Probabilistic Constrained Approach for Clustering in Multi-Cell Wireless Networks

Abstract

In this paper, we consider two probabilistic constrained approaches for clustering in multi-Cell wireless networks, namely a β-Fractile and a β-Risk modeling approaches. The underlying idea is to assign users to different base stations (BSs) in a wireless network while respecting the condition that no two adjacent BSs can operate simultaneously due to interference requirements. For this purpose, we formulate the multi-cell allocation problem as a deterministic problem first, and then we introduce probabilistic constraints in the model. Subsequently, we transform the probabilistic model into deterministic equivalent mixed integer linear and quadratic programming problems by using scenarios for each random parameter. All the proposed models are intended to minimise the total power consumption of the network subject to user assignment and independent set constraints on the BSs. We compare all our proposed models using disk graph instances with radial transmission ranges of 20 to 40 ms and for different number of scenarios. Our preliminary numerical results indicate that the β-Fractile approach allows to achieve higher power savings when compared to the average optimal solution obtained with the original deterministic formulation. Whilst β-Risk models allow to obtain feasible solutions at a significantly less CPU time, although the models in this case are more sensitive to threshold power values.