Transient analysis of non-Markovian models using stochastic state classes

Performance Evaluation

Volumn 69, Issue 7-8, 2012, Pages 315-335

  Horváth, András ^a   Paolieri, Marco ^b   Ridi, Lorenzo ^b   Vicario, Enrico ^b  

^a UNIVERSITY OF TURIN   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Generalised Semi Markov Process; Markov Regenerative Process; Non Markovian Stochastic Petri Net; Stochastic state class; Stochastic Time Petri Net; Transient analysis

Indexed keywords

MARKOV REGENERATIVE PROCESS; SEMI MARKOV PROCESS; STOCHASTIC PETRI NETS; STOCHASTIC STATE CLASS; TIME PETRI NETS;

MARKOV PROCESSES; NUMERICAL METHODS; PETRI NETS; PROBABILITY DENSITY FUNCTION; STOCHASTIC SYSTEMS;

TRANSIENT ANALYSIS;

EID: 84864283564     PISSN: 01665316     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.peva.2011.11.002     Document Type: Article

References (28)

1. P.W. Glynn A GSMP formalism for discrete-event systems Proceedings of the IEEE 77 1989 14 23
2. G. Ciardo, R. German, and C. Lindemann A characterization of the stochastic process underlying a stochastic petri net IEEE Transactions on Software Engineering 20 7 1994 506 515
3. P.J. Haas, and G.S. Shedler Stochastic petri net representation of discrete event simulations IEEE Transactions on Software Engineering 15 4 1989 381 393
4. H. Choi, V.G. Kulkarni, and K. Trivedi Markov regenerative stochastic petri nets Performance Evaluation 20 1994 337 357
5. A. Bobbio, M. Telek, Markov regenerative SPN with non-overlapping activity cycles Int. Computer Performance and Dependability Symp. - IPDS95, pp. 124-133, 1995.
6. R. German, and C. Lindemann Analysis of stochastic petri nets by the method of supplementary variables Performance Evaluation 20 1994 317 335
7. E. Cinlar Introduction to Stochastic Processes 1975 Prentice Hall Englewood Cliffs
8. R. German, D. Logothetis, and K.S. Trivedi Transient analysis of markov regenerative stochastic petri nets: a comparison of approaches PNPM'95: Proceedings of the Sixth International Workshop on Petri Nets and Performance Models 1995 IEEE Computer Society Washington, DC, USA 103
9. D. Cox The analysis of non-markovian stochastic processes by the inclusion of supplementary variables Proceedings of the Cambridge Phylosophical Society 51 1955 433 440
10. M. Telek, A. Horváth, Supplementary variable approach applied to the transient analysis of age-MRSPNs, in: Proceedings of International Performance and Dependability Symposium, 1998, pp. 44-51.
11. R. German, M. Telek, Formal relation of Markov renewal theory and supplementary variables in the analysis of Stochastic Petri Nets, in: Proceedings of 8th International Workshop on Petri Nets and Performance Models, pp. 64-73, 1999.
12. C. Lindemann, and G.S. Shedler Numerical analysis of deterministic and stochastic petri nets with concurrent deterministic transitions Performance Evaluation 27-28 1996 565 582 (Pubitemid 126382465)
13. C. Lindemann, and A. Thuemmler Transient analysis of deterministic and stochastic petri nets with concurrent deterministic transitions Performance Evaluation 36-37 1999 35 54
14. G. Bucci, R. Piovosi, L. Sassoli, E. Vicario, Introducing probability within state class analysis of dense time dependent systems, in: Proceedings of the 2nd International Conference on the Quantitative Evaluation of Systems(QEST), 2005.
15. L. Carnevali, L. Sassoli, and E. Vicario Using stochastic state classes in quantitative evaluation of dense-time reactive systems IEEE Transactions on Software Engineering 2009
16. A. Horváth, E. Vicario, Aggregated stochastic state classes in quantitative evaluation of non-markovian stochastic petri nets, in: Proceedings of 6th International Conference on the Quantitative Evaluation of Systems (QEST), Budapest, Hungary, September 2009.
17. E. Vicario Static analysis and dynamic steering of time dependent systems using time petri nets IEEE Transactions on Software Engineering 2001
18. B. Berthomieu, and M. Diaz Modeling and verification of time dependent systems using time petri nets IEEE Transactions on Software Engineering 17 3 1991
19. D. Dill, Timing assumptions and verification of finite-state concurrent systems, in: Proceedings of Workshop on Computer Aided Verification Methods for Finite State Systems, 1989.
20. L. Carnevali, L. Ridi, E. Vicario, Partial stochastic characterization of timed runs over dbm domains, in: Proceedings of the 9th International Workshop on Performability Modeling of Computer and Communication Systems (PMCCS 2009), Eger, Hungary, September 2009.
21. P. Merlin, and D.J. Farber Recoverability of communication protocols IEEE Transactions on Communications 24 9 1976
22. V.G. Kulkarni Modeling and Analysis of Stochastic Systems 1995 Chapman and Hall
23. A. Horváth, L. Ridi, and E. Vicario Transient analysis of generalised semi-Markov processes using transient stochastic state classes Proceedings of the the 7th International Conference on Quantitative Evaluation of Systems (QEST'10) 2010
24. J. Bengtsson, W. Yi, Timed automata: semantics, algorithms and tools, in: Concurrency and Petri Nets. LNCS, 3098, 2004.
25. R. Sahner, and K. Trivedi Reliability modeling using SHARPE Reliability, IEEE Transactions on 36 2 2009 186 193
26. G. Bucci, L. Carnevali, L. Ridi, and E. Vicario Oris: a tool for modeling, verification and evaluation of real-time systems STTT, International Journal on Software Tools for Technology Transfer 12 5 2010 391 403
27. L. Carnevali, L. Ridi, and E. Vicario A framework for simulation and symbolic state space analysis of non-markovian models SAFECOMP 2011 409 422
28. D. Logothetis, K. Trivedi, and A. Puliafito Markov regenerative models Proceedings of the International Computer Performance and Dependability Symposium on Computer Performance and Dependability Symposium (IPDS'95) 1995 IEEE Computer Society Washington, DC, USA