Estimating equilibrium probabilities for band diagonal Markov chains using aggregation and disaggregation techniques

The purpose of this paper is twofold. First, Aggregation/Disaggregation (A/D) techniques for Markov chains, including the notions of (1) lumpability, (2) near decomposability, and (3) iterative A/D, are surveyed. Next, several design issues for A/D were tested upon several variants of a general class of band diagonal Markov chains. Different (1) cluster entities, (3) methods of combination, (2) methods of dissection, and (4) clustering algorithms were applied to ten levels of seven different types of simulated band diagonal Markov chains of the type that may arise in inventory, queuing, and manpower planning and the results are presented.