  In this paper we study the optimal placement and optimal number of active
relay nodes through the traffic density in mobile sensor ad-hoc networks. We
consider a setting in which a set of mobile sensor sources is creating data and
a set of mobile sensor destinations receiving that data. We make the assumption
that the network is massively dense, i.e., there are so many sources,
destinations, and relay nodes, that it is best to describe the network in terms
of macroscopic parameters, such as their spatial density, rather than in terms
of microscopic parameters, such as their individual placements.
  We focus on a particular physical layer model that is characterized by the
following assumptions: i) the nodes must only transport the data from the
sources to the destinations, and do not need to sense the data at the sources,
or deliver them at the destinations once the data arrive at their physical
locations, and ii) the nodes have limited bandwidth available to them, but they
use it optimally to locally achieve the network capacity.
  In this setting, the optimal distribution of nodes induces a traffic density
that resembles the electric displacement that will be created if we substitute
the sources and destinations with positive and negative charges respectively.
The analogy between the two settings is very tight and have a direct
interpretation in wireless sensor networks.
