  This study aims to introduce and address the problem of traffic load
estimation in the cell switching concept within the evolving landscape of
vertical heterogeneous networks (vHetNets). The problem is that the practice of
cell switching faces a significant challenge due to the lack of accurate data
on the traffic load of sleeping small base stations (SBSs). This problem makes
the majority of the studies in the literature, particularly those employing
load-dependent approaches, impractical due to their basic assumption of perfect
knowledge of the traffic loads of sleeping SBSs for the next time slot. Rather
than developing another advanced cell switching algorithm, this study
investigates the impacts of estimation errors and explores possible solutions
through established methodologies in a novel vHetNet environment that includes
the integration of a high altitude platform (HAPS) as a super macro base
station (SMBS) into the terrestrial network. In other words, this study adopts
a more foundational perspective, focusing on eliminating a significant obstacle
for the application of advanced cell switching algorithms. To this end, we
explore the potential of three distinct spatial interpolation-based estimation
schemes: random neighboring selection, distance-based selection, and
clustering-based selection. Utilizing a real dataset for empirical validations,
we evaluate the efficacy of our proposed traffic load estimation schemes. Our
results demonstrate that the multi-level clustering (MLC) algorithm performs
exceptionally well, with an insignificant difference (i.e., 0.8%) observed
between its estimated and actual network power consumption, highlighting its
potential to significantly improve energy efficiency in vHetNets.
