Abstract
Petri nets in which random firing delays are associated with transitions whose firing is an atomic operation are known under the name “stochastic Petri nets”. These models are discussed, with the purpose of explaining why they were proposed in the performance evaluation field, why random delays with negative exponential probability density functions are mainly used, and what are their strong and weak points. An effort is made to summarize the lines of research that are currently being pursued, and to explain what new results would be regarded as breakthroughs and have the most impact on the use of this modeling technique in the application field.
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References
C.A. Petri, “Communication with Automata”, Tech. Rep. Rep. RADC-TR-65-377, Rome Air Dev. Center, New York, NY, 1966.
W. Reisig, Petri Nets: an Introduction, Springer Verlag, 1985.
J.L. Peterson, Petri Net Theory and the Modeling of Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981.
E. Cinlar, Introduction to Stochastic Processes, Prentice-Hall, Englewood Cliffs, NJ, 1975.
W. Feller, An Introduction to Probability Theory and Its Applications, John Wiley, New York, NY, 1966.
R.A. Howard, Dynamic Probabilistic Systems, John Wiley, New York, NY, 1971.
L. Kleinrock, Queueing Systems Volume I: Theory, John Wiley, New York, NY, 1975.
J.W. Cohen, The Single Server Queue, American Elsevier, New York, NY, 1969.
D.R. Cox and W.L. SmithQueues, John Wiley, New York, NY, 1961.
R.B. Cooper, Introduction to Queueing Theory, Mac Millan New York, NY, 1972.
S.S. Lavenberg, Computer Performance Modeling Handbook, Academic Press, New York, NY, 1983.
E. Gelenbe and I. Mitrani, Analysis and Synthesis of Computer Systems, Academic Press, New York, NY, 1980.
M. Ajmone Marsan, G. Balbo and G. Conte, Performance Models of Multiprocessor Systems, The MIT Press, Cambridge, Massachusetts, 1986.
S. Natkin, “Les Reseaux de Petri Stochastiques et leur Application a l'Evaluation des Systèmes Informatiques”, Thèse de Docteur Ingegneur, CNAM, Paris, France, 1980.
M.K. Molloy, “On the Integration of Delay and Throughput Measures in Distributed Processing Models”, Ph.D. Thesis, UCLA, Los Angeles, CA, 1981.
F.J.W. Symons, “Introduction to Numerical Petri Nets, a General Graphical Model of Concurrent Processing Systems”, Australian Telecommunications Research, Vol. 14, n. 1, pp. 28–33, January 1980.
F.J.W. Symons, “The Description and Definition of Queueing Systems by Numerical Petri Nets”, Australian Telecommunications Research, Vol. 13, pp. 20–31, 1980.
M. Ajmone Marsan, A. Bobbio, G. Conte, A. Cumani “Performance Analysis of Degradable Multiprocessor Systems using Generalized Stochastic Petri Nets”, Distributed Processing T-C Newsletters, IEEE Computer Society, n. 6, SI-1, 1984, pp. 47–54.
J. D. C. Little, “A Proof of the Queueing Formula L = λW”, Operations Research, Vol. 9, 1961, pp. 383–387.
M. Ajmone Marsan, G. Balbo, G. Conte, “A Class of Generalized Stochastic Petri Nets for the Performance Analysis of Multiprocessor Systems”, ACM Transactions on Computer Systems, Vol. 2, n. 1, May 1984, pp. 93–122.
M. Ajmone Marsan, G. Balbo, G. Chiola, G. Conte, “Generalized Stochastic Petri Nets Revisited: Random Switches and Priorities”, Proceedings of the International Workshop on Petri Nets and Performance Models, Madison, WI, USA, August 1987.
G. Balbo, G. Chiola, G. Franceschinis, G. Molinar Roet, “On the Efficient Construction of the Tangible Reachability Graph of Generalized Stochastic Petri Nets”, Proceedings of the International Workshop on Petri Nets and Performance Models, Madison, WI, USA, August 1987.
H. H. Ammar, R. W. Liu, “Analysis of the Generalized Stochastic Petri Nets by State Aggregation”, Proceedings of the International Workshop on Timed Petri Nets, Torino,Italy, July 1985.
J.B. Dugan, K.S. Trivedi, R.M. Geist, V.F. Nicola, “Extended Stochastic Petri Nets: Applications and Analysis”, Proceedings of PERFORMANCE '84, Paris, France, December 1984.
M. Ajmone Marsan, G. Chiola, “On Petri Nets with Deterministic and Exponential Transition Firing Times”, Proceedings of the 7-th European Workshop on Application and Theory of Petri Nets, Oxford, England, June 1986.
M. Ajmone Marsan, G. Chiola, “On Petri Nets with Deterministic and Exponentially Distributed Firing Times”, in: G.Rozenberg (editor), Advances in Petri Nets 1987, Lecture Notes on Computer Science, n. 266, Springer Verlag, 1987.
M. Ajmone Marsan, G. Balbo, A. Bobbio, G. Chiola, G. Conte, A. Cumani, “On Petri Nets with Stochastic Timing”, Proceedings of the International Workshop on Timed Petri Nets, Torino, Italy, July 1985.
M. Ajmone Marsan, G. Balbo, A. Bobbio, G. Chiola, G. Conte, A. Cumani, “The Effect of Execution Policies on the Semantics and Analysis of Stochastic Petri Nets”, IEEE Transactions on Software Engineering, Vol. SE-15, n. 7, July 1989.
M. Ajmone Marsan, G. Chiola, A. Fumagalli, “Improving the Efficiency of the Analysis of DSPN Models”, Proceedings of the 9-th European Workshop on Application and Theory of Petri Nets, Venezia, Italy, June 1988.
W. Henderson, D. Lucic, “Application of Generalized Semi Markov Processes to Stochastic Petri Nets”, Proceedings of the International Seminar on Performance of Distributed and Parallel Systems, Kyoto, Japan, December 1988.
J. Sifakis, “Performance Evaluation of Systems Using Petri Nets”, in Net Theory and Applications, edited by G. Goos and J. Hartmanis, Springer Verlag, New York, NY, 1979.
C.Y. Wong, T.S. Dillon, K.E. Forward, “Timed Places Petri Nets with Stochastic Representation of Place Time”, Proceedings of the International Workshop on Timed Petri Nets, Torino, Italy, July 1985.
R.R. Razouk, C.V. Phelps, “Performance Analysis using Timed Petri Nets”, Proceedings of the International Conference on Parallel Processing, August 1984.
M.A. Holliday, M.K. Vernon, “A Generalized Timed Petri Net Model for Performance Analysis”, Proceedings of the International Workshop on Timed Petri Nets, Torino, Italy, July 1985.
W.M. Zuberek, “Timed Petri Nets and Preliminary Performance Evaluation”, Proceedings of the 7-th Annual Symposium on Computer Architecture, La Baule, France, May 1980.
W.M. Zuberek, “Performance Evaluation using Timed Petri Nets”, Proceedings of the International Workshop on Timed Petri Nets, Torino, Italy, July 1985.
W.M. Zuberek, “M-Timed Petri Nets, Priorities, Preemptions, and Performance Evaluation of Systems”, in Advances on Petri Nets '85 edited by G. Rozenberg, LNCS 222, Springer Verlag, 1986.
M.K. Molloy, “Fast Bounds for Stochastic Petri Nets”, Proceedings of the International Workshop on Timed Petri Nets, Torino, Italy, July 1985.
M.K. Molloy, “Structurally Bounded Stochastic Petri Nets”, Proceedings of the International Workshop on Petri Nets and Performance Models, Madison, WI, USA, August 1987.
G. Balbo, S. C. Bruell, G. Chiola, P. Chen, “An Example of Validation and Evaluation of a Concurrent Program: Lamport's Fast Mutual Exclusion Algorithm”, submitted for publication.
P.J. Haas, G.S. Shedler, “Regenerative Simulation of Stochastic Petri Nets”, Proceedings of the International Workshop on Timed Petri Nets, Torino, Italy, July 1985.
P.J. Haas, G.S. Shedler, “Regenerative Stochastic Petri Nets”, Performance Evaluation, Vol. 6, n. 3, September 1986, pp. 189–204.
P.J. Haas, G.S. Shedler, “Stochastic Petri Nets with Timed and Immediate Transitions”, Stochastic Models, to appear.
G. Chiola, “Compiling Techniques for the Analysis of Stochastic Petri Nets”, Proceedings of the 4-th International Conference on Modeling Techniques and Tools for Computer Performance Evaluation, Palma de Mallorca, Spain, September 1988.
A. Zenie, “Colored Stochastic Petri Nets”, Proceedings of the International Workshop on Timed Petri Nets, Torino, Italy, July 1985.
C. Marinescu, Chuang Lin, “On Stochastic High Level Petri Nets”, Proceedings of the International Workshop on Petri Nets and Performance Models, Madison, WI, USA, August 1987.
G. Chiola, G. Bruno, T. Demaria, “Introducing a Color Formalism into Generalized Stochastic Petri Nets”, Proceedings of the 9-th European Workshop on Application and Theory of Petri Nets, Venezia, Italy, June 1988.
G. Balbo, S. C. Bruell, S. Ghanta, “Combining Queueing Network and Generalized Stochastic Petri Net Models for the Analysis of a Software Blocking Phenomenon”, Proceedings of the International Workshop on Timed Petri Nets, Torino, Italy, July 1985.
G. Balbo, S. C. Bruell, S. Ghanta, “Combining Queueing Network and Generalized Stochastic Petri Net Models for the Analysis of Some Software Blocking Phenomena”, IEEE Transactions on Software Engineering, Vol. SE-12, n. 4, April 1986, pp. 561–576.
G. Florin, S. Natkin, “On Open Synchronized Queuing Networks”, Proceedings of the International Workshop on Timed Petri Nets, Torino, Italy, July 1985.
G. Florin, S. Natkin, “Les Reseaux de Petri Stochastiques”, Technique et Science Informatiques, Vol. 4, n. 1, February 1985, pp. 143–160.
G. Florin, S. Natkin, “A Necessary and Sufficient Saturation Condition for Open Synchronized Queueing Networks”, Proceedings of the International Workshop on Petri Nets and Performance Models, Madison, WI, USA, August 1987.
A. A. Lazar, T. G. Robertazzi, “Markovian Petri Net Protocol Models with Product Form Solution”, Proceedings of INFOCOM 87, San Francisco, CA, USA, March 1987.
A. A. Lazar, T. G. Robertazzi, “The Algebraic and Geometric Structure of Markovian Petri Network Lattices”, Proceedings of the 24-th Annual Allerton Conference on Communications, Control and Computing, Urbana-Champaigne, Illinois, USA, 1986.
I. Y. Wang, T. G. Robertazzi, “Service Stage Petri Net Protocols with Product Form”, submitted for publication.
W. Henderson, P. Taylor, D. Lucic, “A Net Level Performance Analysis of Stochastic Petri Nets with Conflict Sets”, submitted for publication.
F. Baskett, K. M. Chandy, R. R. Muntz, F. Palacios, “Open, Closed and Mixed Networks of Queues with Different Classes of Customers”, Journal of the ACM, Vol. 22, n. 2, April 1975, pp. 248–260.
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© 1990 Springer-Verlag Berlin Heidelberg
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Marsan, M.A. (1990). Stochastic Petri nets: An elementary introduction. In: Rozenberg, G. (eds) Advances in Petri Nets 1989. APN 1988. Lecture Notes in Computer Science, vol 424. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52494-0_23
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DOI: https://doi.org/10.1007/3-540-52494-0_23
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