Optimal speed allocation and sensitivity analysis of hybrid stochastic Petri nets

In this paper we present a method for performance evaluation of hybrid stochastic Petri nets based on sensitivity analysis and parametric linear programming techniques and we show how this approach can be used for optimization. The problem is addressed by determining an optimal firing speed allocation for the continuous transitions obtained by solving a sequence of linear programming problems aimed at optimizing a certain performance index. The primary advantage of our approach is that it gives rise to a dynamic firing speeds allocation that is based on global state information rather than local information. This original formulation allows us to easily solve conflicts, evaluate performance measures and perform gradient estimation very efficiently.