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Simple Product-Form Bounds for Queueing Networks with Finite Clusters

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Abstract

Queueing networks are studied with finite capacities for clusters of stations, rather than for individual stations. First, an instructive tandem cluster example is studied to show that a product-form modification method for networks with finite stations can be extended to networks with finite clusters. Next, general results are established by which finite clusters can be regarded as finite aggregate stations. By these results product-form modifications for finite stations can be extended to product-form modifications for finite clusters by just considering a network at cluster level. This may lead to simple performance bounds. A number of illustrative examples with numerical support are provided.

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Authors and Affiliations

  1. Faculty of Economics and Econometrics, University of Amsterdam, The Netherlands

    Nico M. van Dijk & Erik van der Sluis

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  1. Nico M. van Dijk
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  2. Erik van der Sluis
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van Dijk, N.M., van der Sluis, E. Simple Product-Form Bounds for Queueing Networks with Finite Clusters. Annals of Operations Research 113, 175–195 (2002). https://doi.org/10.1023/A:1020922315539

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