Numerical Methods in Markov Chain Modeling

Bernard Philippe, Youcef Saad and William J. Stewart
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Bernard Philippe: IRISA, Rennes, France
Youcef Saad: University of Minnesota, Minneapolis, Minnesota
William J. Stewart: North Carolina State University, Raleigh, North Carolina

Operations Research, 1992, vol. 40, issue 6, 1156-1179

Abstract: This paper describes and compares several methods for computing stationary probability distributions of Markov chains. The main linear algebra problem consists of computing an eigenvector of a sparse, nonsymmetric matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous, singular linear system. We present several methods based on combinations of Krylov subspace techniques, single vector power iteration/relaxation procedures and acceleration techniques. We compare the performance of these methods on some realistic problems.

Keywords: mathematics; matrices: direct and iterative methods; probability; stochastic model applications: numerical solution of; queues; Markovian: large queueing network models (search for similar items in EconPapers)
Date: 1992
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