Analysis of Jackson networks with infinite supply and unreliable nodes

Jennifer Sommer, Joost Berkhout, Hans Daduna, Bernd Heidergott*

*Corresponding author for this work

Research output: Contribution to JournalArticle

Abstract

Jackson networks are versatile models for analyzing complex networks. In this paper we study generalized Jackson networks with single-server stations, where nodes may have an infinite supply of work. We allow simultaneous breakdown of servers and consider group repair strategies. We establish the existence of a steady-state distribution of the queue-length vector at stable nodes for different types of failure regimes. In steady state the distribution of the failure/repair regime and of the queue-length vector at stable nodes decouples in a product-form way. We provide closed-form solutions for the classical performance measures such as throughput or mean sojourn time at a station.

Original languageEnglish
Pages (from-to)181-207
Number of pages27
JournalQueueing Systems
Volume87
Issue number1-2
DOIs
Publication statusPublished - 1 Oct 2017

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Keywords

  • Group breakdowns
  • Group repairs
  • Infinite supply
  • Jackson networks

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