Matrix-based sequencing in multiple re-entrant flowlines

Abstract

In this article, we address issues related to modelling of a discrete event system in a way that would effectively provide an easy implementation of the scheduling policy on the actual controller and at the same time would provide an answer on how profound the utilization of the system resources is. Herein we propose a method that relies on usage of a matrix model and a max-plus algebra model. The idea is to use the advantages of each of the given models. A system, initially given in matrix form, can be transferred into a max-plus model under the given sequence. In the case of structural changes, the system matrix model can be easily modified and hence supervisory matrix controller redesign is straightforward. On the other hand, the max-plus model is suitable for performance analysis, which in some cases could be difficult if a matrix model is used. Moreover, max-plus algebra represents the system on the higher level of abstraction, which is suitable for investigation of particular properties of discrete event systems. In addition, using both models, we propose a method for determining a scheduling sequence that is not well formed.