Capacity and Stable Scheduling in Heterogeneous Wireless Networks
  Heterogeneous wireless networks (HetNets) provide a means to increase network capacity by introducing small cells and adopting a layered architecture. HetNets allocate resources flexibly through time sharing and cell range expansion/contraction allowing a wide range of possible schedulers. In this paper we define the capacity of a HetNet down link in terms of the maximum number of downloads per second which can be achieved for a given offered traffic density. Given this definition we show that the capacity is determined via the solution to a continuous linear program (LP). If the solution is smaller than 1 then there is a scheduler such that the number of mobiles in the network has ergodic properties with finite mean waiting time. If the solution is greater than 1 then no such scheduler exists. The above results continue to hold if a more general class of schedulers is considered. 
Stephen V. Hanly, Chunshan Liu, Phil Whiting
cs.NI