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 
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/
@article{UZERU_2005_3_a2,
     author = {A. A. Danielyan},
     title = {Extremal property of waiting times in $GI|G|1|\infty$ model},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {47--52},
     year = {2005},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2005_3_a2/}
}
TY  - JOUR
AU  - A. A. Danielyan
TI  - Extremal property of waiting times in $GI|G|1|\infty$ model
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2005
SP  - 47
EP  - 52
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UZERU_2005_3_a2/
LA  - ru
ID  - UZERU_2005_3_a2
ER  - 
%0 Journal Article
%A A. A. Danielyan
%T Extremal property of waiting times in $GI|G|1|\infty$ model
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2005
%P 47-52
%N 3
%U http://geodesic.mathdoc.fr/item/UZERU_2005_3_a2/
%G ru
%F UZERU_2005_3_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] G. I. Ivchenko, V. A. Kashtanov, I. N. Kovalenko, Teoriya massovogo obsluzhivaniya, Vysshaya shkola, M., 1982

[2] A. A. Borovkov, Veroyatnostnye protsessy v teorii massovogo obsluzhivaniya, Nauka, M., 1972 | MR

[3] D. Shtoiyan, Kachestvennye svoistva i otsenki stokhasticheskikh modelei, Mir, M., 1979