On the stationary distributions in some queueing systems
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2021), pp. 5-13 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper deals with two queuing system: $M_{\lambda}|G|n|\infty$ and $GI_{\lambda}^{\nu}|M_{\mu}|1|\infty$. The purpose is to find the steady-state results in terms of the probability-generating functions.
Keywords: queueing system, batch arrivals, probability generating functions, embedded Markov chain, renewal process.
@article{VTPMK_2021_4_a0,
     author = {V. N. Sobolev and A. E. Kondratenko},
     title = {On the stationary distributions in some queueing systems},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {5--13},
     year = {2021},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2021_4_a0/}
}
TY  - JOUR
AU  - V. N. Sobolev
AU  - A. E. Kondratenko
TI  - On the stationary distributions in some queueing systems
JO  - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
PY  - 2021
SP  - 5
EP  - 13
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VTPMK_2021_4_a0/
LA  - ru
ID  - VTPMK_2021_4_a0
ER  - 
%0 Journal Article
%A V. N. Sobolev
%A A. E. Kondratenko
%T On the stationary distributions in some queueing systems
%J Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
%D 2021
%P 5-13
%N 4
%U http://geodesic.mathdoc.fr/item/VTPMK_2021_4_a0/
%G ru
%F VTPMK_2021_4_a0
V. N. Sobolev; A. E. Kondratenko. On the stationary distributions in some queueing systems. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2021), pp. 5-13. http://geodesic.mathdoc.fr/item/VTPMK_2021_4_a0/

[1] Bocharov P. P., Pechinkin A. V., Queuing theory, Publishing House of RUDN, Moscow, 1995, 529 pp. (in Russian)

[2] Solovyov A. D., Sobolev V. N., “One queuing system with group receipt of requirements”, Proceedings of the International Scientific Conference “Analytical and Computational Methods in Probability Theory and its Applications”, ACMPT-2017 (Russia, Moscow, October 23-27, 2017), ed. A. V. Lebedev, Publishing House of RUDN, Moscow, 2017, 171–175 (in Russian)

[3] Soloviev A. D., Sobolev V. N., “One Server Queue with Bulk Arrivals”, Analytical and Computational Methods in Probability Theory, Lecture Notes in Computer Science, 10684, eds. V. Rykov, N. Singpurwalla, A. Zubkov, Springer, Cham, 97–108 | DOI | Zbl

[4] Feller W., Introduction to probability theory and its applications, Mir Publ., Moscow, 1964, 752 pp. (in Russian)

[5] Gnedenko B. V., Kovalenko I. N., Lectures on queuing theory, KVIRTU Publisher, Kyiv, 1963, 315 pp. (in Russian)

[6] Sobolev V. N., “Khinchin's basic law of a stationary queue for single-server queueing systems with batch arrivals”, Large-Scale Systems Control, 2019, no. 77, 6–19 (in Russian) | DOI