Потоки інформації в мережі з обмеженнями кількості потоків, дозволених на кожному вузлі

Abstract

This paper explores a classic problem in transport network research: the analysis of networks with specified total traffic values for each node. We employ linear algebraic methods to derive a comprehensive set of solutions, ensuring statistical reliability and enabling robust analysis of the results. A mathematical model is presented for determining solution sets in fully connected, loop-free networks with three and four nodes. Based on this model, we developed software to calculate the statistical distribution of entropy values within the network. Furthermore, we investigate the statistical properties of information flow entropy for networks with and without constraints that permit uniform flow distribution. This characteristic holds practical significance for analyzing network dynamics and predicting flow redistribution processes from initial unbalanced states, which inherently proceed towards higher entropy. The findings presented in this paper hold additional practical implications for network imbalance detection and adaptability to diverse network topologies. The results can serve as a foundation for algorithms designed to quantify the degree of network imbalance induced by substantial external influences that do not significantly alter the overall network load. This capability proves particularly valuable in identifying covert DDoS (Distributed Denial of Service) attacks that aim to reduce network bandwidth by supplanting legitimate traffic. While the proposed method has been demonstrated on fully connected networks, it demonstrates potential for adaptation to networks with a wide range of topological structures. This includes networks with partial connectivity or loosely connected networks, which constitute a significant proportion of real-world networks. The significance of the method is further amplified by advancements in cloud computing technologies, which offer substantial computational power and enable the accumulation of extensive statistics regarding information flow distributions across networks of diverse purposes. Such advancements create opportunities for the integration of the developed network analysis technique with machine learning and artificial intelligence technologies, fostering enhanced automation, scalability, and adaptability.