FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 4, PAGES 1135-1157

Convergence time to equilibrium for large finite Markov chains

A. D. Manita

Abstract

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For a sequence of finite Markov chains $ \mathcal L(N) $ we introduce a notion of convergence time to equilibrium T(N). For sequences that are constructed by truncation of some countable Markov chain $ \mathcal L $ we find the convergence time to equilibrium in terms of Lyapunov function of the chain $ \mathcal L $. We apply this result to queueing systems with limited number of customers: a priority system with several types of customers and Jackson network.


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