Steady State of High throughput Manufacturing Systems by Continuous Weighted Marked Graphs

Abstract

Continuous Petri nets can be seen as a relaxation of discrete nets, in which the marking of places and firing of transitions are approximated with a fluid model. Several studies have been presented for these models, using linear programming, incidence matrix analysis, or graph theory approaches. In this paper, two approaches for the analysis of time behavior are developed for continuous weighted marked graph structures. Based on linear algebra and graph theory, they are used to compute the steady-state firing speed and the steady-state marking. Such a characterization of the stationary state is applied to a bottling line, Le. a high throughput manufacturing system.