On the metastability of a loss network with diminishing rates

2022/01/10 by Anatolii A. Puhalskii, Puhalskii, Anatolii A.
Computer Science · Physics and Astronomy · #60F10 #60F17 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Opinion Dynamics and Social Influence #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2201.03273

openalex publication_date 2022/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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