Effects of reordering and lumping in the analysis of discrete-time sans

In a recent paper [13],it is shown that discrete-time stochastic automata networks (SANs) are lumpable under rather general conditions. Therein, the authors present an efficient iterative aggregation-disaggregation (IAD) algorithm geared towards computing the stationary vector of discrete-time SANs that satisfy the conditions of lumpability. The performance of the proposed IAD solver essentially depends on two parameters. The first is the order in which the automata are lined up, and the second is the size of the lumped matrix. Based on the characteristics of the SAN model at hand, the user may have some flexibility in the choice of these two parameters. In this paper, we give rules of thumb regarding the choice of these parameters on a model from mobile communications.