Product-form results for two-station networks with shared resources

W. van der Weij, N.M. van Dijk, R.D. van der Mei

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Queueing networks are studied with two stations: either in tandem or in parallel, and with a common service resource shared among the two stations. First, a necessary and sufficient criterion, called adjoint reversibility, is provided to decide whether the system possesses a product form or not. This criterion unifies both the parallel (a reversible) and the tandem (a non-reversible) system in one product-form theorem. Next, the criterion is applied separately for the parallel and tandem system to obtain a number of new productform examples which also includes non-balanced capacity sharing. Despite, but also due to, the different parallel and tandem mechanisms we observe that for certain examples the product form has the same structure, while for others there are essential differences. In addition, it is also proven that several models cannot have a product-form result. The results provide new insights and a step forward in understanding the behavior of multilayered queueing networks in which resources are shared among stations.
Original languageUndefined
Pages (from-to)662-683
Number of pages22
JournalPerformance evaluation
Issue number12
Publication statusPublished - 2012


  • EWI-23221
  • Layered queueing networks
  • Limited processor sharing
  • Adjoint reversibility
  • METIS-297609
  • IR-87156
  • Product forms

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