  There have been a bulk of analytic results about the performance of cellular
networks where base stations are regularly located on a hexagonal or square
lattice. This regular model cannot reflect the reality, and tends to
overestimate the network performance. Moreover, tractable analysis can be
performed only for a fixed location user (e.g., cell center or edge user). In
this paper, we use the stochastic geometry approach, where base stations can be
modeled as a homogeneous Poisson point process. We also consider the user
density, and derive the user outage probability that an arbitrary user is under
outage owing to low signal-to-interference-plus-noise ratio or high congestion
by multiple users. Using the result, we calculate the density of success
transmissions in the downlink cellular network. An interesting observation is
that the success transmission density increases with the base station density,
but the increasing rate diminishes. This means that the number of base stations
installed should be more than $n$-times to increase the network capacity by a
factor of $n$. Our results will provide a framework for performance analysis of
the wireless infrastructure with a high density of access points, which will
significantly reduce the burden of network-level simulations.
