Connectivity properties of a mobile packet radio network model

A model of a packet radio network in which transmitters with a transmission range of R units are distributed according to a two-dimensional Poisson point process is examined. It is a widely held belief that an optimal number of nearest neighbors of a transmitter (the magic number) exists that maximizes the throughput of the network. The authors show that no magic number can exist. However, the notion of a magic number is shown to be useful, and an explanation is provided for why computations based on magic numbers give answers that are good in practice.