Metastability in communication networks

Abstract

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.