Modeling and control of resource sharing problems in dioids

The topic of this paper is the modeling and control of a class of timed Petri nets with resource sharing problems in a dioid framework. We first introduce a signal which denotes the number of resources available for each competing subsystem at each instant of time. Based on this signal, the overall system is modeled in min-plus algebra. Using residuation theory, an optimal control policy is developed, where optimality is in the sense of a lexicographical order reflecting the chosen prioritization of subsystems.