  We study large communication networks of the mean-field type. The input flows
to the nodes of the network are supposed to be stationary and with low rate. We
show that such a network is ergodic, i.e. it goes to the stationary state,
which does not depend on the initial state of the network. This is in contrast
with the high load regime, when the large time behavior of the network might
depend on its initial state. Our technique is based on the coupling
construction, which couples two Non-Linear Markov Processes.
