System Modelling with Petri Nets

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.

[1]  Andrea Bobbio,et al.  Petri Nets Generating Markov Reward Models for Performance/Reliability Analysis of Degradable Systems , 1989 .

[2]  Tilak Agerwala,et al.  Special Feature: Putting Petri Nets to Work , 1979, Computer.

[3]  Kishor S. Trivedi,et al.  An Aggregation Technique for the Transient Analysis of Stiff Markov Chains , 1986, IEEE Transactions on Computers.

[4]  Philip Heidelberger,et al.  Analysis of Performability for Stochastic Models of Fault-Tolerant Systems , 1986, IEEE Transactions on Computers.

[5]  Marco Ajmone Marsan,et al.  A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems , 1984, TOCS.

[6]  Kishor S. Trivedi,et al.  Extended Stochastic Petri Nets: Applications and Analysis , 1984, Performance.

[7]  C. Petri.  Kommunikation mit Automaten , 1962 .

[8]  George S. Fishman,et al.  Solution of Large Networks by Matrix Methods , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[9]  Kishor S. Trivedi,et al.  Numerical transient analysis of markov models , 1988, Comput. Oper. Res..

[10]  Peter J. Haas,et al.  Regenerative Stochastic Petri Nets , 1986, Perform. Evaluation.

[11]  Peter Radford,et al.  Petri Net Theory and the Modeling of Systems , 1982 .

[12]  James L. Peterson,et al.  Petri Nets , 1977, CSUR.

[13]  Michael K. Molloy,et al.  On the integration of delay and throughput measures in distributed processing models , 1981 .

[14]  We-Min Chow,et al.  Analysis of Manufacturing Systems by the Research Queueing Package , 1985, IBM J. Res. Dev..

[15]  Kishor S. Trivedi,et al.  Performability Analysis: Measures, an Algorithm, and a Case Study , 1988, IEEE Trans. Computers.

[16]  T. Agerwala,et al.  Putting Petri nets to work , 1989 .

[17]  John A. Buzacott.  Markov Approach to Finding Failure Times of Repairable Systems , 1970 .

[18]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[19]  Kurt Lautenbach,et al.  System Modelling with High-Level Petri Nets , 1981, Theor. Comput. Sci..

[20]  W. Whitt,et al.  Blocking when service is required from several facilities simultaneously , 1985, AT&T Technical Journal.

[21]  C. V. Ramamoorthy,et al.  Performance Evaluation of Asynchronous Concurrent Systems Using Petri Nets , 1980, IEEE Transactions on Software Engineering.

[22]  Manuel Silva,et al.  A Simple and Fast Algorithm to Obtain All Invariants of a Generalized Petri Net , 1980, Selected Papers from the First and the Second European Workshop on Application and Theory of Petri Nets.

[23]  Aldo Cumani,et al.  ESP - A Package for the Evaluation of Stochastic Petri Nets with Phase-Type Distributed Transition Times , 1985, PNPM.

[24]  S.M.R. Islam,et al.  Performance analysis of degradable multiprocessor systems , 1989, Eighth Annual International Phoenix Conference on Computers and Communications. 1989 Conference Proceedings.

[25]  Kurt Jensen,et al.  Coloured Petri Nets and the Invariant-Method , 1981, Theor. Comput. Sci..

[26]  Joseph Sifakis,et al.  Use of Petri nets for performance evaluation , 1977, Acta Cybern..

[27]  Kishor S. Trivedi,et al.  Probabilistic modeling of computer system availability , 1987 .

[28]  Wolfgang Reisig,et al.  Application and Theory of Petri Nets , 1982, Informatik-Fachberichte.

[29]  A. A. Crane,et al.  An introduction to the regenerative method for simulation analysis , 1977 .

[30]  Marco Ajmone Marsan,et al.  On Petri Nets with Stochastic Timing , 1985, PNPM.

[31]  Istituto elettrotecnico nazionale Galileo Ferraris,et al.  International Workshop on Timed Petri Nets, Torino, Italy, July 1-3, 1985 , 1985, PNPM.

[32]  Willard L. Miranker,et al.  Numerical Methods for Stiff Equations , 1980 .

[33]  Kishor S. Trivedi,et al.  The Design of a Unified Package for the Solution of Stochastic Petri Net Models , 1985, PNPM.

[34]  Marco Ajmone Marsan,et al.  The Effect of Execution Policies on the Semantics and Analysis of Stochastic Petri Nets , 1989, IEEE Trans. Software Eng..

[35]  Wlodzimierz M. Zuberek,et al.  Timed Petri nets and preliminary performance evaluation , 1980, ISCA '80.

[36]  P. Merlin,et al.  Recoverability of Communication Protocols - Implications of a Theoretical Study , 1976, IEEE Transactions on Communications.

[37]  Wolfgang Reisig.  Petri Nets: An Introduction , 1985, EATCS Monographs on Theoretical Computer Science.

[38]  John F. Meyer,et al.  Closed-Form Solutions of Performability , 1982, IEEE Transactions on Computers.

[39]  Gianfranco Ciardo.  Toward a Definition of Modeling Power for Stochastic Petri Net Models , 1987, PNPM.