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Jackson networks with infinite supply and unreliable nodes

Sommer, Jennifer ; Daduna, Hans ; Heidergott, Bernd

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Dokument 1.pdf (372 KB)


DDC-Sachgruppe: Mathematik
Dokumentart: Bericht / Forschungsbericht / Abhandlung
Schriftenreihe: Preprint // Schwerpunkt mathematische Statistik und stochastische Prozesse, Univ. Hamburg
Bandnummer: 2014,3
Sprache: Englisch
Erstellungsjahr: 2014
Publikationsdatum: 16.12.2014
Kurzfassung auf Englisch: We study generalized Jackson networks with single server stations, where some nodes have an infinite supply of work. We allow in our model simultaneous breakdown of groups of servers, and group repair strategies, thereby capturing the feature that repairing several servers simultaneously may lead to more efficient repair actions and thus may reduce the repair time. In addition, we allow for servers to have infinite supply. We will establish the existence of a steady-state distribution of the queue-length vector at stable nodes for different type of failure-regimes. As it turns out, the distribution of the failure/repair regime and the steady-state distribution of the queue-length vector at stable nodes decouple in a product-form way, and we will provide closed-form solutions for the long run throughput of the network. It is a well known problem in reliability, that the distribution of the time between breakdowns is hard to estimate. We illustrate the impact of our results with an analysis of parameter insecurity of the throughput of the systems for different breakdown regimes.


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