Mathematical Models for Minimizing Latency in Software-Defined Networks

In this paper, we propose mixed-integer quadratic and linear programming models to minimize the worst latency in software-defined wireless networks (SDNs). Our models are adapted from classical combinatorial optimization problems referred to as the p-median and stable set problems in the literature. For each of the two adapted models, we further derive two additional formulations. The latter is achieved by applying simple convex and linearization techniques. In summary, we obtain six mathematical formulations for minimizing latency in SDNs. We conduct substantial numerical experiments to compare the behavior of all the proposed models in terms of CPU times, the number of branch and bound nodes, and the optimal solutions obtained with the CPLEX solver. Our numerical results indicate that the first linear model allows one to obtain the optimal solution of each instance in significantly less CPU time than the other ones. Finally, we test all our models for different numbers of controllers and switches in the network while varying the degree of importance between the worst shortest path distances of switch-controller and inter-controller pairs.