Queueing networks in equilibrium and Markov chains: numerical solution methods

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.