Ergodicity of Jackson-type queueing networks

Ergodicity of Jackson-type queueing networks

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Article ID: iaor19951908
Country: United States
Volume: 17
Issue: 1/2
Start Page Number: 5
End Page Number: 72
Publication Date: Sep 1994
Journal: Queueing Systems
Authors: ,
Keywords: Jackson network
Abstract:

This paper gives a pathwise construction of Jackson-type queueing networks allowing the derivation of stability and convergence theorems under general probabilistic assumptions on the driving sequences; namely, it is only assumed that the input process, the service sequences and the routing mechanism are jointly stationary and ergodic in a sense that is made precise in the paper. The main tools for these results are the subadditive ergodic theorem, which is used to derive a strong law of large numbers, and basic theorems on monotone stochastic recursive sequences. The techniques which are proposed here apply to other and more general classes of discrete event systems, like Petri nets or GSMPs. The paper also provides new results on the Jackson-type networks with i.i.d. driving sequences which are studied in the past.

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