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Abstract
The problem of evaluation of Lyapunov exponent in queueing network analysis is considered based on models and methods of idempotent algebra. General existence conditions for Lyapunov exponent to exist in generalized linear stochastic dynamic systems are given, and examples of evaluation of the exponent for systems with matrices of particular types are presented. A method which allow one to get the exponent is proposed based on some appropriate decomposition of the system matrix. A general approach to modeling of a wide class of queueing networks is taken to provide for models in the form of stochastic dynamic systems. It is shown how to find the mean service cycle time for the networks through the evaluation of Lyapunov exponent for their associated dynamic systems. As an illustration, the mean service time is evaluated for some systems including open and closed tandem queues with finite and infinite buffers, forkjoin networks, and systems with roundrobin routing.
Original language  English 

Title of host publication  Proc. MATHMOD 09 Vienna Full Papers CD Volume 
Editors  I. Troch, F. Breitenecker 
Publisher  ARGESIM 
Pages  279 
ISBN (Print)  9783901608353 
State  Published  2009 
Scopus subject areas
 Management Science and Operations Research
 Statistics and Probability
 Algebra and Number Theory
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Evaluation of Lyapunov exponent in generalized linear dynamic models of queueing networks
Николай Кимович Кривулин (Speaker)
9 Feb 2012Activity: Talk types › Oral presentation

6th Vienna Conference on Mathematical Modelling
Николай Кимович Кривулин (Participant)
11 Feb 2009 → 13 Feb 2009Activity: Attendance types › Participating in a conference, workshop, ...