Circulant preconditioners for stochastic automata networks
The authors consider circulant preconditioners for stochastic automata networks (SANs). Circulant matrices have shown to be a good preconditioners for Toeplitz systems in many applications and in particular, in queueing networks. If only one of the automata is large in size compared to the others, then the authors prove that the preconditioned system of the normal equations will converge very fast. The preconditioned system is solved by conjugate gradient type methods. Three practical SANs are considered and the proposed preconditioning method are compared with the classical method, the block Gauss-Seidel method: Overflow queueing systems, telecommunication systems and a manufacturing system.
scientific article; zbMATH DE number 1545476