The Product form Tool for Queueing Networks

  • Nico M. van Dijk
  • Winfried Grassmann
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 24)


Queueing networks are used widely as modelling and evaluation tools in manufacturing, telecommunications, computer networking, and related areas. Much of the research effort has been devoted to so-called Jackson networks, that is, networks with Poisson arrivals, exponential service times and routing independent of the state of the system and the history of the customer. The steady-state distribution of Jackson networks can be expressed in a so-called product form. This computationally attractive form will be shown to be directly related to the principle of balance per station. This principle will be used to provide practical insights concerning the following questions

  1. 1.

    When can a product form be expected?

  2. 2.

    Why is this product form often violated in practice?

  3. 3.

    How can one restore a product form to obtain simple bounds?



Product Form Station Balance Loss Probability Computational Probability Overflow Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Nico M. van Dijk
    • 1
  • Winfried Grassmann
    • 2
  1. 1.Department of Econometrics and Operations ResearchUniversity of AmsterdamThe Netherlands
  2. 2.Department of Computer ScienceUniversity of SaskatchewanSaskatoonCanada

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