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1 results

  • A stochastic lower bound for assemble-transfer batch service queueing networks

  • Part of
  • Antonis Economou
  • Journal:
    Journal of Applied Probability / Volume 37 / Issue 3 / September 2000
    Published online by Cambridge University Press:
    14 July 2016, pp. 881-889
    Print publication:
    September 2000

  • Miyazawa and Taylor (1997) introduced a class of assemble-transfer batch service queueing networks which do not have tractable stationary distribution. However by assuming a certain additional arrival process at each node when it is empty, they obtain a geometric product-form stationary distribution which is a stochastic upper bound for the stationary distribution of the original network. In this paper we develop a stochastic lower bound for the original network by introducing an additional departure process at each node which tends to remove all the customers present in it. This model in combination with the aforementioned upper bound model gives a better sense for the properties of the original network.