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1 results

  • On the concavity of the waiting-time distribution in some GI/G/1 queues

  • R. Szekli
  • Journal:
    Journal of Applied Probability / Volume 23 / Issue 2 / June 1986
    Published online by Cambridge University Press:
    14 July 2016, pp. 555-561
    Print publication:
    June 1986

  • In this paper the concavity property for the distribution of a geometric random sum (geometric compound) X, + · ·· + XN is established under the assumption that Xi are i.i.d. and have a DFR distribution. From this and the fact that the actual waiting time in GI/G/1 queues can be written as a geometric random sum, the concavity of the waiting-time distribution in GI/G/1 queues with a DFR service-time distribution is derived. The DFR property of the idle-period distribution in specialized GI/G/1 queues is also mentioned.