Approximate analysis of wireless systems based on time-scale decomposition

Markov chains are a widely used modeling tool for wireless communication networks. The system size and the existence of different user types often make the analysis of the Markov chain computationally intractable. When the events of each user type occur at sufficiently separated time scales, the so-called quasi-stationary approximation (QSA) has proven to be accurate and highly efficient. Recently, a generalization of the quasi-stationary approximation (GQSA) has been introduced. The new approximation aims to improve the accuracy at the price of higher computational cost. In this paper, we carry out a comparative study of the accuracy and computational cost of both approximation methods QSA and GQSA. In particular, we explore the evolution of accuracy as the separation between time scales varies, and the trade-off between accuracy and computational cost. Our results indicate that while the new GQSA improves the accuracy in some instances, it does not occur in all of them; and more importantly, it is difficult to predict in which cases accuracy can be enhanced by the new method.