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Queueing Networks

  • Randolph Nelson
Chapter

Abstract

In this chapter we derive the mathematics of product form queueing networks. In such networks the stationary distribution of the network is the product of the distributions of each queue analyzed in isolation from the network (for closed networks this is subject to a normalization constant). When first encountered, such a solution is enigmatic since for open networks it implies independence of the stationary distributions of the individual queues, and for closed networks it implies that the dependence between the queues is captured by normalizing the independent solution over a truncated state space. The derivations presented in this chapter provide insight into why simple solutions of this type exist for such complex networks.

Keywords

Stationary Distribution Departure Process Poisson Arrival State Transition Diagram Tandem Queue 
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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Bibliographic Notes

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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Randolph Nelson
    • 1
    • 2
  1. 1.OTA Limited PartnershipPurchaseUSA
  2. 2.Modeling MethodologyIBM T.J. Watson Research CenterYorktown HeightsUSA

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