  This paper thoroughly explored the fundamental interactions between cell
association, cell load and throughput in a green (energy-efficient) small cell
network in which all base stations form a homogeneous Poisson point process
(PPP) of intensity $\lambda_B$ and all users form another independent PPP of
intensity $\lambda_U$. Cell voidness, usually disregarded due to rarity in
cellular network modeling, is first theoretically analyzed under generalized
(channel-aware) cell association (GCA). We showed that the void cell
probability cannot be neglected any more since it is bounded above by
$\exp(-\lambda_U/\lambda_B)$ that is typically not small in a small cell
network. The accurate expression of the void cell probability for GCA was
characterized and it was used to derive the average cell and user throughputs.
We learned that cell association and cell load $\lambda_U/\lambda_B$
significantly affect these two throughputs. According to the average cell and
user throughputs, the green cell and user throughputs are defined respectively
to reflect whether the energy of a base station is efficiently used to transmit
information or not. In order to achieve satisfactory throughput with certain
level of greenness, cell load should be properly determined. We presented the
theoretical solutions of the optimal cell loads that maximize the green cell
and user throughputs, respectively, and verified their correctness by
simulation.
