Load balancing and parallel implementation of iterative algorithms for row-continuous Markov chains

Abstract

Presents the first parallel algorithms for solving row-continuous or generalized birth-death (GBD) Markov chains on distributed memory MIMD multiprocessors. These systems are characterized by very large transition probability matrices, decomposable in heterogeneous tridiagonal blocks. The parallelization of three aggregation/disaggregation iterative methods is carried out by a unique framework that keeps into account the special matrix structure. Great effort has been also devoted to define a general algorithm for approximating the optimum workload. Various computational experiments show that Vantilborgh's (1985) method is the fastest of the three algorithms on any data set dimension.<>