Ergodicity of Jackson-type queueing networks
type: Item
instance of: scholarly article
title: Ergodicity of Jackson-type queueing networks
zbMATH Open document ID: 0826.60081
DOI: 10.1007/BF01158688
author: Francois Baccelli
author: Sergey Foss
published in: Queueing Systems
publication date: 1995-11-29T00:00:00Z
review text: The paper contains stability and convergence theorems for Jackson-type queueing networks under the general assumption that the input process, the service sequences, and the routing mechanism are jointly stationary and ergodic. These results are obtained with the help of the subadditive ergodic theorem and basic theorems on monotone stochastic recursive sequences. All the results are divided into two groups. The first group contains so-called first-order ergodic theorem which is simply the strong law of large numbers. For this purpose, the authors use the graph theoretic considerations which generalize the technique developed by Baccelli et al. for the stability of event graphs. The second group of results is centered around the second order ergodic theorem of Loynes-type which is a sort of convergence to a stationary ergodic regime. A coupling with a stationary ergodic regime and weak convergence to such a regime are considered. As a consequence, new results or new proofs of known results are obtained. In particular, a minimal stationary regime for all models under consideration is constructed. In addition, some restrictions imposed on networks in earlier works are relaxed (for example, the Cramer-type conditions imposed on service times by Borovkov).
Mathematics Subject Classification ID: 60K20
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 90B15
zbMATH DE Number: 698850
zbMATH Keywords: stability and convergence theorems for Jackson-type queueing networks
zbMATH Keywords: subadditive ergodic theorem
zbMATH Keywords: second order ergodic theorem of Loynes-type
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01158688
OpenAlex ID: W1989434274
description: scientific article; zbMATH DE number 698850