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

Published online by Cambridge University Press:  14 July 2016

R. Szekli
R. Szekli*
Affiliation:
University of Wrocχaw
*
∗Postal address: Institute of Mathematics, University of Wrocχaw, PI. Grunwaldzki 2/4, 50–384 Wrocχaw, Poland.
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Abstract

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.

Keywords

GI/G/1 QUEUEDFR DISTRIBUTIONGEOMETRIC COMPOUNDINGACTUAL WAITING TIME
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 555 - 561
Copyright
Copyright © Applied Probability Trust 1986 

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