An Asymptotic Cyclicity Analysis of Live Autonomous Timed Event Graphs

Ja-Hee Kim
2021 Applied Sciences  
Designing a discrete event system converging to steady temporal patterns is an essential issue of a system with time window constraints. Until now, to analyze asymptotic stability, we have modeled a timed event graph's dynamic behavior, transformed it into the matrix form of (max,+) algebra, and then constructed a precedence graph. This article's aim is to provide a theoretical basis for analyzing the stability and cyclicity of timed event graphs without using (max,+) algebra. In this article,
more » ... e propose converting one timed event graph to another with a dynamic behavior equivalent to that of the original without going through the conversion process. This paper also guarantees that the derived final timed event graph has the properties of a precedence graph. It then investigates the relationship between the properties of the derived precedence graph and that of the original timed event graph. Finally, we propose a method to analyze asymptotic cyclicity and stability for a given timed event graph by itself. The analysis this article provides makes it easy to analyze and improve asymptotic time patterns of tasks in a given discrete event system modeled with a live autonomous timed event graph such as repetitive production scheduling.
doi:10.3390/app11114769 fatcat:kamywlqyx5gejaprgtwehc7mbi