An iterative bounding method for stochastic automata networks

Performance Evaluation

Volumn 49, Issue 1-4, 2002, Pages 211-226

  Buchholz, Peter ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Bounding techniques; Markov chains; Performance analysis; Stationary probabilities; Stochastic automata networks

Indexed keywords

AUTOMATA THEORY; EIGENVALUES AND EIGENFUNCTIONS; ITERATIVE METHODS; MARKOV PROCESSES; NUMERICAL ANALYSIS; PROBABILITY; VECTORS;

BOUNDING TECHNIQUES; PERFORMANCE ANALYSIS; STATIONARY PROBABILITIES; STOCHASTIC AUTOMATA NETWORKS;

STOCHASTIC CONTROL SYSTEMS;

EID: 1642416767     PISSN: 01665316     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-5316(02)00123-2     Document Type: Conference Paper

References (18)

1. Buchholz P., Hierarchical structuring of superposed GSPNs. IEEE Trans. Software Eng. 25(2):1999;166-181.
2. Buchholz P., Structured analysis approaches for large Markov chains. Appl. Numer. Math. 31(4):1999;375-404.
3. P. Buchholz, An iterative bounding method for stochastic automata networks. Available under http://www.iai.inf.tu-dresden.de/ms/pb/pb_public.html.
4. Buchholz P., Ciardo G., Donatelli S., Kemper P., Complexity of Kronecker operations and sparse matrices with applications to the solution of Markov models. INFORMS J. Comput. 12(3):2000;203-222.
5. P.J. Courtois, Analysis of large Markovian models by parts. Application to queueing network models, in: H. Beilner (Ed.), Messung, Modellierung und Bewertung von Rechensystemen, IFB 110, Springer, Berlin, 1985, pp. 1-10.
6. Courtois P.J., Semal P., Bounds for the positive eigenvectors of nonnegative matrices and for their approximation by decomposition. J. ACM. 31(4):1984;804-825.
7. Fernandes P., Plateau B., Stewart W.J., Efficient descriptor-vector multiplication in stochastic automata networks. J. ACM. 45(3):1998;381-414.
8. Franceschinis G., Muntz R.R., Bounds for quasi-lumpable Markov chains. Perform. Eval. 20(1-3):1994;223-244.
9. G. Golub, C. Van Loan, Matrix Computations, John Hopkins University Press, Baltimore, MD, 1996.
10. S.M. Islam, H.H. Ammar, On bounds for token probabilities in a class of generalized stochastic Petri nets, in: Proceedings of the Third International Workshop on Petri Nets and Performance Models, IEEE CS-Press, 1989, pp. 221-227.
11. Kemper P., Numerical analysis of superposed GSPNs. IEEE Trans. Software Eng. 22(9):1996;615-628.
12. Mahevas S., Rubino G., Bound computation of dependability and performance measures. IEEE Trans. Comput. 50(5):2001;399-413.
13. R.R. Muntz, E. De Souza e Silva, A. Goyal, Bounding availability of repairable computer systems, IEEE Trans. Comput. 38 (12) (1989).
14. Muntz R.R., Lui J., Computing bounds on steady-state availability of repairable computer systems. J. ACM. 41(4):1994;676-707.
15. Plateau B., On the stochastic structure of parallelism and synchronisation models for distributed algorithms. Perform. Eval. Rev. 13:1985;142-154.
16. Semal P., Refineable bounds for large Markov chains. IEEE Trans. Comput. 44(10):1995;1216-1222.
17. W.J. Stewart, Introduction to the Numerical Solution of Markov Chains, Princeton University Press, Princeton, NJ, 1994.
18. M. Tremolieres, J.M. Vincent, B. Plateau, Determination of the optimal stochastic upper bound of a Markovian generator, Rapport de Recherche RR 906-I, Institut IMAG, 1992.