Shared resources in production systems: (max,+) analysis (Q2431524)

Summary: This paper deals with formal modelling of Petri nets including shared resources. These phenomena appear widely in the production management context, for the modelling of manufacturing cells. But, they usually cannot be formally represented in dioid algebraic structures based on sets of scalars. In this paper, we design a method to describe such a phenomenon in a dioid of intervals. In fact, the resource-sharing problem is turned into a time uncertainty problem, regarding the access to the shared resource. In this new problem, time uncertainties are bounded and can be described by intervals. Both bounds of the behaviours of the studied production systems can be manipulated in the scope of the \(\overline {\mathbb Z_{\text{max}}}\) dioid, even though the original systems are not \(\overline {\mathbb Z_{\text{max}}}\) linear by essence.