IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v79y1998i0p295-31910.1023-a1018978823209.html
   My bibliography  Save this article

Bounds and error bounds for queueing networks

Author

Listed:
  • Nico van Dijk

Abstract

Queueing networks are an important means to model and evaluate a variety of practical systems. Unfortunately, analytic results are often not available. Numerical computation may then have to be employed. Or, system modifications might be suggested to obtain simple bounds or computationally easy approximations. Formal analytic support for the accuaracy or nature of such modifications or approximations then becomes of interest. To this end, the Markov reward approach is surveyed and illustrated as a technique to conclude a priori error bounds as well as to formally prove bounds when comparing two related systems. More precisely, the technique can be applied to: perturbations, finite truncations, infinite approximations, system modifications, or system simplifications (bounds). A general comparison and error bound theorem are provided. The conditions and technical steps are illustrated in detail for a non-product form queueing network subject to breakdowns. This illustration highlights the technical difference with and extension of the stochastic comparison approach. In addition, some practical applications are given which illustrate the various types of applications. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • Nico van Dijk, 1998. "Bounds and error bounds for queueing networks," Annals of Operations Research, Springer, vol. 79(0), pages 295-319, January.
    • Handle: RePEc:spr:annopr:v:79:y:1998:i:0:p:295-319:10.1023/a:1018978823209
    DOI: 10.1023/A:1018978823209
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/A:1018978823209
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/A:1018978823209?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nico M. van Dijk & Erik van der Sluis, 2001. "Simple Product-Form Bounds for Queueing Networks with Finite Clusters," Tinbergen Institute Discussion Papers 01-107/4, Tinbergen Institute.
    2. 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.
    3. Ana Bušić & Ingrid Vliegen & Alan Scheller-Wolf, 2012. "Comparing Markov Chains: Aggregation and Precedence Relations Applied to Sets of States, with Applications to Assemble-to-Order Systems," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 259-287, May.
    4. Ke Fu & Vernon N. Hsu & Chung‐Yee Lee, 2011. "Approximation methods for the analysis of a multicomponent, multiproduct assemble‐to‐order system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(7), pages 685-704, October.
    5. Nico M. van Dijk & Masakiyo Miyazawa, 2004. "Error Bounds for Perturbing Nonexponential Queues," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 525-558, August.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:79:y:1998:i:0:p:295-319:10.1023/a:1018978823209. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.