2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135313This paper derives a lower bound to the per-node throughput achievable by a wireless network when n source-destination pairs are randomly distributed throughout a disk of radius $n^γ$, $ γ\geq 0$, propagation is modeled by attenuation of the form $1/(1+d)^α$, $α>2$, and successful transmission occurs at a fixed rate W when received signal to noise and interference ratio is greater than some threshold $β$, and at rate 0 otherwise. The lower bound has the form $n^{1-γ}$ when $γ< 1/2$, and $(n \ln n)^{-1/2}$ when $γ\geq 1/2$. The methods are similar to, but somewhat simpler than, those in the seminal paper by Gupta and Kumar.28 pages, 4 figuresInformation TheoryH.1.1; E.4.xtext