On Marking of Continuous Generalized Timed Events Graphs
We study fluid analogues of a subclass of Petri Nets, called Continuous Generalized
Timed Event Graphs, which are a time extension of
weighted T-Systems studied in the Petri Net literature. These
event graphs can be studied in the algebraic structure called
(min,+) algebra. In this paper we deal with the problem of
allocating an initial marking in a Continuous Generalized
Timed Event Graphs for a desired cycle time. for that, to calculate the
marking of some places, we proceed by linearization of the
mathematical model reflecting the behavior of these graphs in order to
obtain a (min, +) linear model. From the latter, we determine the
marking which satisfiers the desired cycle time fixed initially.
Keywords: Timed Petri net, Fluid Timed Event Graphs, (min,+) algebra, Cycle time, Linearization
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ABOUT THE AUTHORS
Samir Hamaci
Samir HAMACI is currently Assistant Professor at the School of Electrical Engineering and Industrial Management (EPMI), Cergy, France. He received his PhD in Automatic degrees from the University of Angers in 2005. His research interests include modeling, performance analysis, control and resources optimization of dynamic systems modeled by discrete and hybrid Petri nets in dioid algebra.
Karim Labadi
Karim Labadi received his Master's degree in Automation and Applied Computer Science from the "Ecole Centrale de Nantes (ECN)", France, in 2001, and the Ph.D degree in Industrial Engineering from the University of Technology of Troyes (UTT), France in 2005. K. Labadi has been with Graduate School of Electrical Engineering and Industrial Management (EPMI), and System Control Laboratory (ESC-Lab), Cergy-Pontoise, France, since 2006 as Assistant Professor. His current research interests are in Petri nets theory, discrete event systems, modelling, analysis, performance evaluation, and optimization of production and logistic systems.
A.-Moumen Darcherif
A.-Moumen DARCHERIF is Accreditation to Supervise Research (HDR) and IEEE member. He received the Ph.D. degree in Electrical Engineering degree from INPG - Grenoble. Currently head of the EPMI School, author of several scientific papers, published at national and international journals, conference proceedings as well as book chapters.
Samir Hamaci
Samir HAMACI is currently Assistant Professor at the School of Electrical Engineering and Industrial Management (EPMI), Cergy, France. He received his PhD in Automatic degrees from the University of Angers in 2005. His research interests include modeling, performance analysis, control and resources optimization of dynamic systems modeled by discrete and hybrid Petri nets in dioid algebra.
Karim Labadi
Karim Labadi received his Master's degree in Automation and Applied Computer Science from the "Ecole Centrale de Nantes (ECN)", France, in 2001, and the Ph.D degree in Industrial Engineering from the University of Technology of Troyes (UTT), France in 2005. K. Labadi has been with Graduate School of Electrical Engineering and Industrial Management (EPMI), and System Control Laboratory (ESC-Lab), Cergy-Pontoise, France, since 2006 as Assistant Professor. His current research interests are in Petri nets theory, discrete event systems, modelling, analysis, performance evaluation, and optimization of production and logistic systems.
A.-Moumen Darcherif
A.-Moumen DARCHERIF is Accreditation to Supervise Research (HDR) and IEEE member. He received the Ph.D. degree in Electrical Engineering degree from INPG - Grenoble. Currently head of the EPMI School, author of several scientific papers, published at national and international journals, conference proceedings as well as book chapters.
