A new parallel block aggregated algorithm for solving Markov chains

In this paper, we propose a new scalable parallel block aggregated iterative method (PBA) for computing the stationary distribution of a Markov chain. The PBA technique is based on aggregation of groups (block) of Markov chain states. Scalability of the PBA algorithm depends on varying the number of blocks and their size, assigned to each processor. PBA solves the aggregated blocks very efficiently using a modified LU factorization technique. Some Markov chains have been tested to compare the performance of PBA algorithm with other block techniques such as parallel block Jacobi and block Gauss–Seidel. In all the tested models PBA outperforms the other parallel block methods.