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Simple Product-Form Bounds for Queueing Networks with Finite Clusters

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  • Nico M. van Dijk

    (University of Amsterdam)

  • Erik van der Sluis

    (University of Amsterdam)

Abstract

This discussion paper resulted in a publication in 'Annals of Operations Research' . Queueing networks are studied with finite capacity constraints forclusters of stations. First, by an instructive tandemcluster example it is shown how a product-form modification methodfor networks with finite stations can be extended tonetworks with finite clusters. Next, a general result is establishedby which networks with finite clusters can be studied atcluster level by merely keeping track of the total number of jobs atthese clusters, that is, by regarding these clusters asaggregate stations. This result is of practical interest to concludesimple performance bounds at global network level. Anumber of illustrative examples with numerical support are provided.

Suggested Citation

  • 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.
    • Handle: RePEc:tin:wpaper:20010107
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    References listed on IDEAS

    as
    1. Nico van Dijk, 1998. "Bounds and error bounds for queueing networks," Annals of Operations Research, Springer, vol. 79(0), pages 295-319, January.
    2. P. G. Taylor & N. M. Van Dijk, 1998. "Strong Stochastic Bounds for the Stationary Distribution of a Class of Multicomponent Performability Models," Operations Research, INFORMS, vol. 46(5), pages 665-674, October.
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