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 $\mathcal L\left(N\right)$ we introduce a notion of convergence time to equilibrium $T\left(N\right)$. 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.

All articles are published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/99/994/99410h.htm