Limit of the Transport Capacity of a Dense Wire- Less Network

It is known that the transport capacity of a dense wireless ad hoc network with n nodes scales like √ n. We show that the transport capacity divided by √ n approaches a non-random limit with probability one when the nodes are i.i.d uniformly distributed on the unit square. To show the existence of the limit we prove that the transport capacity under the protocol model is a subadditive Euclidean functional and use the machinery of subadditive functions in the spirit of Steele.