EXTREMAL PROPERTY OF WAITING TIMES IN $GI|G|1|∞$ MODEL - Danielyan, A. A. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2005)
In the present paper stationary distribution functions W and W* of waiting times, which are limits for actual and virtual waiting times across the time axis, in the GI|G| 1 |∞ model under FIFO discipline are examined. The following extremal property is proved. For all x ∊(0,+∞) in the case of non-Poissonian entering stream of demands the strict inequalities W(x)>W*(x)> Ŵ(x) are valid, where Ŵ is the waiting times’ stationary distribution function in the case of the Poissonian entering stream.
Keywords: waiting times; FIFO discipline; Poissonian entering stream