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Decomposition and Aggregation in Queueing Networks

In: Queueing Networks

Author

Listed:
  • Tijs Huisman

    (ProRail)

  • Richard J. Boucherie

    (University of Twente)

Abstract

This chapter considers the decomposition and aggregation of multiclass queueing networks with state-dependent routing. Combining state-dependent generalisations of quasi-reversibility and biased local balance, sufficient conditions are obtained under which the stationary distribution of the network is of product-form. This product-formfactorises into one part that describes the nodes of the network in isolation, and one part that describes the routing and the global network state. It is shown that a decomposition holds for general nodes if the input-output behaviour of these nodes is suitably compensated by the state-dependent routing function.When only a subset of the nodes is of interest, it is shown that the other nodes may be aggregated into nodes that only capture their global behaviour. The results both unify and extend existing classes of product-form networks, as is illustrated by several cases and an example of an assembly network.

Suggested Citation

  • Tijs Huisman & Richard J. Boucherie, 2011. "Decomposition and Aggregation in Queueing Networks," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. Dijk (ed.), Queueing Networks, chapter 0, pages 313-344, Springer.
    • Handle: RePEc:spr:isochp:978-1-4419-6472-4_7
    DOI: 10.1007/978-1-4419-6472-4_7
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    Citations

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    Cited by:

    1. Richard J. Boucherie, 2022. "Norton’s theorem and insensitivity," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 181-183, April.
    2. Jean-Sébastien Tancrez, 2020. "A decomposition method for assembly/disassembly systems with blocking and general distributions," Flexible Services and Manufacturing Journal, Springer, vol. 32(2), pages 272-296, June.
    3. Tsai, Eline R. & Demirtas, Derya & Tintu, Andrei N. & de Jonge, Robert & de Rijke, Yolanda B. & Boucherie, Richard J., 2023. "Design of fork-join networks of First-In-First-Out and infinite-server queues applied to clinical chemistry laboratories," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1101-1117.

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