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Product Form Solution for Generalized Stochastic Petri Nets
October 2002 (vol. 28 no. 10)
pp. 915-932

Abstract—In this paper, we show the structural characteristics that a particular class of Generalized Stochastic Petri Nets must exhibit in order for their stationary probabilities to have a product-form. Sufficient conditions for identifying such a class are derived and proven with the development of a series of transformations that can also be used to construct, for any GSPN of the class, an equivalent SPN. These resulting SPNs represent the structures that can be analyzed with standard methods for Product-Form SPNs to establish whether the original GSPNs have Product-Form solutions and to compute their performance indices with effective approaches based on computationally efficient algorithms that avoid the generation of their underlying state spaces.

[1] M. Ajmone Marsan, G. Balbo, G. Conte, S. Donatelli, and G. Franceschinis, Modelling with Generalized Stochastic Petri Nets. John Wiley&Sons, 1995.
[2] Performance Models for Discrete Event Systems with Synchronisation: Formalisms and Analysis Techniques, G. Balbo and M. Silva, eds., Book of the MATCH Advanced School, KRONOS, Zaragoza, Spain, 1998.
[3] F. Baskett, K.M. Chandy, R.R. Muntz, and R. Palacios, “Open, Closed and Mixed Networks of Queues with Different Classes of Customers,” J. ACM, vol. 22, no. 2, pp. 248-260, 1975.
[4] R.J. Boucherie and M. Sereno, “On Closed Support t-Invariants and Traffic Equations,” J. Applied Probability, vol. 35, pp. 473–481, 1998.
[5] G. Chiola, S. Donatelli, and G. Franceschinis, "GSPNs versus SPNs: What is the Actual Role of Immediate Transitions? Proc. Fourth Int'l Workshop Petri Nets and Performance Models, pp. 20-31,Melbourne, Australia, IEEE CS Press, Dec. 1991.
[6] J.L. Coleman, W. Henderson, and P.G. Taylor, “Product form Equilibrium Distributions and an Algorithm for Classes of Batch Movement Queueing Networks and Stochastic Petri Nets,” Performance Evaluation, vol. 26, no. 3, pp. 159–180, Sept. 1996.
[7] W.J. Gordon and G.F. Newell, “Closed Queueing Systems with Exponential Servers,” Operations Research, vol. 15, pp. 254–265, 1967.
[8] S. Haddad, P. Moreaux, M. Sereno, and M. Silva, “Structural Characterization and Qualitative Properties of Product Form Stochastic Petri Nets,” Proc. 22nd Int'l Conf., June 2001.
[9] W. Henderson, D. Lucic, and P.G. Taylor, “A Net Level Performance Analysis of Stochastic Petri Nets,” J. Australian Math. Soc. Series B., vol. 31, pp. 176–187, 1989.
[10] W. Henderson and P.G. Taylor, “Embedded Processes in Stochastic Petri Nets,” IEEE Trans. Software Eng., vol. 17, pp. 108–116, Feb. 1991.
[11] J.R. Jackson, “Jobshop-Like Queueing Systems,” Management Science, vol. 10, no. 1, pp. 131–142, Oct. 1963.
[12] T. Murata, “Petri Nets: Properties, Analysis and Application,” Proc. IEEE, vol. 77, no. 4, 1989.
[13] M. Sereno and G. Balbo, “Computational Algorithms for Product form Solution Stochastic Petri Nets,” Proc. Fifth Int'l Workshop Petri Nets and Performance Models, pp. 98–107, Oct. 1993.
[14] M. Sereno and G. Balbo, "Mean Value Analysis of Stochastic Petri Nets," Performance Evaluation, vol. 29, no. 1, pp. 35-62, 1997.
[15] M. Silva, Las Redes de Petri en la Automatica y la Informatica. Madrid, Spain: AC, 1985.

Index Terms:
Generalized stochastic Petri nets, product form solution.
Citation:
G. Balbo, S.C. Bruell, M. Sereno, "Product Form Solution for Generalized Stochastic Petri Nets," IEEE Transactions on Software Engineering, vol. 28, no. 10, pp. 915-932, Oct. 2002, doi:10.1109/TSE.2002.1041049
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