Analysis of Cell Sojourn Time in Heterogeneous Networks With Small Cells

Recently, heterogeneous networks with small cells have been widely used to increase the capacity of mobile systems. In such environments, accurate estimation of the mean cell sojourn time is critical for evaluating the performance of the network and its applications. It is especially important to analyze the cell sojourn times of mobile users as they reside in different network tiers: either macro-cell-only or small-cell-covered areas. But because small cells are deployed in an irregular manner, it is difficult to derive the analytical mean cell sojourn time in a macro-cell-only area. In this letter, we propose a novel approach to resolve this difficulty. We developed a simple but effective trick that approximates the heterogeneous network to a discrete grid so that it becomes tractable, making it possible to derive the analytical mean sojourn time in the macro-cell-only area. Simulation results confirm that the proposed method has excellent accuracy for general random walk mobility models including random waypoint, Brownian motion, tailored Brownian motion, and truncated Levy walk.