Abstract
Petri Nets (PN) are a graphical formalism which is gaining popularity in recent years as a tool for the representation of complex logical interactions (like synchronization, sequentiality, concurrency and conflict) among physical components or activities in a system. This notes are devoted to introduce the formalism of Petri nets with particular emphasis on the application of the methodology in the area of the performance and reliability modelling and analysis of systems. The quantitative analysis of the behaviour of systems in time requires the superposition of a stochastic timing mechanism to the classical representation of PN. Timed Petri nets and, in particular, Stochastic Petri nets (SPN) are the object of the second part of the notes. Finally, some fully developed examples enlighten peculiar aspects which differentiate PNs from other modelling techniques usual in reliability analysis. In few words, the goal of these notes is to show that the proposed methodology based on the PN formalism can be conveniently used as a user-friendly language to represent and evaluate complex stochastic systems.
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References
International Workshop Petri Nets and Performance Models, IEEE Computer Society Press No. 796, Madison, 1987.
International Workshop Timed Petri Nets, IEEE Computer Society Press No. 674, Torino (Italy), 1985.
T. Agerwala. Putting Petri nets to work. Computer, 85–94, December 1979.
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. To be published on: IEEE Transactions on Software Engineering, 1989.
M. Ajmone Marsan, G. Balbo, A. Bobbio, G. Chiola, G. Conte, and A. Cumani. On Petri nets with stochastic timing. In Proceedings International Workshop on Timed Petri Nets, pages 80–87, IEEE Computer Society Press no. 674, Torino (Italy), 1985.
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, A. Bobbio, G. Conte, and A. Cumani. Performance analysis of degradable multiprocessor systems using generalized stochastic Petri nets. IEEE Computer Society Newsletters, 6, SI-1:47–54, 1984.
R.E. Barlow and F. Proschan. Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York, 1975.
M.D. Beaudry. Performance-related reliability measures for computing systems. IEEE Transactions on Computers, C-27:540–547, 1978.
A. Bobbio. Petri nets generating Markov reward models for performance reliability analysis of degradable systems. In Proceedings of the 4-th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, pages 413–431, Palma de Mallorca, 1988.
A. Bobbio, A.Cumani, and R. Del Bello. Reduced markovian representation of stochastic Petri net models. Systems Science, 10:5–23, 1984.
A. Bobbio and K.S. Trivedi. An aggregation technique for the transient analysis of stiff Markov chains. IEEE Transactions on Computers, C-35:803–814, 1986.
G.W. Brams. Réseaux de Petri: Théorie et pratique. Masson, 1983. (in French).
J.A. Buzacott. Markov approach to finding failure times of repairable systems. IEEE Transactions on Reliability, R-19:128–134, 1970.
W.M. Chow, E.A. McNair, and C.H. Sauer. Analysis of manufacturing systems by Research Queueing Package. IBM Journal of Research and Development, 29:330–341, 1985.
G. Ciardo. Toward a definition of modeling power for stochastic Petri net models. In Proceedings International Workshop on Petri Nets and Performance Models, pages 54–62, IEEE Computer Society Press no. 796, Madison, 1987.
P.J. Courtois. Decomposability: Queueing and Computer System Applications. Academic Press, New York, 1977.
A. Cumani. Esp - A package for the evaluation of stochastic Petri nets with phase-type distributed transition times. In Proceedings International Workshop Timed Petri Nets, IEEE Computer Society Press no. 674, Torino (Italy), 1985.
J. Bechta Dugan. Extended stochastic Petri nets: applications and analysis. Technical Report, Phd Thesis, Department of Computer Science, Duke University, 1984.
J. Bechta Dugan, A. Bobbio, G. Ciardo, and K. Trivedi. The design of a unified package for the solution of stochastic Petri net models. In Proceedings International Workshop on Timed Petri Nets, pages 6–13, IEEE Comp Soc 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.S. Fishman. Concepts and methods in discrete event digital simulation. Wiley, New York, 1973.
G. Florin and S. Natkin. Les reseaux de Petri stochastiques. Technique et Science Informatique, 4:143–160, 1985.
H.J. Genrich and K. Lautenbach. System modelling with high level Petri nets. Theoretical Computer Science, 13:109–136, 1981.
A. Goyal, S. Lavenberg, and K.S. Trivedi. Probabilistic modeling of computer system availability. Annals of Operations Research, 8:285–306, 1987.
P.J. Haas and G.S. Shedler. Regenerative stochastic Petri nets. Performance Evaluation,6:189–204, 1986.
B.R. Iyer, L. Donatiello, and P. Heidelberger. Analysis of performability for stochastic models of fault-tolerant systems. IEEE Transactions on Computers, C-35:902–907, 1986.
K. Jensen. Coloured Petri nets and the invariant method. Theoretical Computer Science,14:317–336, 1981.
L. Kleinrock. Queuing systems, Volume 1: Theory. Wiley Interscience, New York, 1975.
A.J. Lemoine, M.A. Crane. An introduction to the regenerative method for simulation analysis. In A.V. Balakrishnan and M. Thorna, editors, Lecture Notes in Control and Information Sciences, Springer-Verlag, 1977.
J. Martinez and M. Silva. A simple fast algorithm to obtain all invariants of a generalized Petri net. In Proceedings 2-nd European Workshop on Application and Theory of Petri Nets, Springer-Verlag, 1981.
P.M. Merlin and D.J. Faber. Recoverability of communication protocols - Implication of a theoretical study. IEEE Transactions on Communication, COM-24:1036–1043, 1976.
J.F. Meyer. Closed form solution of performability. IEEE Transactions on Computers, C-31:648–657, 1982.
W.L. Miranker. Numerical Methods for Stiff Equations. Reidel, Dordrecht, 1981.
M.K. Molloy. On the integration of delay and throughput measures in distributed processing models. Technical Report, Phd Thesis, UCLA, 1981.
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.
J.L. Peterson. Petri net theory and the modeling of systems. Prentice Hall, Englewood Cliffs, 1981.
J.L. Peterson. Petri nets. Computing Surveys, 9:223–252, 1977.
C.A. Petri. Kommunikation mit automaten. Technical Report, Doctoral Thesis, University of Bonn, 1962. (Available in English as: Communication with automata, Technical Report RADC-TR-65–377, Rome Air Development Center, Griffis NY, 1966).
C.V. Ramamoorthy and G.S. Ho. Performance evaluation of asynchronous concurrent systems using Petri nets. IEEE Transactions on Software Engineering, SE-6:440–449, 1980.
A. Reibman and K.S. Trivedi. Numerical transient analysis of Markov models. Computers and Operations Research, 15:19–36, 1988.
W. Reisig. Petri nets - An introduction. Springer-Verlag, 1982.
J. Sifakis. Use of Petri nets for performance evaluation. In H. Beilner and E. Gelenke, editors, Measuring, modelling and evaluating computer systems, pages 75–93, North Holland, 1977.
M. Silva. Las redes de Petri en la Automatica y la Informatica. AC, Madrid, 1985.
R. Smith, K. Trivedi, and A.V. Ramesh. Performability analysis: measures, an algorithm and a case study. IEEE Transactions on Computers, C-37:406–417, 1988.
W. Whitt. Blocking when service is required from several facilities simultaneously. AT&T Technical Journal, 64:1807–1856, 1985.
W.M. Zuberek. Timed Petri nets and preliminary performance evaluation. In Proceedings 7-th Annual Symposium on Computer Architecture, pages 88–96, 1980.
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© 1990 ECSC, EEC, EAEC, Brussels and Luxembourg
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Bobbio, A. (1990). System Modelling with Petri Nets. In: Colombo, A.G., de Bustamante, A.S. (eds) Systems Reliability Assessment. ISPRA Courses, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0649-5_6
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DOI: https://doi.org/10.1007/978-94-009-0649-5_6
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