Lumpable continuous-time stochastic automata networks
Fourneau, J. M.
European Journal of Operational Research
436 - 451
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Gusak, O., Dayar, T., & Fourneau, J. M. (2003). Lumpable continuous-time stochastic automata networks. European Journal of Operational Research, 148(2), 436-451.
Please cite this item using this persistent URLhttp://hdl.handle.net/11693/11258
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. © 2002 Elsevier Science B.V. All rights reserved.