Analysis of Queueing Networks in Equilibrium: Numerical Steady-State Solutions of Markov Chains

Abstract

Equilibria of queueing networks are a means for performance analysis of real communication networks introduced as Markov chains. In this paper, the authors developed, evaluated, and compared computational procedures to obtain numerical solutions for queueing networks in equilibrium with the use of direct, iterative, and aggregative techniques in steady-state analysis of Markov chains. Advanced computational procedures are developed with the use of Gaussian elimination, power iteration, Courtois’ decomposition, and Takahashi’s iteration techniques. Numerical examples are provided together with comparative analysis of obtained results. The authors consider these procedures are also applicable to other domains where systems are described with comparable queuing models and stochastic techniques are sufficiently relevant. Several suitable domains of applicability are proposed.