Aggregation of variables in load models for interference-coupled cellular data networks

In order to meet increasing traffic demands, future generations of cellular networks are characterized by decreasing cell sizes at full frequency reuse. Due to inevitable inter-cell interference, load conditions in neighboring cells can no longer be considered independent. Unfortunately, the adequate flow level model for such a setup is analytically intractable. Utilizing aggregation techniques, which were originally proposed to analyze large state models in economics, we propose a framework to compute the average base station loads based on an approximation of the joint stationary distribution of the number of active flows in all cells. The technique proposed requires solving a system of linear equations whose dimension increases exponentially with the number of cells. Since such a system is essentially intractable for large networks, we propose a fixed point algorithm to compute approximate base station loads based on the notion of average interference. Numerical results validate the accuracy of both modeling techniques. The modeling approach presented in this paper is essential for accurate characterization of cell throughput as well as base station energy consumption under varying load conditions.