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Non-ergodic Jackson networks with infinite supply : local stabilization and local equilibrium analysis

Sommer, Jennifer ; Daduna, Hans ; Heidergott, Bernd

Dokument 1.pdf (291 KB)

DDC-Sachgruppe: Mathematik
Dokumentart: Bericht / Forschungsbericht / Abhandlung
Schriftenreihe: Preprint // Schwerpunkt mathematische Statistik und stochastische Prozesse, Univ. Hamburg
Bandnummer: 2014,4
Sprache: Englisch
Erstellungsjahr: 2014
Publikationsdatum: 16.12.2014
Kurzfassung auf Englisch: 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 instable nodes. Our results complement the results known in the literature for the sub-cases 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 nodes present. Building on our product-form results, we provide closed-form solutions for common customer and system oriented performance measures.

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