Distributed numerical markov chain analysis

Abstract

Very large systems of linear equations arise from numerous fields of application, e.g. analysis of continuous time Markov chains yields homogeneous, singular systems with millions of unknowns. Despite the availability of high computational power sophisticated solution methods like distributed iterative methods combined with space-efficient matrix representations are necessary to make the solution of such systems feasible. In this paper we combine block-structured matrices represented by Kronecker operators [3,4] with synchronous and asynchronous two-stage iterative methods [11] using the PVM message-passing tool. We describe, how these methods profit from the proposed matrix representation, how these methods perform in wide-spread local area networks and what difficulties arise from this setting.