Application of IPA to Fluid Petri Nets

Infinitesimal Perturbation Analysis (IPA) recently has been extensively investigated in the setting of fluid queues, where it was shown to yield simple algorithms for computing the gradients of several performance functions. More lately, efforts have been made to extend its application domain from fluid queueing networks to other kinds of stochastic hybrid systems. In this vein, the present paper inaugurates a study of the application of IPA to a class of hybrid Petri nets. The main point of concern is the modeling element of the fluid transition with multiple input places, representing concurrency and synchronization in Petri nets, and not yet studied in the context of IPA. We first derive the IPA gradient of the throughput with respect to fluid flow parameters at the input places, and then consider an example of optimizing throughput in a fork-join system. Simulation experiments are presented in support of the theoretical results. We point out that the main purpose of the paper is to initiate a study of IPA in the setting of hybrid Petri nets, and not to consider application examples.