We study particle systems corresponding to highly connected queuing
networks, like Internet. We examine the validity of the so called Poisson
Hypothesis (PH), which predicts that such particle system, if started
from a reasonable initial state, relaxes to its equilibrium in time
independent of the size of the network. We show that this is indeed the
case in many situations.

However, there are networks for which the relaxation process slows down.
This behavior reflects the fact that the corresponding infinite system
undergoes a phase transition. Such transition can happen only when the
load per server exceeds some critical value, while in the low load
situation the PH behavior holds. Thus, the load plays here the same role
as the inverse temperature in statistical mechanics.