\(V\)-uniform ergodicity for state-dependent single class queueing networks
type: Item
instance of: scholarly article
title: \(V\)-uniform ergodicity for state-dependent single class queueing networks
zbMATH Open document ID: 1191.60102
author: Chihoon Lee
published in: Queueing Systems
publication date: 2010-05-21T00:00:00Z
review text: The paper considers single class queueing networks in which arrival and service rates depend on the state of the network. The primary result is concerned with a rate of convergence to the steady-state distribution. Under the uniform (in state) stability condition, it is shown that the queue length process is \(V\)-uniformly ergodic; that is, it has a transition probability kernel which converges to its limit geometrically quickly in the \(V\)-norm sense. As consequences of \(V\)-uniform ergodicity, one can obtain several meaningful asymptotic properties of the process such as a strong form of the large deviation principle and mixing results, a functional central limit theorem and a Strassen-type functional law of the iterated logarithm result. The proofs rely on a critical use of the Lyapunov function methods.
reviewed by: Oleg K. Zakusilo
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 93E15
zbMATH DE Number: 5710664
zbMATH Keywords: State-dependent networks
zbMATH Keywords: \(V\)-uniform ergodicity
zbMATH Keywords: functional law of the iterated logarithm
MaRDI profile type: Publication
full work available at URL: s11134-010-9165-2
OpenAlex ID: W2041495501
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DOI: 10.1007/S11134-010-9165-2
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description: scientific article; zbMATH DE number 5710664