Steady State Analysis of Flexible Nets

Abstract

The modeling and analysis of complex dynamic systems, such as those in manufacturing, logistics, and biology, require powerful analysis methods for their study and optimization. A significant modeling and analysis challenge posed by both, artificial and natural systems, is the existence of uncertain parameters. Flexible Nets (FNs) is a novel modeling formalism, inspired by Petri nets, that can handle different types of uncertain parameters in a natural way. This paper develops an efficient method to analyse the evolution of a system modeled by an FN in the long run. More precisely, the method focuses on the computation of steady state bounds for an objective function of interest. The method makes use of a set of constraints, expressed as linear inequalities, that the state variables must satisfy in the steady state. In order to account for systems that do not reach a constant steady state, the developed constraints allow the system state to switch among different values, i.e., the steady state variables are not forced to be constant.