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This article is cited in 1 scientific paper (total in 1 paper)
B. A. Sevastyanov's famous theorem
I. N. Kovalenko Glushkov Institute of Cybernetics NAS Ukraine, Kiev, Ukraine
Abstract:
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.
Received in October 2012
Citation:
I. N. Kovalenko, “B. A. Sevastyanov's famous theorem”, Branching processes, random walks, and related problems, Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 282, MAIK Nauka/Interperiodica, Moscow, 2013, 132–134; Proc. Steklov Inst. Math., 282 (2013), 124–126
Linking options:
https://www.mathnet.ru/eng/tm3483https://doi.org/10.1134/S0371968513030114 https://www.mathnet.ru/eng/tm/v282/p132
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