Geodesic
Exponential queueing networks with countable set of flows of negative customers and limited sojourn time
Problemy fiziki, matematiki i tehniki, no. 2 (2023), pp. 39-43.

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

An exponential queuing network with one-line nodes is considered. The network receives a Poisson flow of requests with a parameter $\Lambda$ and a countable number of Poisson flows of negative customers with parameters $\lambda_l$, ($l=\overline{1,\infty}$), respectively. The incoming request with probability $p_i$ and the negative customer of the $l$-th flow with probability $q_{il}$ are sent to the $i$-th node $\left(\sum_{i=1}^N p_i=\sum_{i=1}^N q_{il}=1, l=\overline{1,\infty}\right)$. Negative customers are not served. The customer of the $l$-th flow arriving at the $i$-th node, immediately deletes exactly $l$ requests (if there are any), and deletes all the requests if their number is less than $l$, $i=\overline{1,N}$, $l=\overline{1,\infty}$. The sojourn time of requests in network nodes is a random variable with exponential conditional distribution for a fixed number of requests. The requests served at nodes and the requests leaving nodes for the sojourn time is over can remain requests, become customers of the $i$-th flow, or leave the network.
Keywords: network, negative customer, limited sojourn time, stationary distribution. 
@article{PFMT_2023_2_a6,
     author = {N. N. Borodin and Yu. V. Malinkovskii},
     title = {Exponential queueing networks with countable set of flows of negative customers and limited sojourn time},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {39--43},
     publisher = {mathdoc},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2023_2_a6/}
}
TY  - JOUR
AU  - N. N. Borodin
AU  - Yu. V. Malinkovskii
TI  - Exponential queueing networks with countable set of flows of negative customers and limited sojourn time
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2023
SP  - 39
EP  - 43
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2023_2_a6/
LA  - ru
ID  - PFMT_2023_2_a6
ER  - 
%0 Journal Article
%A N. N. Borodin
%A Yu. V. Malinkovskii
%T Exponential queueing networks with countable set of flows of negative customers and limited sojourn time
%J Problemy fiziki, matematiki i tehniki
%D 2023
%P 39-43
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2023_2_a6/
%G ru
%F PFMT_2023_2_a6
N. N. Borodin; Yu. V. Malinkovskii. Exponential queueing networks with countable set of flows of negative customers and limited sojourn time. Problemy fiziki, matematiki i tehniki, no. 2 (2023), pp. 39-43. http://geodesic.mathdoc.fr/item/PFMT_2023_2_a6/

[1] Yu.V. Malinkovskii, N.N. Borodin, “Seti massovogo obsluzhivaniya s konechnym chislom potokov otritsatelnykh zayavok i s ogranichennym vremenem prebyvaniya”, Problemy fiziki, matematiki i tekhniki, 2018, no. 1 (34), 64–68

[2] P.P. Bocharov, A.V. Pechinkin, Teoriya massovogo obsluzhivaniya, RUDN, M., 1995, 529 pp.

[3] I.I. Gikhman, A.V. Skorokhod, Vvedenie v teoriyu sluchainykh protsessov, Nauka, M., 1977, 568 pp.

[4] E. Gelenbe, “Product-form Queueing Networks with Negative and Positive Customers”, J. Appl. Prob., 28 (1991), 656–663 | DOI | MR | Zbl