On the Metastability of a Loss Network with Diminishing Rates} \runtit{On the metastability
A.A. Puhalskii
2022, v.28, Issue 3, 365-398
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 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.
Keywords: large deviations; stochastic networks; metastability; invariant measures
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