On comparison of accuracy of approximations in the cross aggregation method

The cross aggregation method was developed to get approximate values of stationary probabilities of large Markov chains such as ones used for analyses of queueing systems. In the method, a system is decomposed into several subsystems, and using the aggregation technique a family of approximate models is derived by grouping subsystems in various ways. Each model supplies a set of approximate values. For a given system, usually subsystems are defined in a natural way. However, in some cases, there are several alternatives when choosing subsystems. The accuracy of the approximate values depends on the choice. So it is of great interest to know how subsystems can be chosen to get more accurate approximate values. In this paper the authors propose three indices for roughly estimating the order of accuracy of the candidate approximate models, and test them for Kanban systems or tandem queueing systems with minimal blocking.