Dealing with Mutual Exclusion Sections in Production Systems: from Shared Resources to Parallel TEG's

Abstract This paper deals with the disambiguation of the behaviour of Petri nets including shared resources. In the production management context, they are often used for the modelling of manufacturing cells. But this representation has a poor transposition into dioid algebra. In this article, we design a method to describe such a phenomenon in a dioid of interval. The latter expresses this class of Petri nets models in a formal way. Their input/output behaviours are guaranteed to be greater than the lower bound of the reference model set and lower than the upper bound of this set. In fact, the resource sharing problem is turned into a time uncertainty problem, concerning the access to the shared resource. In this new problem, time uncertainties are bounded and can be described by intervals. Both bounds “confining” the behaviours of the studied production systems in intervals can be manipulated in the scope of the &ℤbar;max algebra, even though the original systems are not &ℤbar;max linear by essence.