Explicit Lyapunov functions and estimates of the essential spectral radius for Jackson networks

2012/06/14 by Irina Ignatiouk-Robert, Danielle Tibi, Ignatiouk-Robert, Irina +1
Mathematics · #37B25 #60J27 #60K25 #90B15 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:37B25 #msc:60J27 #msc:60K25 #msc:90B15

paper · pdf · doi:10.48550/arxiv.1206.3066

arxiv created 2012/06/14 · arxiv updated 2012/06/15

Abstract

A family of explicit Lyapunov function for positive recurrent Markovian Jackson network is constructed. With this result we obtain explicit estimates of the tail distribution of the first time, when the process returns to large compact sets, and some explicit estimates of the essential spectral radius of the process. The essential spectral radius of the process provides the best geometric convergence rate to equilibrium that one can get by changing the transitions of the process in a finite set.

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