A Compressed Cyclic Reduction for QBD processes with Low-Rank Upper and Lower Transitions

Abstract

In this chapter we consider quasi-birth and death processes with low rank downward and upward transitions. We show how such structure can be exploited to reduce the computational cost of the cyclic reduction iteration. The proposed algorithm saves computation by performing multiplications and inversions of matrices of small size (equal to the rank instead of to the phase space dimension) and inherits the stability property of the customary cyclic reduction. Numerical experiments show the gain of the new algorithm in terms of computational cost. Quasi-birth and death process, Low rank matrix, Cyclic reduction. © Springer Science+Business Media New York 2013.