December 2016 Nonergodic Jackson networks with infinite supply–local stabilization and local equilibrium analysis
Jennifer Sommer, Hans Daduna, Bernd Heidergott
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J. Appl. Probab. 53(4): 1125-1142 (December 2016).

Abstract

Classical Jackson networks are a well-established tool for the analysis of complex systems. In this paper we analyze Jackson networks with the additional features that (i) nodes may have an infinite supply of low priority work and (ii) nodes may be unstable in the sense that the queue length at these nodes grows beyond any bound. We provide the limiting distribution of the queue length distribution at stable nodes, which turns out to be of product form. A key step in establishing this result is the development of a new algorithm based on adjusted traffic equations for detecting unstable nodes. Our results complement the results known in the literature for the subcases of Jackson networks with either infinite supply nodes or unstable nodes by providing an analysis of the significantly more challenging case of networks with both types of nonstandard node present. Building on our product-form results, we provide closed-form solutions for common customer and system oriented performance measures.

Citation

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Jennifer Sommer. Hans Daduna. Bernd Heidergott. "Nonergodic Jackson networks with infinite supply–local stabilization and local equilibrium analysis." J. Appl. Probab. 53 (4) 1125 - 1142, December 2016.

Information

Published: December 2016
First available in Project Euclid: 7 December 2016

zbMATH: 1356.60159
MathSciNet: MR3581246

Subjects:
Primary: 60K25
Secondary: 90B15

Keywords: bottleneck analysis , instability , Jackson network , product-form solution , Shortest path , stability

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 4 • December 2016
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