A β-Fractile Probabilistic Constrained Approach for Visible Light Communication Networks

In this paper, we propose a stochastic mixed integer linear programming (MILP) model in order to minimize the total number of slots and power consumption in a visible light communication (VLC) network subject to spatial time division multiple access constraints. The stochastic nature in our model comes from the fact that power in each link of the network is affected by wireless channel conditions which can be modelled by means of random variables. In particular, we apply a β-Fractile probabilistic constrained approach and transform the proposed model into a deterministic equivalent MILP using scenario samples for each random variable. We generate random disk graph instances with different densities and radial transmission ranges for direct Line of Sight (LOS) communication using VLC formulas. Our preliminary numerical results indicate that less optimal power values can be achieved using scenarios compared to the averaged model. Although, the optimal solutions are obtained at a significantly higher CPU time.