EXTREMAL PROPERTY OF WAITING TIMES IN $GI|G|1|\infty$ MODEL

Abstract

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.