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Importance Function Derivation for RESTART Simulations of Petri Nets

The RESTART method is an efficient algorithm to estimate low probabilities by simulation. It forces a rare event to be visited more frequently by splitting promising paths at certain thresholds. The achievable speedup depends heavily on the quality of the importance function, which controls the splitting behavior. It is well-known from the literature that the specification of a good importance function is a subtle task for non-trivial systems. In this paper we present ideas that have the potential to support finding an importance function for models expressed as a stochastic Petri net. It is shown how the frequency of a rare event of interest can be estimated a-priori to set the number of thresholds close to its optimal value. A measure for the distance between a current marking and the rare state is given as well. Both contributions rely on an algebraic formulation of the Petri net structure and use results for their further analysis as a linear programming problem.