In recent years, many research efforts were dedicated towards modeling and analyzing denser and denser wireless networks, in terms of the number of devices per km2 or m2. The terminology used ranges from “ultradense” to “hyperdense”, “massively dense”, and “extremely dense”.
IEEE Xplore lists more than 500 journal papers on “ultradense” networks, 25 on “hyperdense” networks (generally published more recently than the ultradense ones), and about 90 on “extremely dense” networks. There even exist 15 on “massively dense” networks. The natural question is how they are ordered. Is “ultradense” denser than “hyperdense” or vice versa? How does “extremely dense” fit in? Are there clear definitions what the different levels of densities mean? And what term do we use when networks get even denser?
Perhaps we can learn something from the terminology used for frequency bands. There is “high frequency” (HF), “very high frequency” (VHF), “ultrahigh frequency” (UHF), followed by “super high frequency” (SHF), “extremely high frequency” (EHF), and “tremendously high frequency” (THF). The first five each span an order of magnitude in frequency (or wavelength), while the last ones spans two order of magnitude, from 300 GHz to 30 THz.
So how about we follow that approach and classify network density levels as follows:
HD: 1-10 km-2
VHD: 10-100 km-2
UHD: 100-1’000 km-2
SHD: 1’000-10’000 km-2
EHD: 10’000-100’000 km-2
THD: 0.1-10 m-2
So, who will be the first to write a paper on tremendously dense networks?
What comes after THD? Not unexpectedly, there is a mathematical answer to that question. A dense set has a well-defined meaning. So in the super tremendously extreme case, we can just say that the devices are dense on the plane, without further qualification. This is achieved, for instance, by placing a device at each location with rational x and y coordinates. This is a dense network model, and almost surely there is no denser one.