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Convergence time to equilibrium for large finite Markov chains

A. D. Manita

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 519.217.2

Received: 01.12.1996

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