Geodesic
B.\,A.~Sevastyanov's famous theorem
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Branching processes, random walks, and related problems, Tome 282 (2013), pp. 132-134.

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

In 1956, at the Third All-Union Mathematical Congress, Boris Aleksandrovich Sevastyanov gave a talk on the ergodic theorem proved by him for Markov processes and on its application to queueing systems. In 1957, this result was published in the journal Teoriya Veroyatnostei i Ee Primeneniya (Theory of Probability and Its Applications). An important corollary to the ergodic theorem is a generalization of Erlang's well-known formula to a queueing system with a Poisson input flow and an arbitrary distribution of the service time. This result of Sevastyanov has served as a starting point for numerous studies on the problem, which was later called the insensitivity (invariance) problem for queueing systems with losses. There are hundreds of references to this result of Sevastyanov. 
@article{TM_2013_282_a10,
     author = {I. N. Kovalenko},
     title = {B.\,A.~Sevastyanov's famous theorem},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {132--134},
     publisher = {mathdoc},
     volume = {282},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2013_282_a10/}
}
TY  - JOUR
AU  - I. N. Kovalenko
TI  - B.\,A.~Sevastyanov's famous theorem
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2013
SP  - 132
EP  - 134
VL  - 282
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2013_282_a10/
LA  - ru
ID  - TM_2013_282_a10
ER  - 
%0 Journal Article
%A I. N. Kovalenko
%T B.\,A.~Sevastyanov's famous theorem
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2013
%P 132-134
%V 282
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2013_282_a10/
%G ru
%F TM_2013_282_a10
I. N. Kovalenko. B.\,A.~Sevastyanov's famous theorem. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Branching processes, random walks, and related problems, Tome 282 (2013), pp. 132-134. http://geodesic.mathdoc.fr/item/TM_2013_282_a10/

[1] Fortet R.M., “Random distributions with an application to telephone engineering”, Proc. 3rd Berkeley Symp. Math. Stat. Probab., V. 2, Univ. California Press, Berkeley, 1956, 81–88 | MR

[2] Khinchin A.Ya., Raboty po matematicheskoi teorii massovogo obsluzhivaniya, ed. B.V. Gnedenko, URSS, M., 2004

[3] Sevastyanov B.A., “Formuly Erlanga v telefonii pri proizvolnom zakone raspredeleniya dlitelnosti razgovora”, Tr. 3-go Vsesoyuz. mat. s'ezda, M., 1956, T. 4, Izd-vo AN SSSR, M., 1959, 58–70

[4] Sevastyanov B.A., “Ergodicheskaya teorema dlya markovskikh protsessov i ee prilozhenie k telefonnym sistemam s otkazami”, Teoriya veroyatn. i ee primen., 2:1 (1957), 106–116 | MR | Zbl

[5] Gnedenko B.V., Kovalenko I.N., Vvedenie v teoriyu massovogo obsluzhivaniya, URSS, M., 2011

[6] König D., Matthes K., Nawrotzki K., Verallgemeinerungen der Erlangschen und Engsetschen Formeln, Akad.-Verlag, Berlin, 1967 | Zbl

[7] Franken P., Kënig D., Arndt U., Shmidt F., Ocheredi i tochechnye protsessy, Nauk. dumka, Kiev, 1984 | Zbl

[8] Kelly F.P., Reversibility and stochastic networks, J. Wiley Sons, Chichester, 1979 | MR

[9] Ivnitskii V.A., Teoriya setei massovogo obsluzhivaniya, Fizmatlit, M., 2004

[10] Kovalenko I.N., Atkinson J.B., Mykhalevych K.V., “Three cases of light-traffic insensitivity of the loss probability in a $GI/G/m/0$ loss system to the shape of the service time distribution”, Queueing Syst., 45:3 (2003), 245–271 | DOI | MR | Zbl