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On product form tandem structures

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  • Nico Dijk

Abstract

This paper is written in honour to A. Hordijk. It establishes product form results for a generic and instructive multi-class tandem queue with blocking, to which A. Hordijk has directly and indirectly contributed. First, a sufficient and necessary product form characterization is provided. Next, three special cases are briefly presented. These illustrate the possibility of product forms despite finite capacity constraints (blocking), unproportional processor sharing mechanisms and resource contentions (such as for access control). The results are partially new and of interest for present-day applications. In essence these rely upon the pioneering work by A. Hordijk Copyright Springer-Verlag 2005

Suggested Citation

  • Nico Dijk, 2005. "On product form tandem structures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 429-436, December.
    • Handle: RePEc:spr:mathme:v:62:y:2005:i:3:p:429-436
    DOI: 10.1007/s00186-005-0043-3
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    References listed on IDEAS

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    1. Hordijk, A. & Schassberger, R., 1982. "Weak convergence for generalized semi-Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 12(3), pages 271-291, May.
    2. Nico van Dijk, 1998. "Bounds and error bounds for queueing networks," Annals of Operations Research, Springer, vol. 79(0), pages 295-319, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Tandem queues; Product forms; 60K25; 90B22;
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