  In this study, we investigate the operation of user-number threshold-based
base station (BS) on/off control, in which the BS turns off when the number of
active users is less than a specific threshold value. This paper presents a
space-based analysis of the BS on/off control system to which a stochastic
geometric approach is applied. In particular, we derive the approximated
closed-form expression of the coverage probability of a homogeneous network
(HomNet) with the user-number threshold-based on/off control. Moreover, the
optimal user-number threshold for maximizing the coverage probability is
analytically derived. In addition to HomNet, we also derive the overall
coverage probability and the optimal user-number thresholds for a heterogeneous
network (HetNet). The results show that HetNet, the analysis of which seems
intractable, can be analyzed in the form of a linear combination of HomNets
with weighted densities. In addition, the optimal user-number threshold of each
tier is obtained independently of other tiers. The modeling and analysis
presented in this paper are not only limited to the case of user-number
threshold-based on/off control, but also applicable to other novel on/off
controls with minor modifications. Finally, by comparing with the simulated
results, the theoretical contributions of this study are validated.
