On truncations for weakly ergodic inhomogeneous birth and death processes

• Autorzy: Alexander Zeifman , Yacov Satin , Victor Korolev , Sergey Shorgin
• Języki publikacji: EN

Abstrakty

EN

We investigate a class of exponentially weakly ergodic inhomogeneous birth and death processes. We consider special transformations of the reduced intensity matrix of the process and obtain uniform (in time) error bounds of truncations. Our approach also guarantees that we can find limiting characteristics approximately with an arbitrarily fixed error. As an example, we obtain the respective bounds of the truncation error for an Mt /Mt /S queue for any number of servers S. Arbitrary intensity functions instead of periodic ones can be considered in the same manner.

Słowa kluczowe

EN

birth and death process; weak ergodicity; truncation; forward Kolmogorov system; nonstationary Markovian queueing models

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2014
• Tom: 24
• Numer: 3
• Strony: 503-518

Daty

wydano

2014

otrzymano

2013-07-30

poprawiono

2014-02-03

Twórcy

autor

Alexander Zeifman

• Institute of Socio-Economic Development of Territories, Russian Academy of Sciences, Gorkogo Str., 56A, Vologda, Russia
• Department of Applied Mathematics, Vologda State University, Vologda, S. Orlova, 6, Russia

autor

Yacov Satin

• Department of Applied Mathematics, Vologda State University, Vologda, S. Orlova, 6, Russia

autor

Victor Korolev

• Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory, Moscow, Russia
• Institute of Problems of Informatics, Russian Academy of Sciences, Vavilova str., 44-2, Moscow, Russia

autor

Sergey Shorgin

• Institute of Problems of Informatics, Russian Academy of Sciences, Vavilova str., 44-2, Moscow, Russia

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Identyfikatory

DOI

10.2478/amcs-2014-0037