302 World Review of Entrepreneurship, Management and Sust. Development, Vol. 3, Nos. 3/4, 2007
Copyright © 2007 Inderscience Enterprises Ltd.
Queueing networks in equilibrium and Markov
chains: numerical solution methods
Dimitar Radev*
Department of Communication Techniques and Technologies,
University of Rousse,
8 Studentska Street, 7017 Rousse, Bulgaria
E-mail: dradev@abv.bg
*Corresponding author
Izabella Lokshina
Division of Economics and Business,
SUNY Oneonta, 324B Netzer Administration Bldg.,
Oneonta, NY 13820, USA
E-mail: lokshiiv@oneonta.edu
Vladimir Denchev
Department of Communication Techniques and Technologies,
University of Rousse,
8 Studentska Street, 7017 Rousse, Bulgaria
E-mail: vndenchev@abv.bg
Abstract: This paper is devoted to research and development of the
computational procedures to obtain the steady-state probability vectors in the
queueing networks. The numerical methods for the Markov chains performance
evaluation and analysis, such as direct, iterative and aggregative methods,
are considered and compared. The enhanced computational procedures,
developed with use of Gaussian elimination direct approach, iterative power
approach, Courtois’s approximation method and Takahashi’s iterative method
are implemented and explored. Numerical examples for the steady state
solutions based on the proposed algorithms are demonstrated; and comparative
analysis of the obtained results is made.
Keywords: mobile communication networks; Markov chains; performance
evaluation; steady state analysis; numerical solutions.
Reference to this paper should be made as follows: Radev, D., Lokshina, I.
and Denchev, V. (2007) ‘Queueing networks in equilibrium and Markov
chains: numerical solution methods’, World Review of Entrepreneurship,
Management and Sustainable Development, Vol. 3, Nos. 3/4, pp.302–316.
Biographical notes: Dimitar Radev, PhD is an Associate Professor at
Department of Communication Techniques and Technologies at University of
Rousse, Bulgaria. He is the author of numerous publications. His main research
interests are connected with teletraffic theory, simulation and modelling
of communication networks, rare event simulation, evaluation of quality of
service parameters, performance analysis of queueing systems and neural
network modelling.