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Combinatorial Approach to an r-node Tandem Queue

  • Walter Böhm
  • S. G. Mohanty
  • J. L. Lain
Conference paper

Abstract

Consider an r- node tandem queueing model, r > 1, subject to the following assumptions:
  • customers arrive at the first node according to a Poisson process with rate λ

  • the service times at node i, 0 ≤ i ≤ rare i.i.d. random variables having an exponential distribution with mean 1/μ i

  • the service times at various nodes and interarrival times are independent

  • initially there are m i > 0 customers waiting at node i

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References

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    McMahon P.A. (1915) Combinatory Analysis, VoL 1, Cambridge University Press, London.Google Scholar
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    Watanabe T., Mohanty S.G. (1987) On an inclusion-exclusion formula based on the reflection principle. Discrete Math., 64, 281–288.CrossRefGoogle Scholar
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    Zeilberger D. (1983) Andre’s reflection proof generalized to the many candidate ballot problem. Discrete Math., 44, 325–326.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Walter Böhm
    • 1
  • S. G. Mohanty
    • 2
  • J. L. Lain
    • 3
  1. 1.Dept. of Math. StatisticsUniversity of EconomicsWienAustria
  2. 2.McMaster UniversityHamiltonCanada
  3. 3.University of New DelhiNew DelhiIndia

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