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Bounds and error bounds for queueing networks

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  • 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
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.

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