Allocating resources of weighted T‐system for adaptive behaviour

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.