On the metastability of a loss network with diminishing rates

TL;DR

This paper establishes a large deviation principle for a multiclass loss network with diminishing rates, revealing its metastable behavior and identifying stable equilibria in the mean field thermodynamic limit.

Contribution

It introduces a trajectorial large deviation principle for such networks and characterizes metastability and stable equilibria using a maxingale problem.

Findings

The invariant measure satisfies a large deviation principle.

The network exhibits metastability, spending long times near stable equilibria.

A specific two-class network case confirms multiple stable and unstable equilibria.

Abstract

A trajectorial large deviation principle is established in a mean field thermodynamic limit for a multiclass loss network with diminishing rates, which may have several stable equilibria. The large deviation limit is identified as a unique solution to a maxingale problem with a Markov property. The invariant measure of the network process obeys a large deviation principle as well. The network is metastable in that it spends exponentially long periods of time in the neighbourhoods of stable equilibria. A specific case of a two--class network with two stable equilibria and one unstable equilibrium is examined.