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2 results

  • On up- and downcrossings

  • J. W. Cohen
  • Journal:
    Journal of Applied Probability / Volume 14 / Issue 2 / June 1977
    Published online by Cambridge University Press:
    14 July 2016, pp. 405-410
    Print publication:
    June 1977

  • For the sample functions of the stationary virtual waiting-time process vt of the GI/G/1 queueing system some properties of the number of up- and downcrossings of level v by the vt-process during a busy cycle are investigated. It turns out that the simple fact that this number of upcrossings is equal to that of downcrossings leads in a rather easy way to basic relations for the waiting-time distributions. This approach to the study of the vt-process of the GI/G/1 system seems to be applicable to many other types of stochastic processes. As another example of this approach the infinite dam with non-constant release rate is briefly discussed.