Lefranc, G., Osorio-Comparán, R., & Lomas-Barrie, V. Time series analysis of computer network traffic in a dedicated link aggregation. Preprint for IEEE Transactions on Information Theory 2021. 7 р. DOI: 10.48550/arXiv.2107.05484.

Dymora, P., & Mazurek, M. Influence of model and traffic pattern on determining the self-similarity in IP networks. Applied sciences, 2021, vol. 11, iss. 1, article 190. DOI: 10.3390/app11010190.

Millán, G., & Lefranc, G. Presentation of an estimator for the Hurst parameter for a self-similar process representing the traffic in IEEE 802.3 networks. International Journal of Computers, Communications & Control (IJCCC), 2009, vol. 4, no. 2, pp. 137-147. DOI:10.15837/ijccc.2009.2.2421.

Bunimovich, L., & Skums, P. Fractal networks: Topology, dimension, and complexity. Chaos, 2024, vol. 34, iss. 4, article 042101. ISSN: 1054-1500. DOI: 10.1063/5.0200632.

Mohammed, A. M., & Agamy, A. F. A survey on the common network traffic source models. International Journal of Computer Networks (IJCN), 2011, vol. 3, iss. 2, pp. 103-115. Available at: https://www.cscjournals.org/library/manuscriptinfo.php?mc=IJCN-136 (accessed 20.01.2025).

Melo, E. F., & de Oliveira, H. M. An overview of self-similar traffic: its implications in the network design. Revista de Tecnologia da Informação e Comunicação, 2020, vol. 9, no. 1, pp. 38-46. DOI: 10.48550/arXiv.2005.02858.

Dymora, P., Mazurek, M., & Strzalka, D. Computer network traffic analysis with the use of statistical self-similarity factor. Annales Universitatis Maiae Curie-Sklodowska, Sectio AI Informatica, 2013, vol. 13, no. 1, pp. 69-81. DOI:10.2478/v10065-012-0040-0.

Bhoi, R., & Mishra, S. Analysis and fractal behavior of network traffic data based on topology. International Journal of Engineering Science Invention, 2017, vol. 6, iss. 10, no. 1, pp. 66-69. Available at: http://www.ijesi.org/papers/Vol(6)10/Version-1/K0610016669.pdf (accessed 20.01.2025).

Millan, G., Osorio-Comparan, R., & Lefranc, G. Preliminaries on the accurate estimation of the hurst exponent using time series. Proceedings of 2021 IEEE International Conference on Automation/24th Congress of the Chilean Association of Automatic Control, (ICA - ACCA), 2021, article 9465274. DOI: 10.1109/ICAACCA51523.2021.9465274.

Sivaroopan, N., Silva, K., Madarasingha, C., Dahanayaka, T., Jourjon, G., Jayasumana, A., & Thilakarathna, K. A Comprehensive survey on network traffic synthesis: from statistical models to deep learning. arXiv e-prints, 2025. 33 р. DOI: 10.48550/arXiv.2507.01976.

Han, D., Li, H., Fu, X., & Zhou, S. Traffic feature selection and distributed denial of service attack detection in software-defined networks based on machine learning. Sensors, 2024, vol. 24, article no. 4344. 22 р. DOI:10.3390/s24134344.

Zaidyn, M., Akhtanov, S., Turlykozhayeva, D., Temesheva, S., Akhmetali, A., Skabylov, A., & Ussipov, N. Fractality of wireless mesh networks: dimensional effects on network performance. arXiv e-prints, 2025. 11 р. DOI: 10.48550/arXiv.2506.19366.

Meleshko, Y., Drieieva, H., Drieiev, O., Yakymenko, M., Mikhav, V., & Shymko, S. A method of routing of fractal-like traffic with prediction of router load for reduce the probability of network packet loss. Proceedings of the 7th International Conference on Computational Linguistics and Intelligent Systems (CoLInS), 2023, vol. 3 pp. 434-448. Available at: https://ceur-ws.org/Vol-3403/paper34.pdf (accessed 20.01.2025).

Castellanos-López, S. L., Cruz-Perez, F. A., Rivero Ángeles, M. E., & Hernandez-Valdez, G. Count and Teletraffic Analysis of G/M/1 Queueing Systems with Log-Normal Interarrival Time of Bursty IoT Traffic. IEEE Access, 2025, vol. 13, pp. 50611-50634. DOI: 10.1109/ACCESS.2025.3543460.