Parallel randomization for large structured Markov chains

Abstract

Multiprocessor architectures with few but powerful processors are gaining more and more popularity. We describe a parallel iterative algorithm to perform randomization for a continuous time Markov chain with a Kronecker representation on a shared memory architecture. The Kronecker representation is modified for a parallel matrix-vector multiplication with a fast multiplication scheme and no write conflicts on iteration vectors. The proposed technique is applied on a model of a workstation cluster for dependability analysis, corresponding computations are performed on two multiprocessor architectures, a Sun enterprise and a SGI Origin 2000 to measure its performance.