Ergodicity and perturbation bounds for inhomogeneous birth and death processes with additional transitions from and to the origin

• Autorzy: Zeifman A. , Korotysheva A. , Satin Y. , Korolev V. , Shorgin S. , Razumchik R.

Identyfikatory

DOI

10.1515/amcs-2015-0056

• Języki publikacji: EN

Abstrakty

EN

Service life of many real-life systems cannot be considered infinite, and thus the systems will be eventually stopped or will break down. Some of them may be re-launched after possible maintenance under likely new initial conditions. In such systems, which are often modelled by birth and death processes, the assumption of stationarity may be too strong and performance characteristics obtained under this assumption may not make much sense. In such circumstances, time-dependent analysis is more meaningful. In this paper, transient analysis of one class of Markov processes defined on non-negative integers, specifically, inhomogeneous birth and death processes allowing special transitions from and to the origin, is carried out. Whenever the process is at the origin, transition can occur to any state, not necessarily a neighbouring one. Being in any other state, besides ordinary transitions to neighbouring states, a transition to the origin can occur. All possible transition intensities are assumed to be non-random functions of time and may depend (except for transition to the origin) on the process state. To the best of our knowledge, first ergodicity and perturbation bounds for this class of processes are obtained. Extensive numerical results are also provided.

Słowa kluczowe

EN

inhomogeneous birth process; inhomogeneous death process; ergodicity bound; perturbation bound

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2015
• Tom: Vol. 25, no. 4
• Strony: 787--802
• Opis fizyczny: Bibliogr. 16 poz., wykr.

Twórcy

autor

Zeifman A.

• Department of Applied Mathematics, Vologda State University, S. Orlova, 6, Vologda, Russia; Institute of Socio-Economic Development of Territories, Russian Academy of Sciences, Gorkogo Str., 56A, Vologda, Russia; Institute of Informatics Problems, FRC CSC, Russian Academy of Sciences, Vavilova str., 44-2, Moscow, 119333, Russia

autor

Korotysheva A.

• Department of Applied Mathematics, Vologda State University, S. Orlova, 6, Vologda, Russia; Institute of Informatics Problems, FRC CSC, Russian Academy of Sciences, Vavilova str., 44-2, Moscow, 119333, Russia

autor

Satin Y.

• Department of Applied Mathematics, Vologda State University, S. Orlova, 6, Vologda, Russia; Institute of Informatics Problems, FRC CSC, Russian Academy of Sciences, Vavilova str., 44-2, Moscow, 119333, Russia

autor

Korolev V.

• Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory, Moscow, Russia; Institute of Informatics Problems, FRC CSC, Russian Academy of Sciences, Vavilova str., 44-2, Moscow, 119333, Russia

autor

Shorgin S.

• Institute of Informatics Problems, FRC CSC, Russian Academy of Sciences, Vavilova str., 44-2, Moscow, 119333, Russia

autor

Razumchik R.

• Institute of Informatics Problems, FRC CSC, Russian Academy of Sciences, Vavilova str., 44-2, Moscow, 119333, Russia; Department of Applied Informatics and Probability Theory, Peoples’ Friendship University of Russia, Miklukho-Maklaya str., 6, Moscow, 117198, Russia

Bibliografia

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