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Modeling Power of Stochastic Petri Nets for Simulation

Published online by Cambridge University Press:  27 July 2009

Peter J. Haas
Affiliation:
IBM Almaden Research Center San Jose, California 95120-6099
Gerald S. Shedler
Affiliation:
IBM Almaden Research Center San Jose, California 95120-6099

Extract

Generalized semi-Markov processes and stochastic Petri nets have been proposed as general frameworks for a discrete event simulation on a countable state space. The two formal systems differ, however, with respect to the clock setting (event scheduling) mechanism, the state transition mechanism, and the form of the state space. We obtain conditions under which the marking process of a stochastic Petri net “mimics” a generalized semi-Markov process in the sense that the two processes (and their underlying general state-space Markov chains) have the same finite dimensional distributions. The results imply that stochastic Petri nets have at least the modeling power of generalized semiMarkov processes for discrete event simulation.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1988

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References

1.Ajmone, Marsan M., Conte, G., & Balbo, G. (1984). A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Transactions on Computer Systems 2: 93122.CrossRefGoogle Scholar
2.Asmussen, S. (1987). Applied probability and queues. New York: John Wiley.Google Scholar
3.Billingsley, P. (1979). Probability and measure. New York: John Wiley.Google Scholar
4.Chung, K.L. (1974). A course in probability theory, 2nd ed. New York: Academic Press.Google Scholar
5.Dugan, J.B., Trivedi, K.S., Geist, R.M., & Nicola, V.F. (1984). Extended stochastic Petri nets: applications and analysis. Performance 84: 419441.Google Scholar
6.Clynn, P.W. (1983). On the role of generalized semi-Markov processes in simulation output analysis. Proceedings of the ACM 1983 Winter Simulation Conference, pp. 3942.Google Scholar
7.Haas, P.J. (1985). Recurrence and regeneration in non-Markovian simulations. Ph.D. Dissertation, Department of Operations Research, Stanford University, California.Google Scholar
8.Haas, P.J. & Shedler, G.S. (1985). Regenerative simulation methods for local area computer networks, IBM Journal Research and Development 29: 194205.CrossRefGoogle Scholar
9.Haas, P.J. & Shedler, G.S. (1986). Regenerative stochastic Petri nets. Performance Evaluation 6: 189204.CrossRefGoogle Scholar
10.Haas, P.J. & Shedler, G.S. (1987). Regenerative generalized semi-Markov processes. Stochastic Models 3: 409438.CrossRefGoogle Scholar
11.Haas, P.J. & Shedler, G.S. (1987). Stochastic Petri nets with simultaneous transition firings. International Workshop on Petri Nets and Performance Models. IEEE Computer Society Press, Washington, DC, pp. 2432.Google Scholar
12.Haas, P.J. & Shedler, G.S. (1987). Modeling power for discrete event simulation. Technical Report RJ5978, IBM Almaden Research Center. San Jose, California.Google Scholar
13.Haas, P.J. & Shedler, G.S. (1989). Stochastic Petri nets with timed and immediate transitions. To appear in Communications in Statistics-Stochastic Models.CrossRefGoogle Scholar
14.Haas, P.J. & Shedler, G.S. (1989). Stochastic Petri net representation of discrete event simulations. To appear in IEEE Transactions on Software Engineering.CrossRefGoogle Scholar
15.Iglehart, D.L. & Shedler, G.S. (1983). Simulation of non-Markovian systems. IBM Journal Research and Development 27: 472480.CrossRefGoogle Scholar
16.König, D., Matthes, K., & Nawrotzki, K. (1967). Verallgemeinerungen der erlangschen und engsetschen formeln. Berlin: Akademie-Verlag.Google Scholar
17.König, D., Matthes, K., & Nawrotzki, K. (1974). Unempfindlichkeitseigenshaften von Bedienungsprozessen. Appendix to Gnedenko, B.V. and IN. Kovalenko, Introduction to Queueing Theory, German edition, Berlin: Akademie-Verlag.Google Scholar
18.Lamperti, J. (1977). Stochastic processes: a survey of the mathematical theory. New York: Springer-Verlag.CrossRefGoogle Scholar
19.Matthes, K. (1962). Zur Theorie der Bedienungsprozessen. Transactions of the 3rd Prague conference on information theory and statistical decision functions. Prague, Czechoslovakia.Google Scholar
20.Molloy, M.K. (1981). On the integration of delay and throughput measures in distributed processing models. Ph.D. Dissertation; Department of Computer Science, University of California, Los Angeles, California.Google Scholar
21.Molloy, M.K. (1982). Performance analysis using stochastic Petri nets. IEEE Transactions on Computers C-31: 913917.CrossRefGoogle Scholar
22.Natkin, S. (1980). Les réseaux de Petri stochastiques et leur application a l'evaluation des systemes informatiques. These de Docteur Ingénieur, Conservatoire National des Arts et Metier, Paris, France.Google Scholar
23.Orey, S. (1971). Lecture notes on limit theorems for Markov chain transition probabilities. London: Van Nostrand Reinhold Co.Google Scholar
24.Peterson, J.L. (1981). Petri net theory and the modeling of systems. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.Google Scholar
25.Symons, F.J.W. (1980). The description and definition of queueing systems by numerical Petri nets, Australian Telecommunications Research 13: 2031.Google Scholar
26.Whitt, W. (1980). Continuity of generalized semi-Markov processes. Mathematics of Operations Research 5: 494501.CrossRefGoogle Scholar