  Future mobile networks are converging toward heterogeneous multi-tier
networks, where various classes of base stations (BS) are deployed based on
user demand. So it is quite necessary to utilize the BSs resources rationally
when BSs are sufficient. In this paper, we develop a more realistic model that
fully considering the inter-tier dependence and the dependence between users
and BSs, where the macro base stations (MBSs) are distributed according to a
homogeneous Poisson point process (PPP) and the small base stations (SBSs)
follows a Matern cluster process (MCP) whose parent points are located in the
positions of the MBSs in order to offload the users from the over-loaded MBSs.
We also assume the users are just randomly located in the circles centered at
the MBSs. Under this model, we derive the association probability and the
average ergodic rate by stochastic geometry. An interesting result that the
density of MBS and the radius of the clusters jointly affect the association
probabilities in a joint form is obtained. We also observe that using the
clustered SBSs results in aggressive offloading compared with previous cellular
networks.
