  For two-tier networks consisting of macrocells and femtocells, the channel
access mechanism can be configured to be open access, closed access, or hybrid
access. Hybrid access arises as a compromise between open and closed access
mechanisms, in which a fraction of available spectrum resource is shared to
nonsubscribers while the remaining reserved for subscribers. This paper focuses
on a hybrid access mechanism for multi-channel femtocells which employ
orthogonal spectrum access schemes. Considering a randomized channel assignment
strategy, we analyze the performance in the downlink. Using stochastic geometry
as technical tools, we model the distribution of femtocells as Poisson point
process or Neyman-Scott cluster process and derive the distributions of
signal-to-interference-plus-noise ratios, and mean achievable rates, of both
nonsubscribers and subscribers. The established expressions are amenable to
numerical evaluation, and shed key insights into the performance tradeoff
between subscribers and nonsubscribers. The analytical results are corroborated
by numerical simulations.
