  Two models of loss networks, introduced by Gibbens et al. and by Antunes et
al., are known to exhibit a mean field limiting regime with several stable
equilibria. These models are reexamined in the light of Freidlin and Wentzell's
large deviation approach of randomly perturbed dynamical systems. Assuming that
some of their results still hold under slightly relaxed conditions, the
metastability property is derived for both systems. A Lyapunov function
exhibited by Antunes et al. is next identified with the quasipotential
associated with a slightly modified, asymptotically reversible, Markovian
perturbation of the same dynamical system. Another interpretation, in terms of
entropy dissipation, of this Lyapunov function is finally given. The argument
extends to another, similar but closed model.
