Merging Jacobi and Gauss-Seidel methods for solving Markov chains on computer clusters

The authors consider the use of the parallel iterative methods for solving large sparse linear equation systems resulting from Markov chains-on a computer cluster. A combination of Jacobi and Gauss-Seidel iterative methods is examined in a parallel version. Some results of experiments for sparse systems with over 3 times 10⁷ equations and about 2 times 10⁸ nonzeros which we obtained from a Markovian model of a congestion control mechanism are reported.