ON COMPARISON OF ACCURACY OF APPROXIMATIONS IN THE CROSS AGGREGATION METHOD

抄録

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 are 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, we have several alternatives to choose subsystems. The accuracy of the approximate values depends on the choice. So it is of great interest how we can choose subsystems to get more accurate approximate values. In this paper we 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.