Allocating resources of weighted T-system for adaptive behaviour
by Abderrahim Benfekir; Samir Hamaci; Moumen Darcherif
International Journal of Operational Research (IJOR), Vol. 14, No. 1, 2012

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.

Online publication date: Sun, 11-Jan-2015

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