Product form solution for an insensitive stochastic process algebra structure

Performance Evaluation

Volumn 50, Issue 2-3, 2002, Pages 129-151

  Clark, G ^a   Hillston, J ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

Generally distributed random variables; Insensitivity; Product form solution; Stochastic process algebra

Indexed keywords

ALGEBRA; COMPUTER SIMULATION; PERFORMANCE; SYSTEMS ANALYSIS;

STOCHASTIC PROCESS ALGEBRA (SPA);

STOCHASTIC CONTROL SYSTEMS;

EID: 6444245627     PISSN: 01665316     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-5316(02)00103-7     Document Type: Article

References (28)

1. J. Hillston, A Compositional Approach to Performance Modelling, Cambridge University Press, Cambridge, 1996.
2. N. Götz, U. Herzog, M. Rettelbach, Multiprocessor and distributed system design: the integration of functional specification and performance analysis using stochastic process algebras, in: Proceedings of the Performance'93, 1993.
3. M. Bernardo, R. Gorrieri, A tutorial on EMPA: a theory of concurrent processes with nondeterminism, priorities, probabilities and time, Theor. Comput. Sci. 202 (1-2) (1998) 1-54 (Tutorial).
4. H. Hermanns, Interactive Markov chains, Ph.D. Thesis, University of Erlangen-Nürnberg, Germany, 1998.
5. K. Matthes, Zur Theorie der Bedienungsprozesse, in: Trans. 3rd Prague Conference Inf. Th., Stat. Dec. Fns. Rand. Proc., 1962, pp. 513-528.
6. Molloy M.K., Performance analysis using stochastic Petri nets IEEE Trans. Comput. C-31 1982 913-917.
7. J.B. Dugan, K.S. Trivedi, R. Geist, V. Nicola, Extended stochastic Petri nets: applications and analysis, Technical Report DUKE-TR-1984-16, Department of Computer Science, Duke University, 1984.
8. W. Henderson, D. Lucic, Applications of generalised semi-Markov processes to stochastic Petri nets, in: Performance of Distributed and Parallel Systems, Proc. IFIP TC7/WG 7.3 International Seminar on Performance of Distributed and Parallel Systems, Kyoto, Japan, 7-9 December 1988, North Holland, Amsterdam, 1989.
9. M. Ajmone Marsan, C. Chiola, On Petri nets with deterministic and exponentially distributed firing times, in: Lecture Notes in Computer Science "Advances in Petri Nets", Vol. 266, Springer, Berlin, 1987, 132-145.
10. Rumsewicz M., Henderson W., Insensitivity with age-dependent routing Adv. Appl. Prob. 21 1989 398-408.
11. P.G. Harrison, B. Strulo, Stochastic process algebra for discrete event simulation, Esprit Basic Research Series, Springer, Berlin, 1995, pp. 18-37.
12. Bravetti M., Bernardo M., Gorrieri R., Towards performance evaluation with general distributions in process algebras Lect. Notes Comput. Sci. 1466 1998 405-422.
13. M. Bravetti, R. Gorrieri, The theory of interactive generalized semi-Markov processes, Theor. Comput. Sci. 282 (1) (2002) 5-32.
14. P.R. D'Argenio, J.-P. Katoen, E. Brinksma, A stochastic automata model and its algebraic approach, in: Proceedings of the Fifth Process Algebras and Performance Modelling Workshop, 1997, pp. 1-16.
15. A. El-Rayes, M. Kwiatkowska, G. Norman, Solving infinite stochastic process algebra models through matrix geometric methods, in: J. Hillston, M. Silva (Eds.), Proceedings of the Seventh Workshop on Process Algebras and Performance Modelling, Prensas Universitarias de Zaragoza, September 1999, pp. 41-62.
16. J. Hillston, PEPA: performance enhanced process algebra, Technical Report CSR-24-93, Department of Computer Science, The University of Edinburgh, 1993.
17. Hillston J., Thomas N., Product form solution for a class of PEPA models Perform. Eval. 35 1999 171-192.
18. G. Clark, Techniques for the construction and analysis of algebraic performance models, Ph.D. Thesis, The University of Edinburgh, 2000.
19. Thomasian A., Concurrency control: methods, performance, and analysis ACM Comput. Sur. 30 1 1998 70-119.
20. J. Hillston, N. Thomas, A syntactical analysis of reversible PEPA models, in: C. Priami (Ed.), Proceedings of the Sixth Annual Workshop on Process Algebra and Performance Modelling, Nice, France, September 1998, Università degli studi di Verona, pp. 37-49.
21. Sereno M., Towards a product form solution for stochastic process algebras Comput. J. 38 7 1995 622-632.
22. M. Bhabuta, P.G. Harrison, K. Kanani, Detecting reversibility in Markovian process algebras, in: Proceedings of the 11th UK Performance Engineering Workshop for Computer and Telecommunication Systems, Springer, Berlin, 1995.
23. Harrison P., Hillston J., Exploiting quasi-reversible structures in Markovian process algebra models Comput. J. 38 7 1995 510-520.
24. Henderson W., Lucic D., Taylor P.G., A net level performance analysis of stochastic Petri nets J. Aust. Math. Soc., Ser. B 31 1989 176-187.
25. Henderson W., Taylor P.G., Embedded processes in stochastic Petri nets IEEE Trans. Software Eng. 17 2 1991 108-116.
26. R.J. Boucherie, M. Sereno, On the traffic equations of batch routing queueing networks and stochastic Petri nets, Technical Report, European Research Consortium for Informatics and Mathematics, 1994.
27. Boucherie R.J., A characterisation of independence for competing Markov chains with applications to stochastic Petri nets IEEE Trans. Software Eng. 20 7 1994 536-544.
28. Baskett F., Chandy K.M., Muntz R.R., Palacios F.G., Open, closed and mixed networks of queues with different classes of customers J. ACM 22 2 1975 248-260.