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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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    1. Yonatan Levy & Uri Yechiali, 1975. "Utilization of Idle Time in an M/G/1 Queueing System," Management Science, INFORMS, vol. 22(2), pages 202-211, October.
    2. VANDAELE, Nico & VAN WOENSEL, Tom & VERBRUGGEN, Aviel, 1999. "A queueing based traffic flow model," Working Papers 1999015, University of Antwerp, Faculty of Business and Economics.
    3. James R. Jackson, 1957. "Networks of Waiting Lines," Operations Research, INFORMS, vol. 5(4), pages 518-521, August.
    4. Shaler Stidham, 1974. "Technical Note—A Last Word on L = λ W," Operations Research, INFORMS, vol. 22(2), pages 417-421, April.
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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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