On the use of IPA in performance optimization of continuous marked graphs: A case study

This paper demonstrates the application of Infinitesimal Perturbation Analysis (IPA) to performance optimization of fluid marked graphs. Recent developments in the theory of stochastic hybrid systems concern IPA techniques for gradient estimation of performance functions defined on Petri nets and their use in sample-path optimization. This paper takes a first step towards eventual applications in manufacturing by considering an example of workload balancing in a marked graph. In particular, it addresses the problem of balancing parts' inventories and product backorders in a production-system's model by controlling the parts' inflow rates. The paper defines the problem, describes the algorithm, and presents simulation results. Although the considered system is simple it captures the salient features of our approach, and the simulation results suggest its potential viability in future applications.