A Survey of Aggregation-Disaggregation in Large Markov Chains
Paul J. Schweitzer · 2021
This paper surveys results since 1984 on aggregation-disaggregation for large Markov chains. The topics covered include alternative forms of the aggregate equations; alternative forms ofthe disaggregation equations; alternative schemes for iterative aggregation-disaggregation; aggregation for generalized birth-and-death (row-continuous) processes; and aggregation for nearly completely decomposable systems. Implementation issues are described, including overrelaxation, Gauss-Seidel variants, and block scaling. Many topics for further research are identified, including adaptive aggregation, multilevel aggregation, parallel computation, bounds, and applications.