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2014 | 24 | 3 | 503-518
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On truncations for weakly ergodic inhomogeneous birth and death processes

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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.
Opis fizyczny
  • 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
  • Department of Applied Mathematics, Vologda State University, Vologda, S. Orlova, 6, Russia
  • 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
  • Institute of Problems of Informatics, Russian Academy of Sciences, Vavilova str., 44-2, Moscow, Russia
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