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On the Large Deviations Approximation for the Stationary Distribution

Summary: On the Large Deviations Approximation
for the Stationary Distribution
of Skip Free Regulated Queueing Networks
Florin Avram
Department of Statistics and Actuarial Science
Heriot Watt University,Edinburgh, Scotland and
Laboratoire de Mathematiques Appliquees
Universite de Pau
Abstract: Large deviations papers like Ignatyouk, Malyshev and Scherbakov [19] have
shown that asymptotically, the stationary distribution of homogeneous regulated networks is of
the form
PfX(t)  ng  Ke n ;
with the coeÆcient being di erent in various "boundary in uence domains" and also depending
in some of these domains on n:
In this paper we focus on the case of constant exponents and on a subclass of networks we
call "strongly skip-free" (which includes all Jackson and all two dimensional skip free networks).
We conjecture that an asymptotic exponent is constant i it corresponds to a large deviations
escape path which progresses gradually (from the origin to the interior) through boundary facets
whose dimension always increases by one. Solving the corresponding large deviations problem


Source: Avram, Florin - Laboratoire de Mathématiques Appliquées, Université de Pau et des Pays de l'Adour


Collections: Mathematics