GSPN models often generate high cardinality state spaces, whose analysis requires the solution of very large and sparse nonsymmetric linear systems for the associated Markov chain. In this paper we report the results of an empirical investigation of three well-known iterative methods for linear systems of equations: Gauss-Seidel, GMRES, and Bi-CGstab. We evaluate these methods on several large Markov chains generated by GSPN models proposed in the literature. Issues addressed include state space characterization, problem conditioning, numerical accuracy and stability, and computation time. Results show that increased attention should be paid to the numerical issues underlying performance and reliability analyses when dealing with large state spaces.

Evaluation of Iterative Methods on Large Markov Chains Generated by GSPN Models / Caselli, Stefano; Conte, Gianni; Diligenti, Mauro. - 825(2018), pp. 139-155. [10.1007/978-3-319-91632-3_11]

Evaluation of Iterative Methods on Large Markov Chains Generated by GSPN Models

Caselli, Stefano
;
Conte, Gianni;Diligenti, Mauro
2018

Abstract

GSPN models often generate high cardinality state spaces, whose analysis requires the solution of very large and sparse nonsymmetric linear systems for the associated Markov chain. In this paper we report the results of an empirical investigation of three well-known iterative methods for linear systems of equations: Gauss-Seidel, GMRES, and Bi-CGstab. We evaluate these methods on several large Markov chains generated by GSPN models proposed in the literature. Issues addressed include state space characterization, problem conditioning, numerical accuracy and stability, and computation time. Results show that increased attention should be paid to the numerical issues underlying performance and reliability analyses when dealing with large state spaces.
978-3-319-91631-6
978-3-319-91632-3
Evaluation of Iterative Methods on Large Markov Chains Generated by GSPN Models / Caselli, Stefano; Conte, Gianni; Diligenti, Mauro. - 825(2018), pp. 139-155. [10.1007/978-3-319-91632-3_11]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2849404
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