An aggregation/disaggregation algorithm for stochastic automata networks

Probability in the Engineering and Informational Sciences

Volumn 11, Issue 2, 1997, Pages 229-253

  Buchholz, Peter ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATA THEORY; MARKOV CHAINS; ROBOTS; STOCHASTIC SYSTEMS;

AGGREGATION/DISAGGREGATION; COMPACT REPRESENTATION; GENERATOR MATRIX; ITERATIVE TECHNIQUE; LOOSELY COUPLED; SOLUTION METHODS; STATIONARY SOLUTIONS; STOCHASTIC AUTOMATA NETWORKS;

ITERATIVE METHODS;

EID: 0031510546     PISSN: 02699648     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0269964800004782     Document Type: Article

References (20)

1. Buchholz, P. (1994). Markovian process algebra: Composition and equivalence. In U. Herzog & M. Rettelbach (eds.), Proceedings of the 2nd Workshop on Process Algebras and Performance Modelling. Arbeitsberichte des IMMD, University of Erlangen, Erlangen, Germany, No. 27, pp. 11-30.
2. Buchholz, P. (1995). Equivalence relations for stochastic automata networks. In W.J. Stewart (ed.), Computation with Markov chains. Dordrecht: Kluwer, pp. 197-216.
3. Chatelin, F. & Miranker, W.L. (1982). Acceleration by aggregation successive approximation methods. Linear Algebra and Its Applications 43: 17-47.
4. Courtois, P.J. (1977). Decomposability queueing and computer system applications. New York: Academic Press.
5. Davio, M. (1981). Kronecker products and shuffle algebra. IEEE Transactions on Computers 30: 116-125.
6. Donatelli, S. (1993). Superposed stochastic automata: A class of stochastic Petri nets amenable to parallel solution. Performance Evaluation 18: 21-26.
7. Fernandes, P., Plateau, B., & Stewart, W.J. (1994). Efficient descriptor-vector multiplications in stochastic automata networks. Rapport Apache (LGI, LMC) 12. Institut National Polytechnique de Grenoble, France.
8. Fourneau, J.M. & Quessette, F. (1995). Graphs and stochastic automata networks. In W.J. Stewart (ed.), Computation with Markov chains. Dordrecht: Kluwer, pp. 217-235.
9. Haviv, M. (1986). Aggregation/disaggregation methods for computing the stationary distribution of a Markov chain. SIAM Journal on Numerical Analysis 24: 952-966.
10. Heyman, D.P. & Goldsmith, M.J. (1995). Comparisons between aggregation/disaggregation and a direct algorithm for computing the stationary probabilities of a Markov chain. ORSA Journal on Computing 7: 101-108.
11. Horton, G. & Leutenegger, S. (1995). On the utility of the multi-level algorithm for the solution of nearly completely decomposable Markov chains. In W.J. Stewart (ed.), Computation with Markov chains. Dordrecht: Kluwer, pp. 425-442.
12. Kemper, P. (1995). Numerical analysis of superposed GSPNs. In Proceedings of the 6th International Workshop on Petri Nets and Performance Models. Los Alamitos: IEEE CS-Press, pp. 52-61.
13. Plateau, B. (1985). On the stochastic structure of parallelism and synchronization models for distributed algorithms. Performance Evaluation Review 13: 142-154.
14. Plateau, B. & Atif, K. (1991). Stochastic automata networks for modeling parallel systems. IEEE Transactions on Software Engineering 17: 1093-1108.
15. Plateau, B. & Fourneau, J.M. (1991). A methodology for solving Markov models of parallel systems. Journal of Parallel and Distributed Computing 12: 370-387.
16. Schweitzer, P.J. (1991). A survey of aggregation/disaggregation methods in large Markov chains. In W.J. Stewart (ed.), Numerical solution of Markov chains. New York: Marcel Dekker, pp. 63-88.
17. Schweitzer, P.J. & Kindle, K.W. (1986). An iterative aggregation/disaggregation algorithm for solving linear equations. Applied Mathematics and Computation 18: 313-353.
18. Siegle, M. (1994). Structured Markovian performance modelling with automatic symmetry exploitation. In Tools and Posters of the 7th International Conference on Modeling Techniques and Tools for Computer Performance Evaluation. Technical Report, Institut für Angewandte Informatik und Informationssysteme, Universität Wien, Austria, pp. 77-83.
19. Stewart, W.J. (1994). Introduction to the numerical solution of Markov chains. Princeton, NJ: Princeton University Press.
20. Stewart, W.J., Atif, K., & Plateau, B. (1995). The numerical solution of stochastic automata networks. European Journal of Operations Research 86: 503-525.