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A Fourth-Order Algorithm with Automatic Stepsize Control for the Transient Analysis of DSPNs
March/April 1999 (vol. 25 no. 2)
pp. 194-206

Abstract—This paper presents an efficient and numerically reliable method for the transient analysis of deterministic and stochastic Petri nets. The transient behavior is described by state equations derived by the method of supplementary variables. Significant features of the proposed solution algorithm of fourth order are an automatic stepsize control and a two-stage relative error control. Furthermore, a formal way of dealing with discontinuities in the transient state equations is developed. This resolves the problems posed by initially enabled deterministic transitions and also improves the accuracy of numerical results. Experiments with a queuing system with failure and repair illustrate the efficiency (with respect to both CPU-time and memory space) and the numerical quality of the new algorithm.

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Index Terms:
Deterministic and stochastic Petri nets, transient analysis, adaptive numerical method.
Citation:
Armin Heindl, Reinhard German, "A Fourth-Order Algorithm with Automatic Stepsize Control for the Transient Analysis of DSPNs," IEEE Transactions on Software Engineering, vol. 25, no. 2, pp. 194-206, March-April 1999, doi:10.1109/32.761445
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