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

TL;DR

This paper proves that the transport capacity of a dense wireless network with randomly distributed nodes converges to a non-random limit, using subadditive Euclidean functionals and probabilistic methods.

Contribution

It establishes the asymptotic behavior of transport capacity as a subadditive Euclidean functional, providing a rigorous limit for dense wireless networks.

Findings

Transport capacity scales like rac12; (n) for n nodes

Transport capacity divided by rac12; (n) approaches a non-random limit

The transport capacity functional is subadditive and Euclidean

Abstract

The transport capacity of a dense ad hoc network with n nodes scales like \sqrt(n). We show that the transport capacity divided by \sqrt(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.