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.