Stochastic Geometry Analysis of Sojourn Time in RF/VLC Hybrid Networks

The spectrum scarcity in the radio frequency (RF) communication in indoor environments motivates the integration of an alternative technology like visible light communication (VLC) with the existing RF architecture that results in a hybrid RF/VLC network. While VLC helps offloading the congested RF spectrum by offering capacity-per-area improvements, the resulting heterogeneity and narrow coverage areas of optical base stations (BSs) impose several challenges for user mobility such as unnecessary handovers. To help addressing these challenges, in this paper, we derive the mean and the distribution of sojourn time in RF/VLC hybrid networks. The mathematical analysis conducted in this paper makes use of the tools from stochastic geometry and abstracting the BSs’ locations via two independent homogeneous Poisson point processes (PPPs). Since PPP modeling is yet to be well established for RF/VLC hybrid networks, we compare the PPP based analytical results to those obtained for an actual deployment, a Matérn hard-core point process (MHCPP) based deployment, and a deterministic square lattice deployment of VLC luminaries. Furthermore, we utilize the sojourn time distribution to calculate the unnecessary handover probability. Our numerical results show the interplay between the sojourn time and the receiver field of view as a function of BS density and they highlight the cost of BS densification in terms of unnecessary handovers.