Computational Aspects for Steady State Analysis of QBD Processes

Abstract

In this paper, we give a survey on computational methods developed for steady state solution of QBD (Quasi Birth-Death) processes. Moreover, we adopt and implement a comparative framework to evaluate the capability of some chosen methods (spectral expansion, matrix geometric and its enhanced versions) in both finite and infinite cases. Numerical aspects concerning complexity, memory requirement and numerical stability are examined to expose the benefits and vulnerability of each method.