Perturbation analysis of stochastic Petri nets

This paper addresses the sensitivity analysis of stochastic Petri nets (SPNs) using simulations. The goal is to evaluate the derivatives of performance measures with respect to timing parameters. To characterize the underlying stochastic processes of SPNs, we use a generalized semi-Markov process (GSMP) representation and propose a new representation, called GSMP*, which differs from GSMP in the routing mechanism. By using existing results on perturbation analysis of GSMPs and by extending them to GSMP*, unbiased sensitivity estimators are obtained for SPNs simulated under a GSMP or GSMP* framework. Most importantly, we prove that only one simulation run is needed for evaluating both the performance measures and their derivatives for a class of free-choice nets simulated under a GSMP framework and for any free-choice net simulated under a GSMP* framework