Abstract
The analysis of stochastic systems with non-exponential timing requires the development of suitable modeling tools. Recently, some effort has been devoted to generalize the concept of Stochastic Petri nets, by allowing the firing times to be generally distributed. The evolution of the PN in time becomes a stochastic process, for which in general, no analytical solution is available. The paper describes suitable restrictions of the PN model with generally distributed transition times, that have appeared in the literature, and compares these models from the point of view of the modeling power and the numerical tractability.
Preview
Unable to display preview. Download preview PDF.
References
M. Ajmone Marsan, G. Balbo, and G. Conte. A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Transactions on Computer Systems, 2:93–122, 1984.
M. Ajmone Marsan and G. Chiola. On Petri nets with deterministic and exponentially distributed firing times. In Lecture Notes in Computer Science, pages 132–145, Springer Verlag, 1987.
M. Ajmone Marsan, G. Balbo, A. Bobbio, G. Chiola, G. Conte, and A. Cumani. The effect of execution policies on the semantics and analysis of stochastic Petri nets. IEEE Transactions on Software Engineering, SE-15:832–846, 1989.
D. Aldous and L. Shepp. The least variable phase type distribution is Erlang. Stochastic Models, 3:467–473, 1987.
A. Bertoni and M. Torelli. Probabilistic Petri nets and semi Markov processes. In Proceedings 2-nd European Workshop on Petri Nets, 1981.
A. Bobbio. Petri nets generating Markov reward models for performance/reliability analysis of degradable systems. In R. Puigjaner and D. Poitier, editors, Modeling Techniques and Tools for Computer Performance Evaluation, pages 353–365, Plenum Press, 1989.
A. Bobbio and M. Telek. A benchmark for PH estimation algorithms: Results for acyclic PH. Stochastic Models, 10:3, 1994.
G. Chiola. GreatSPN 1.5 Software architecture. In G. Balbo and G. Serazzi, editors, Computer Performance Evaluation, pages 121–136, Elsevier Science Publishers, 1992.
Hoon Choi, V.G. Kulkarni, and K. Trivedi. Transient analysis of deterministic and stochastic Petri nets. In Proceedings of the 14-th International Conference on Application and Theory of Petri Nets, Chicago, June 1993.
Hoon Choi, V.G. Kulkarni, and K. Trivedi. Markov regenerative stochastic Petri nets. In G. Iazeolla ans S.S. Lavenberg, editor, Proceedings International Conference PERFORMANCE'93, pages 339–352, 1993.
G. Ciardo, J. Muppala, and K.S. Trivedi. On the solution of GSPN reward models. Performance Evaluation, 12:237–253, 1991.
G. Ciardo, R. German, and C. Lindemann. A characterization of the stochastic process underlying a stochastic Petri net. In Proceedings International Workshop on Petri Nets and Performance Models — PNPM93, pages 170–179. IEEE Computer Society, 1993.
G. Ciardo and C. Lindemann. Analysis of deterministic and stochastic Petri nets. In Proceedings International Workshop on Petri Nets and Performance Models — PNPM93, pages 160–169. IEEE Computer Society, 1993.
E. Cinlar. Introduction to Stochastic Processes. Prentice Hall, Englewood Cliffs, 1975.
D.R. Cox. The analysis of non-Markov stochastic processes by the inclusion of supplementary variables. Proceedings of the Cambridge Philosophical Society, 51:433–441, 1955.
A. Cumani. Esp — A package for the evaluation of stochastic Petri nets with phasetype distributed transition times. In Proceedings International Workshop Timed Petri Nets, pages 144–151, IEEE Computer Society Press no. 674, Torino (Italy), 1985.
J. Bechta Dugan, K. Trivedi, R. Geist, and V.F. Nicola. Extended stochastic Petri nets: applications and analysis. In Proceedings PERFORMANCE '84, Paris, 1984.
G. Florin and S. Natkin. Les reseaux de Petri stochastiques. Technique et Science Informatique, 4:143–160, 1985.
R. German and C. Lindemann. Analysis of SPN by the method of supplementary variables. In G. Iazeolla and S.S. Lavenberg, editors, Proceedings International Conference PERFORMANCE'93, pages 320–338, 1993.
P.J. Haas and G.S. Shedler. Regenerative stochastic Petri nets. Performance Evaluation, 6:189–204, 1986.
D.L. Jagerman. An inversion technique for the Laplace transform. The Bell System Technical Journal, 61:1995–2002, October 1982.
R. Lepold. PEPNET: A new approach to performability modelling using stochastic Petri nets. In Proceedings 1st International Workshop on Performability Modelling of Computer and Communication Systems, pages 3–17, University of Twente-Enschede (NL), 1991.
C. Lindemann. An improved numerical algorithm for calculating steady-state solutions of deterministic and stochastic Petri net models. Performance Evaluation, 8, 1993.
J.F. Meyer, A. Movaghar, and W.H. Sanders. Stochastic activity networks: structure, behavior and application. In Proceedings International Workshop Timed Petri Nets, pages 106–115, IEEE Computer Society Press no. 674, Torino (Italy), 1985.
M.K. Molloy. Performance analysis using stochastic Petri nets. IEEE Transactions on Computers, C-31:913–917, 1982.
S. Natkin. Les reseaux de Petri stochastiques et leur application a l'evaluation des systemes informatiques. Technical Report, These de Docteur Ingegneur, CNAM, Paris, 1980.
M.F. Neuts. Matrix Geometric Solutions in Stochastic Models. Johns Hopkins University Press, Baltimore, 1981.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bobbio, A., Telek, M. (1994). Computational restrictions for SPN with generally distributed transition times. In: Echtle, K., Hammer, D., Powell, D. (eds) Dependable Computing — EDCC-1. EDCC 1994. Lecture Notes in Computer Science, vol 852. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58426-9_128
Download citation
DOI: https://doi.org/10.1007/3-540-58426-9_128
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58426-1
Online ISBN: 978-3-540-48785-2
eBook Packages: Springer Book Archive