  This paper studied the fundamental modeling defect existing in
Poisson-distributed cellular networks 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 $\lambda_U$. The modeling defect,
hardly discovered in prior works, is the void cell issue that stems from the
independence between the distributions of users and BSs and "user-centric" cell
association, and it could give rise to very inaccurate analytical results. We
showed that the void probability of a cell under generalized random cell
association is always bounded above zero and its theoretical lower bound is
$\exp(-\frac{\lambda_U}{\lambda_B})$ that can be achieved by large association
weighting. An accurate expression of the void probability of a cell was derived
and simulation results validated its correctness. We also showed that the
associated BSs are essentially no longer a PPP such that modeling them as a PPP
to facilitate the analysis of interference-related performance metrics may
detach from reality if the BS intensity is not significantly large if compared
with the user intensity.
