naa a22 4500 510812112 CHVBK 20180411083447.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1134/S0081543813060114 doi (NATIONALLICENCE)springer-10.1134/S0081543813060114 Kovalenko I. V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, pr. Akademika Glushkova 40, 03680, Kyiv, Ukraine aut B.A. Sevastyanov's famous theorem [Elektronische Daten] [I. Kovalenko] 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. Pleiades Publishing, Ltd., 2013 Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 124-126 0081-5438 282:1<124 2013 282 11501 https://doi.org/10.1134/S0081543813060114 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813060114 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kovalenko I. V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, pr. Akademika Glushkova 40, 03680, Kyiv, Ukraine aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 124-126 0081-5438 282:1<124 2013 282 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer