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1 results

  • On sojourn time in Jackson networks of queues

  • Austin J. Lemoine
  • Journal:
    Journal of Applied Probability / Volume 24 / Issue 2 / June 1987
    Published online by Cambridge University Press:
    14 July 2016, pp. 495-510
    Print publication:
    June 1987

  • This paper is about representations for equilibrium sojourn time distributions in Jackson networks of queues. For a network with N single-server nodes let hi be the Laplace transform of the residual system sojourn time for a customer ‘arriving' to node i, ‘arrival' meaning external input or internal transfer. The transforms {hi : i = 1, ···, N} are shown to satisfy a system of equations we call the network flow equations. These equations lead to a general recursive representation for the higher moments of the sojourn time variables {Ti : i = 1, ···, N}. This recursion is discussed and then, by way of illustration, applied to the single-server Markovian queue with feedback.