Geodesic
Investigation of stationary characteristics in some variable queueing systems
Dalʹnevostočnyj matematičeskij žurnal, Tome 1 (2000) no. 1, pp. 58-62 
G. Sh. Tsitsiashvili; M. A. Osipova. Investigation of stationary characteristics in some variable queueing systems. Dalʹnevostočnyj matematičeskij žurnal, Tome 1 (2000) no. 1, pp. 58-62. http://geodesic.mathdoc.fr/item/DVMG_2000_1_1_a7/
@article{DVMG_2000_1_1_a7,
     author = {G. Sh. Tsitsiashvili and M. A. Osipova},
     title = {Investigation of stationary characteristics in some variable queueing systems},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {58--62},
     year = {2000},
     volume = {1},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2000_1_1_a7/}
}
TY  - JOUR
AU  - G. Sh. Tsitsiashvili
AU  - M. A. Osipova
TI  - Investigation of stationary characteristics in some variable queueing systems
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2000
SP  - 58
EP  - 62
VL  - 1
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DVMG_2000_1_1_a7/
LA  - ru
ID  - DVMG_2000_1_1_a7
ER  - 
%0 Journal Article
%A G. Sh. Tsitsiashvili
%A M. A. Osipova
%T Investigation of stationary characteristics in some variable queueing systems
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2000
%P 58-62
%V 1
%N 1
%U http://geodesic.mathdoc.fr/item/DVMG_2000_1_1_a7/
%G ru
%F DVMG_2000_1_1_a7

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

A stationary distribution in simplest queueing system with variable intensity of input flow and constant load coefficient is calculated. A generalization of this result in a form of some multiplicative theorem is made. An algorythm of a calculation of stationary distributions for discrete Markovian processes with finite number of states, devoted to investigation of queueing systems with variable load coefficient, is constructed.

[1] D. M. Lucantoni, “New results on the single server queue with a batch Markovian arrival process”, Communications in Statistic Models, 7:1 (1991), 1–46, Marcel Dekker Inc | DOI | MR | Zbl

[2] D. M. Lucantoni, “The BMAP/G$|$1 Queue: A Tutorial”, Models and Techniques for Perfomance Evalution of Computer and Communication Systems, eds. L. Donatello, R. Nelson, Springer, Berlin, 1991, 1–46 | MR

[3] D. Baum, On Markovian Spatial Arrival Processes for the Performance Analysis of Mobile Communication Networks, Research Rep. No98-07, University of Trier, Submitted to Advances in Performance Analysis, Notable Publications, Inc

[4] F. Machihara, “The BMAP/SM/1 Queue With Service Times Depending on the Arrival Process”, Queueing systems, 32:1-3 (1999), 1–15

[5] N. I. Golovko, V. I. Katrakhov, T. A. Pisarenko, “Analiz sistem massovogo obsluzhivaniya s diffuzionnoi intensivnostyu vkhodnogo potoka”, Dalnevostochnyi matematicheskii sbornik, 1999, no. 7

[6] G. I. Ivchenko, V. A. Kashtanov, I. N. Kovalenko, Teoriya massovogo obsluzhivaniya, Vysshaya shkola, M., 1982, 256 pp. | Zbl

[7] A. N. Shiryaev, Veroyatnost, Nauka, M., 1989, 640 pp. | MR