Memory-efficient kronecker algorithms with applications to the modelling of parallel systems

Proceedings - International Parallel and Distributed Processing Symposium, IPDPS 2003

Volumn , Issue , 2003, Pages

  Benoit, Anne ^a   Plateau, Brigitte ^a   Stewart, William J ^b  

^a INP Grenoble ENSIMAG   (France)

^b North Carolina State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISTRIBUTED PARAMETER NETWORKS; MARKOV PROCESSES; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; TENSORS; VECTOR SPACES;

GENERALIZED TENSOR ALGEBRAS; MARKOV CHAIN MODELS; MATHEMATICAL STRUCTURE; NUMERICAL ALGORITHMS; PARALLEL AND DISTRIBUTED SYSTEMS; SHUFFLE ALGORITHMS; STOCHASTIC AUTOMATA; TENSOR STRUCTURES;

ALGORITHMS;

EID: 84947276344     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/IPDPS.2003.1213494     Document Type: Conference Paper

References (32)

1. S. Alouf, F. Huet, and P. Nain. Forwarders vs. centralized server: An evaluation of two approaches for locating mobile agents. Performance Evaluation, 49:299-319, Sept. 2002.
2. A. Benoit, P. Fernandes, B. Plateau, and W. Stewart. On the Benefits of Using Functional Transitions in Kronecker Modelling. Submitted to Performance Evaluation, 2002.
3. A. Benoit, B. Plateau, and W. Stewart. Memory Efficient Iterative Methods for Stochastic Automata Networks. Technical report, Rapport de recherche INRIA n. 4259, France, Sept. 2001.
4. M. Bozga and O. Maler. On the Representation of Probabilities over Structured Domains. In N. Halbwachs and D. Peled, editors, Proc. CAV'99, volume 1633 of LNCS, pages 261-273. Springer, June 1999.
5. P. Buchhloz. Hierarchical structuring of Superposed GSPNs. In Proc. 7th Int. Workshop on Petri Nets and Performance Models PNPM'97, pages 81-90, Saint Malo, France. IEEE CS Press, 1997.
6. P. Buchholz, G. Ciardo, S. Donatelli, and P. Kemper. Complexity of memory-efficient Kronecker operations with applications to the solution of Markov models. INFORMS Journal on Computing, 12(3):203-222, 2000.
7. G. Ciardo and A. Miner. A data structure for the efficient Kronecker solution of GSPNs. In In proc. 8th Workshop on Petri Nets and Performance models, IEEE CS Press, Zaragossa, 1999.
8. G. Ciardo and A. Miner. Efficient reachability set generation and storage using decision diagram. In In proc. 20th int. Conf. Application and Theory of Petri Nets, LNCS 1639, Springer, 1999.
9. D. Deavours and W. Sanders. "On-The-Fly" Solution Techniques for Stochastic Petri Nets and Extensions. In Proceedings of the Seventh International Workshop on Petri Nets and Performance Models, pages 132-141, Saint Malo, France, June 1997. IEEE Computer Society.
10. D. Deavours and W. Sanders. An Efficient Disk-Based Tool for Solving Large Markov Models. Performance Evaluation, 33(1):67-84, 1998.
11. S. Donatelli. Superposed Stochastic Automata: A class of stochastic Petri nets with parallel solution and distributed state space. Performance Evaluation, 18(1):21-36, 1993.
12. S. Donatelli. Superposed Generalized Stochastic Petri nets: Definition and efficient solution. In Valette, R., editor, Lecture Notes in Computer Science; Application and Theory of Petri Nets 1994, Proceedings 15th International Conference, Zaragoza, Spain, volume 815, pages 258-277. Springer-Verlag, 1994.
13. P. Fernandes. Méthodes Numériques pour la solution de systèmes Markoviens À grand espace d'états. PhD thesis, Institut National Polytechnique de Grenoble, France, 1998.
14. P. Fernandes, B. Plateau, and W. Stewart. Efficient Descriptor-Vector Multiplications in Stochastic Automata Networks. JACM, 45(3):381-414, 1998.
15. J. Fourneau and B. Plateau. PEPS: A package for solving complex Markov models of parallel systems. In Proceedings of the Fourth International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, Palma, Spain, 1988.
16. H. Garavel and H. Hermanns. On Combining Functional Verification and Performance Evaluation using CADP. Technical report, Rapport de recherche INRIA n. 4492, France, July 2002.
17. E. Gelenbe and G. Pujolle. Introduction to Queueing Networks, second edition. John Wiley & Sons, 1998.
18. J. Granata, M. Conner, and R. Tolimeri. Recursive fast algorithm and the role of the tensor product. IEEE Transactions on Signal Processing, 40(12):2921-2930, Dec. 1992.
19. H. Hermanns, J. Meyer-Kayser, and M. Siegle. Multi Terminal Binary Decision Diagram to Represent and Analyse Continuous Time Markov Chains. In Proc. 3rd int. workshop on the numerical solution of Markov chains, Prensas Universitarias de Zaragossa, Zaragossa, Spain, 2000.
20. J.-P. Katoen, M. Kwiatkowska, G. Norman, and D. Parker. Faster and Symbolic CTMC Model Checking. Lecture Notes in Computer Science, 2165, 2001.
21. P. Kemper. Numerical Analysis of superposed GSPNs. IEEE Trans. on Software Engineering, 22(9), Sept. 1996.
22. P. Kemper. Reachability analysis based on structured representations. In W. R. J. Billington, editor, Proc. 17th int. conf. Application and Theory of Petri Nets, Springer LNCS 1091, pages 269-288, 1996.
23. M. Marsan, G. Balbo, G. Conte, S. Donatelli, and G. Franceschinis. Modelling with generalized stochastic Petri nets. John Wiley & Sons, 1995.
24. A. Miner. Efficient solution of GSPNs using Canonical Matrix Diagrams. In Proc. PNPM'01, 9th International Workshop on Petri Nets and Performance Models, pages 101-110, Aachen, Germany, Sept. 2001.
25. J. K. Muppala, G. Ciardo, and K. S. Trivedi. Modeling Using Stochastic Reward Nets. In MASCOTS'93 International Workshop on Modeling, Analysis and Simulation of Computer and Telecommunication Systems, San Diego, CA, pages 367-372. IEEE Comp. Soc. Press., Jan 1993.
26. B. Plateau. De l'Evaluation du parallélisme et de la synchronisation. PhD thesis, Université de Paris XII, Orsay (France), 1984.
27. Y. Saad. Iterative Methods for Sparse Linear Systems. PWS Publishing Company, Boston, 1996.
28. W. H. Sanders and J. F. Meyer. Reduced Base Model Construction Methods for Stochastic Activity Networks. IEEE Journal on Selected Areas in Communications, 9(1):25-36, 1991.
29. R. Stansifer and D. Marinescu. Petri net models of concurrent Ada programs. Microelectronics and Reliability, 31(4):577-594, 1991.
30. W. Stewart. MARCA: Markov chain analyzer, a software package for Markov modelling. In W. Stewart, editor, Numerical Solution of Markov Chains, Marcel Dekker, 1991.
31. W. J. Stewart. An introduction to numerical solution of Markov chains. Princeton University Press, New Jersey, 1994.
32. C. Tadonki and B. Philippe. Parallel Multiplication of a Vector by a Kronecker product of Matrices. Journal of Parallel and Distributed Computing and Practices, 2(4), Dec. 1999.