Averaging in Markov models with fast Markov switches and applications to Queueing models
Date
2002
Authors
Anisimov, V. V.
Editor(s)
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Annals of Operations Research
Print ISSN
0254-5330
Electronic ISSN
Publisher
Springer
Volume
112
Issue
1-4
Pages
63 - 82
Language
English
Type
Journal Title
Journal ISSN
Volume Title
Series
Abstract
An approximation of Markov type queueing models with fast Markov switches by Markov models with averaged transition rates is studied. First, an averaging principle for two-component Markov process (x n (t),ζ n (t)) is proved in the following form: if a component x n (⋅) has fast switches, then under some asymptotic mixing conditions the component ζ n (⋅) weakly converges in Skorokhod space to a Markov process with transition rates averaged by some stationary measures constructed by x n (⋅). The convergence of a stationary distribution of (x n (⋅),ζ n (⋅)) is studied as well. The approximation of state-dependent queueing systems of the type MM,Q/MM,Q/m/N with fast Markov switches is considered.