Minimizing the Worst Arc Flow Localizing Switch and Controller-Type Nodes in a Software-Defined Network

This article considers the strategic management of traffic within a Software-Defined Network (SDN) framework. We explore two different models. The first one is designed with a clear objective: to minimize the worst flow of data through individual connections within the studied SDN. This entails identifying and addressing potential bottlenecks to optimize network performance. Moreover, we aim to achieve this objective while strategically selecting an appropriate number of controllers. Conversely, the second model takes on a similar challenge but within the context of a predefined and fixed number of controllers. To facilitate our study, we use 13 real-world network scenarios. We subject these networks to rigorous testing using our models and harness the computational capabilities of the CPLEX software to derive the solutions. Our endeavor represents a pioneering effort in the mathematical modeling of optimization within this specific network paradigm. After a rigorous analysis of our test results, it becomes apparent that the efficacy of the first model is closely correlated with the scale of the network under consideration. Furthermore, we observe that solutions derived from the second model remain remarkably stable despite fluctuations in the number of controllers, ranging from 20% to 40% of the network size. These empirical insights provide a deep understanding of the underlying functionalities and optimization dynamics of these models. Ultimately, these findings contribute to the refinement of network efficiency and performance within the realm of SDN.