Mathematics and Computer Science: Algorithms, Trees, Combinatorics and 
Probabilities, 2000

TITLE: Effects of Reordering and Lumping in the Analysis of Discrete-Time SANs

AUTHOR: Tugrul Dayar

ABSTRACT: 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. 

KEY WORDS: Stochastic automata networks, discrete-time Markov chains,
lumpability, iterative aggregation-disaggregation