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Analysis of Jackson networks with infinite supply and unreliable nodes

Author

Listed:
  • Jennifer Sommer

    (HPC Hamburg Port Consulting GmbH)

  • Joost Berkhout

    (Centrum Wiskunde & Informatica (CWI)
    Vrije Universiteit)

  • Hans Daduna

    (University of Hamburg)

  • Bernd Heidergott

    (Vrije Universiteit)

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.

Suggested Citation

  • Jennifer Sommer & Joost Berkhout & Hans Daduna & Bernd Heidergott, 2017. "Analysis of Jackson networks with infinite supply and unreliable nodes," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 181-207, October.
    • Handle: RePEc:spr:queues:v:87:y:2017:i:1:d:10.1007_s11134-017-9542-1
    DOI: 10.1007/s11134-017-9542-1
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    References listed on IDEAS

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    Cited by:

    1. Joost Berkhout & Bernd Heidergott & Jennifer Sommer & Hans Daduna, 2019. "Robustness analysis of generalized Jackson network," Computational Management Science, Springer, vol. 16(4), pages 697-714, October.

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