IPA for Continuous Petri Nets with Threshold-Based Flow Control

This paper considers an application of the Infinitesimal Perturbation Analysis (IPA) gradient-estimation technique to a class of continuous Petri nets. In particular, it proposes a systematic approach for computing the derivatives of the sample performance functions with respect to structural and control parameters. The resulting algorithms are recursive in both time and network flows, and their steps are computed in response to the occurrence and propagation of certain events in the network. Such events correspond to discontinuities in the network flow-rates, and their special characteristics are due to the properties of continuous transitions and fluid places. Following a general outline of the framework we focus on a simple yet canonical example, and investigate throughput and workload-related performance criteria as functions of a threshold control variable. Simulation experiments support the analysis and testify to the potential viability of the proposed approach.