Numerical Evaluation of Stochastic Automata Networks

Authors:
Paulo Fernandes;Brigitte Plateau;William J. Stewart
Affiliations:
-;-;-
Venue:
MASCOTS '95 Proceedings of the 3rd International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems
Year:
1995

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Abstract

This paper examines some numerical issues in computing solutions to networks of stochastic automata. It is well-known that when the automata are completely independent, the cost of performing the operation basic to all iterative solution methods, that of matrix-vector multiply, is given by /spl rho//sub N/=/spl Pi//sub i=1//sup N/n/sub i//spl times//spl Sigma//sub i=1//sup N/n/sub i/, where n/sub i/ is the number of states in the i/sup th/ automaton and N is the number of automata in the network. We provide a number of lemmas that show that this relatively small number of operations is sufficient in many other cases in which the automata are not independent and we show how the automata should be ordered to achieve this.