The Transport Capacity of a Wireless Network is a Subadditive Euclidean Functional

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The transport capacity of a dense 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. 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.