Geodesic
Convergence time to equilibrium for large finite Markov chains
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 4, pp. 1135-1157
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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. 
@article{FPM_1999_5_4_a9,
     author = {A. D. Manita},
     title = {Convergence time to equilibrium for large finite {Markov} chains},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1135--1157},
     year = {1999},
     volume = {5},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a9/}
}
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A. D. Manita. Convergence time to equilibrium for large finite Markov chains. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 4, pp. 1135-1157. http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a9/