Optimizing the Number of Fog Nodes for Finite Fog Radio Access Networks under Multi-Slope Path Loss Model

Fog Radio Access Network (F-RAN) is a promising technology to address the bandwidth bottlenecks and network latency problems, by providing cloud-like services to the end nodes (ENs) at the edge of the network. The network latency can further be decreased by minimizing the transmission delay, which can be achieved by optimizing the number of Fog Nodes (FNs). In this context, we propose a stochastic geometry model to optimize the number of FNs in a finite F-RAN by exploiting the multi-slope path loss model (MS-PLM), which can more precisely characterize the path loss dependency on the propagation environment. The proposed approach shows that the optimum probability of being a FN is determined by the real root of a polynomial equation of a degree determined by the far-field path loss exponent (PLE) of the MS-PLM. The results analyze the impact of the path loss parameters and the number of deployed nodes on the optimum number of FNs. The results show that the optimum number of FNs is less than 7% of the total number of deployed nodes for all the considered scenarios. It also shows that optimizing the number of FNs achieves a significant reduction in the average transmission delay over the unoptimized scenarios.