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Sensitivity analysis and optimization of stochastic Petri nets

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Abstract

In this paper we define the notion of controlled stochastic Petri net (CSPN), which is a stochastic Petri net with controlled parameters and performance indices. Specifically, transition times and/or conflict resolution rules can depend on controlled parameters and transition times can have arbitrary distribution functions. A method for computing statistical estimates of performance indices and their gradients (sensitivities) with respect to controlled parameters is described. This method, which needs only one simulation of a CSPN, is considerably superior to conventional finite differences both in terms of precision and required amount of simulation and is based on likelihood ratio/score function approach, other possibilities based on extensions of infinitesimal perturbation analysis are outlined. These gradient estimates are used in stochastic optimization algorithms to obtain the optimal value of the aggregated performance function of the CSPN. A combined optimization and simulation tool is developed which includes approaches to the gradient estimation mentioned above. The numerical experiments presented in this paper confirm the efficiency of the proposed techniques.

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Authors and Affiliations

  1. Universita' degli Studi di Milano, Milano, Italy

    F. Archetti

  2. Castelletto di Settimo Milanese (MI), ITALTEL, Italy

    A. Gaivoronski

  3. Universita' degli Studi di Milano, Milano, Italy

    A. Sciomachen

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  1. F. Archetti
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  2. A. Gaivoronski
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  3. A. Sciomachen
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Archetti, F., Gaivoronski, A. & Sciomachen, A. Sensitivity analysis and optimization of stochastic Petri nets. Discrete Event Dyn Syst 3, 5–37 (1993). https://doi.org/10.1007/BF01439175

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  • DOI: https://doi.org/10.1007/BF01439175

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