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Queueing Networks

In: Probability, Stochastic Processes, and Queueing Theory

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  • Randolph Nelson

    (OTA Limited Partnership
    IBM T.J. Watson Research Center, Modeling Methodology)

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.

Suggested Citation

  • Randolph Nelson, 1995. "Queueing Networks," Springer Books, in: Probability, Stochastic Processes, and Queueing Theory, chapter 10, pages 429-501, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-2426-4_10
    DOI: 10.1007/978-1-4757-2426-4_10
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