Yavorska O. Traffic flow optimization in software-defined telecommunication networks via the minimum-transit method on an ST-planar free-oriented graph.

This dissertation addresses the pressing scientific and practical problem of improving the performance of software-defined telecommunications networks based on modern models of optimization and digital traffic distribution. The main focus is on developing a method that effectively utilizes the property of modern communication channels to dynamically redistribute bandwidth in the forward and reverse directions. The dissertation presents the results of scientific research and practical developments aimed at improving known methods for optimizing transport flows. This made it possible to increase the performance of a software-configurable telecommunications network by developing a minimum transit method on an ST-planar freely-oriented graph and by implementing software algorithms to solve forward and reverse optimization problems. The study analyzes existing MaxFlow models and identifies their limitations in dynamically reconfigurable networks, particularly within SDN architectures. The use of an ST-planar free-oriented graph is substantiated as an adequate mathematical model for modern telecommunication networks. An improved telecommunication network model based on a normalized Free-Oriented Graph (FOG) is proposed. In this model, each edge has a fixed total capacity that can be flexibly distributed between opposite directions. A forward optimization problem is formulated to determine edge load metrics for a given flow distribution, along with a corresponding solution algorithm. A reverse optimization problem is developed to determine both the maximum flow and its distribution across independent paths. A modified iterative algorithm (MIA) is proposed, incorporating batch path processing and a Max Selection procedure. The algorithm is implemented in Python and adapted for operation in an SDN environment using Mininet and the Ryu controller. Simulation and experimental studies confirm the correctness and efficiency of the proposed approach. The method demonstrates advantages over classical routing strategies (Shortest Path, ECMP, Adaptive Routing) due to better bandwidth utilization and avoidance of bottlenecks. Experimental validation under high traffic load conditions confirms the stability and effectiveness of the MIA algorithm. The main results of the work are as follows: 1. The model of a software-defined telecommunication network (SDN) is improved by introducing an adaptive network graph metric, which differs from known models in that each edge has a fixed total bandwidth capacity that can be arbitrarily distributed between flows in forward and reverse directions. This ensures maximal utilization of SDN network resources and increases network performance. 2. The method for solving the maximum flow problem in an SDN network is improved through packet-based computation of flow distribution over independent routes between the poles of a free-oriented graph. Unlike known methods, at each iteration only the residual weights of edges included in previously found routes are updated. This allows the SDN controller to analyze the current channel load state and direct computational resources exclusively toward modification of active routes. 3. The method of route selection for flow distribution in an SDN network is improved by analyzing routes of equal length with shared edges, differing from known approaches in that the route with the maximum possible flow is selected first, which reduces the number of algorithm iterations and increases its execution speed. The results of the study have been implemented in an experimental SDN network of the Joint-Stock Company “Ukrtelecom” (Odesa) and in the educational process of the State University of Intelligent Technologies and Telecommunications. Keywords: Software-Defined Networking (SDN), telecommunication network, wireless channel, maximum flow problem (MaxFlow), optimization, transport flows, throughput, computer modeling, minimal transit method, Modified Iterative Algorithm (MIA), ST-planar free-oriented graph, traffic, Quality of Service (QoS), routing, network configuration.