Geodesic
Extremal property of waiting times in $GI|G|1|\infty$ model
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2005), pp. 47-52

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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 $GI|G|1|\infty$ model under $FIFO$ discipline are examined. The following extremal property is proved. For all $x\in(0,+\infty)$ in the case of non-Poissonian entering stream of demands the strict inequalities $W(x)>W^*(x)>\hat{W}(x)$ are valid, where $\hat{W}$ is the waiting times’ stationary distribution function in the case of the Poissonian entering stream. 
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     author = {A. A. Danielyan},
     title = {Extremal property of waiting times in $GI|G|1|\infty$ model},
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     pages = {47--52},
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A. A. Danielyan. Extremal property of waiting times in $GI|G|1|\infty$ model. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2005), pp. 47-52. http://geodesic.mathdoc.fr/item/UZERU_2005_3_a2/