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Applied Probability Trust (5 December 2003) PERTURBATION ANALYSIS FOR DENUMERABLE MARKOV
 

Summary: Applied Probability Trust (5 December 2003)
PERTURBATION ANALYSIS FOR DENUMERABLE MARKOV
CHAINS WITH APPLICATION TO QUEUEING MODELS
EITAN ALTMAN,  INRIA
KONSTANTIN E. AVRACHENKOV,  INRIA
RUDESINDO N 
U ~
NEZ-QUEIJA,  CWI
Abstract
We study the parametric perturbation of Markov chains with denumer-
able state spaces. We consider both regular and singular perturbations.
By the latter we mean that transition probabilities of a Markov chain,
with several ergodic classes, is perturbed such that (rare) transitions
among the di erent ergodic classes of the unperturbed chain are allowed.
Singularly perturbed Markov chains have been studied in literature under
more restrictive assumptions such as strong recurrence ergodicity or
Doeblin conditions. We relax these conditions so that our results can
be applied to queueing models (where the conditions mentioned above
typically fail to hold). Assuming -geometric ergodicity, we are able to
explicitly express the steady state distribution of the perturbed Markov

  

Source: Avrachenkov, Konstantin - INRIA Sophia Antipolis

 

Collections: Computer Technologies and Information Sciences