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Technical Note—On Normalizing Constants in Queueing Networks

Author

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  • P. G. Harrison

    (Imperial College of Science and Technology, London, England)

Abstract

We present a method for deriving the normalizing constant for the state space probabilities in a closed Markovian queueing network with constant service rates. Our method produces a much simpler expression than any obtained previously. This expression takes the form of a sum of only M terms (if the visitation rate to service rate ratios are distinct), and is easily generalized to the degenerate case. The expression also yields a closed form solution for time delay distributions in cyclic networks of any length and with any number of customers.

Suggested Citation

  • P. G. Harrison, 1985. "Technical Note—On Normalizing Constants in Queueing Networks," Operations Research, INFORMS, vol. 33(2), pages 464-468, April.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:2:p:464-468
    DOI: 10.1287/opre.33.2.464
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