  To further improve the energy efficiency of heterogeneous networks, a
separation architecture called hyper-cellular network (HCN) has been proposed,
which decouples the control signaling and data transmission functions.
Specifically, the control coverage is guaranteed by macro base stations (MBSs),
whereas small cells (SCs) are only utilized for data transmission. Under HCN,
SCs can be dynamically turned off when traffic load decreases for energy
saving. A fundamental problem then arises: how many SCs can be turned off as
traffic varies? In this paper, we address this problem in a theoretical way,
where two sleeping schemes (i.e., random and repulsive schemes) with vertical
inter-layer offloading are considered. Analytical results indicate the
following facts: (1) Under the random scheme where SCs are turned off with
certain probability, the expected ratio of sleeping SCs is inversely
proportional to the traffic load of SC-layer and decreases linearly with the
traffic load of MBS-layer; (2) The repulsive scheme, which only turns off the
SCs close to MBSs, is less sensitive to the traffic variations; (3) deploying
denser MBSs enables turning off more SCs, which may help to improve network
energy-efficiency. Numerical results show that about 50% SCs can be turned off
on average under the predefined daily traffic profiles, and 10% more SCs can be
further turned off with inter-layer channel borrowing.
