Geodesic
On the number of served customers in $BMAP(t) | G |\infty$ model
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2009), pp. 26-31.

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

In the present paper the $BMAP(t) | G |\infty$ model with non-stationary input stream of customers is considered. The distribution of customers’ number served during time $t$ and its mean value are obtained. Estimates for characteristics of $MAP (t)|G|\infty$ and $M^x(t) |G|\infty$ models are obtained as well.
Keywords: queuing model, $MAP$ stream, infinite number of servers. 
@article{UZERU_2009_3_a3,
     author = {A. R. Khajkhnidi},
     title = {On the number of served customers in $BMAP(t) | G |\infty$ model},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {26--31},
     publisher = {mathdoc},
     number = {3},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2009_3_a3/}
}
TY  - JOUR
AU  - A. R. Khajkhnidi
TI  - On the number of served customers in $BMAP(t) | G |\infty$ model
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2009
SP  - 26
EP  - 31
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2009_3_a3/
LA  - en
ID  - UZERU_2009_3_a3
ER  - 
%0 Journal Article
%A A. R. Khajkhnidi
%T On the number of served customers in $BMAP(t) | G |\infty$ model
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2009
%P 26-31
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2009_3_a3/
%G en
%F UZERU_2009_3_a3
A. R. Khajkhnidi. On the number of served customers in $BMAP(t) | G |\infty$ model. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2009), pp. 26-31. http://geodesic.mathdoc.fr/item/UZERU_2009_3_a3/

[1] H.C. Tijms, A First Course in Stochastic Models, John Wily $\$ Sons, 2003, 480 pp. | MR | Zbl

[2] A.K. Erlang, “Solution of some problems in the theory of significance in automatic telephone exchanges”, The Post Office Electrical Engineers’ Journal, 10 (1918), 189–197

[3] Theory Probab. Appl., 2:1 (1957), 104–112 | DOI | MR | Zbl

[4] B.V. Gnedenko, I.N. Kovalenko, Introduction of Theory of Queues, Nauka, M., 1987 (in Russian) | MR

[5] Kh.V. Kerobyan, “Resource Sharing Performance Models for Estimating Internet Service Characteristic in View of Restrictions on Buffer Capacity”, Int. NATO Conf. DF for SM, Kluwer Academic Pb., 2003

[6] T.A. Grigorian, The Development and Study of Internet-Service Proecting Models for Enter to Datebuses, PhD Thesis, Yer., 2004 (in Russian)

[7] I.A. Ushakov (ed.), The Relabily of Technical Systems, Radio i Sviaz, 1985, 608 pp. (in Russian)

[8] K. Leung, W.A. Massey, W. Whitt, “Traffic models for wireless communication networks”, Journal on Selected Areas in Communications, 12 (1994), 1353–1364 | DOI

[9] W.A. Massey, “The Analysis of Queues with Time-Varying Rates for Telecommunication Models”, Telecommunication Systems, 21:2–4 (2002), 173–204 | DOI

[10] M.F. Neuts, “A versatile Markovian point process”, J. Appl. Probab., 16 (1979), 764–779 | DOI | MR

[11] D.M. Lucantoni, “New Results for the Single Server Queue with a Batch Markovian Arrival Process”, Commun. Statist. Stochastic Models, 7:1 (1991), 1–46 | DOI | MR | Zbl

[12] V. Paxson, S. Floyd, “Wide-area Traffic: The Failure of Poisson Modeling”, Proc. Of the ACM94, 257–268

[13] K. Park, G. Kim, M. Crovella, “On the Effect of Traffic Self-Si,ilarity on Network Performance”, Proc. SPIE Int’l. Conf. Perf. and Control, 1997, 296–310

[14] S. Eick, W.A. Massey, W. Whitt, “Infinite-server queues with sinusoidal arrival rates”, Management Science, 39 (1993), 241–252 | DOI | Zbl

[15] S. Eick, W.A. Massey, W. Whitt, “The physics of the $M(t)/G/|\infty$ queue”, Operations Research, 41 (1993), 400–408 | DOI | MR

[16] J. Keilson, L.D. Servi, Networks of Non-homogenous $M|G|\infty$ Systems, GTE Laboratories, Waltham, MA, 1989

[17] L. Breuer, Spatial Queues, Ph.D. Thesis, University of Trier, Germany, 2000

[18] H. Masuyama, Studies on Algorithmic Analysis of Queues with Batch Markovian Arrival Streams, Ph.D. Thesis, Kyoto University, 2003, 146 pp.

[19] D. Baum, V. Kalashnikov, “Spatial No–Waiting Stations with Moving Customers. Queueing Systems”, Queueing Systems, 46 (2004), 231–247 | DOI | MR | Zbl

[20] V. Ramaswami, M.F. Neuts, “Some explicit formulas and computational methods for infinite-server queues with phase-type arrivals”, Journal of Applied Probability, 1980, no. 17, 498–514 | DOI | MR | Zbl

[21] B. L. Nelson, R. M. Taaffe, “The $Pht/\infty$ Queueing System: Part I: The Single Node”, Informs Journal on Computing, 16:3 (2004), 266–274 | DOI | MR | Zbl

[22] V.F. Matveev, V.G. Ushakov, Systems of Queues, 1984, MGU, M., 239 pp. (in Russian)