1. bookVolume 25 (2015): Issue 4 (December 2015)
    Special issue: Complex Problems in High-Performance Computing Systems, Editors: Mauro Iacono, Joanna Kołodziej
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05 Apr 2007
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Ergodicity and Perturbation Bounds for Inhomogeneous Birth and Death Processes with Additional Transitions from and to the Origin

Published Online: 30 Dec 2015
Page range: 787 - 802
Received: 28 Nov 2014
Journal Details
License
Format
Journal
First Published
05 Apr 2007
Publication timeframe
4 times per year
Languages
English

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.

Keywords

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