A Bi-Level Programming Approach for Software Defined Networks

This paper addresses the management of software-defined networks (SDN) by minimizing latency for switches and controllers. We consider scenarios with a fixed number of controllers as well as scenarios where the model determines the optimal number of controllers. Our goal is to maximize link capacity utilization while imposing an upper bound to prevent overload and maintain balanced infrastructure. More precisely, we propose a Bilevel Programming approach for the problem where the goal is to optimize latency for the leader and maximize capacity for the lower-level user programming problem. To tackle the proposed model, we derive two alternative models while using linearization techniques to make the problem more computationally tractable using the Gurobi solver. To our knowledge, this is the first time that a bilevel approach is considered for latency management and capacity in SDN, offering an innovative and efficient solution. Based on numerical experiments, we observe that the model with variable controller allocation outperforms the fixed-controller model in terms of CPU time and solution quality for most of the studied Benchmark instances. Our proposed models achieve optimal solutions for most of the tested instances, highlighting the importance of proper mathematical formulations and demonstrating how efficient optimization can enhance SDN performance. Finally, enabling applications in larger and more complex wireless network scenarios. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.