The transport capacity of a wireless network is a subadditive euclidean functional

The transport capacity of a dense ad hoc network with n nodes scales like radicn. We show that the transport capacity divided by radicn approaches a non-random limit with probability one when the nodes are i.i.d. distributed on the unit square. 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 to show the existence of the limit.