<abstract xmlns="http://www.w3.org/1999/xhtml"> 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.</abstract>

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.

On truncations for weakly ergodic inhomogeneous birth and death processes

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On truncations for weakly ergodic inhomogeneous birth and death processes"}

We investigate a class of exponentially weakly ergodic inhomogeneous birth and death processes. We consider special transformations of the reduced intensity...

On truncations for weakly ergodic inhomogeneous birth and death processes

Published Online: Sep 25, 2014

Page range: 503 - 518

Received: Jul 30, 2013

DOI: https://doi.org/10.2478/amcs-2014-0037

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

© by Alexander Zeifman

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On truncations for weakly ergodic inhomogeneous birth and death processes

Published Online: Sep 25, 2014

Page range: 503 - 518

Received: Jul 30, 2013

DOI: https://doi.org/10.2478/amcs-2014-0037

Keywordsbirth and death process, weak ergodicity, truncation, forward Kolmogorov system, nonstationary Markovian queueing models

© by Alexander Zeifman

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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