Minimizing Latency and Number of Controllers in Software Defined Networking

In this paper, we propose models of mathematical programming for the Placement Problem of Controllers (CPP). in wireless Software-Defined Networks (SDNs). This problem consists of locating controllers in a wireless network in such a way that each switch node can connect to at least one of the controllers with minimum latency cost. In particular, we minimize the worst latency between switch and controllers and between controllers themselves. In the objective function of our models, we further consider the minimization of the quantity of controllers in the grid. For this purpose, we assume that there is a fixed installation cost of each controller to be installed. We provide models of linear and quadratic programming that are obtained from a classic combinatorial optimization problem, namely, the installation location problem. Afterwards, by using simple convex and linearization transformation techniques, we derive three mathematical formulations for SDNs. In our numerical results, we solve optimally 12 real benchmark SDNs and compare the performance of the proposed models in terms of CPU times and number of nodes processed within the CPLEX branch and cut solver. Three scenarios were studied, the first one weights mostly the distances between switches, in which the performance of the 3 models is balanced, with higher performance of the M
3
model. The second scenario reduces the importance of the weights of the switches, in this case the M
2
model, followed by M
3
, report the best results. Finally, the last model increases the weight of the importance of having active controllers, in this case, the M
3
model clearly has a higher performance in most of the studied networks. The performance of the models was evaluated by the CPU time used to solve the instances.