Lumpable continuous-time stochastic automata networks

Lumpable continuous-time stochastic automata networks

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Article ID: iaor20042800
Country: Netherlands
Volume: 148
Issue: 2
Start Page Number: 436
End Page Number: 451
Publication Date: Jul 2003
Journal: European Journal of Operational Research
Authors: , ,
Abstract:

The generator matrix of a continuous-time stochastic automata network (SAN) is a sum of tensor products of smaller matrices, which may have entries that are functions of the global state space. This paper specifies easy to check conditions for a class of ordinarily lumpable partitionings of the generator of a continuous-time SAN in which aggregation is performed automaton by automaton. When there exists a lumpable partitioning induced by the tensor representation of the generator, it is shown that an efficient aggregation-iterative disaggregation algorithm may be employed to compute the steady-state distribution. The results of experiments with two SAN models show that the proposed algorithm performs better than the highly competitive block Gauss–Seidel in terms of both the number of iterations and the time to converge to the solution.

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