Title: Allocating resources of weighted T-system for adaptive behaviour

Authors: Abderrahim Benfekir; Samir Hamaci; Moumen Darcherif

Addresses: USTO, BP 1505 El Mnaouer, Algérie ' EPMI-ECS, 13 Boulvard de l'Hautil, Cergy 95092, France ' EPMI-ECS, 13 Boulvard de l'Hautil, Cergy 95092, France

Abstract: We study a subclass of discrete event systems, modelled by timed event graphs with multipliers (TEGM). These graphs are an extension of weighted T-systems studied in the Petri net literature. These models do not admit a linear representation in (min, +) algebra. This non-linearity is due to the presence of the weights on arcs. In this paper, we are particularly interested to the problem of allocating an initial marking in a TEGM for a desired cycle time. For this, to define the marking of some places, we proceed by linearisation of the mathematical model reflecting the behaviour of a TEGM in order to obtain a (min, +) linear model. From the latter, we determine the marking which satisfies the desired cycle time.

Keywords: timed Petri nets; timed event graphs; (min, +) algebra; cycle time; linearisation; resource allocation; mathematical modelling; weighted T-systems; discrete event systems; adaptive behaviour.

DOI: 10.1504/IJOR.2012.046342

International Journal of Operational Research, 2012 Vol.14 No.1, pp.31 - 49

Published online: 11 Jan 2015 *

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