A Dioid Model for Invariant Resource Sharing Problems

This paper proposes a model for invariant resource sharing problems in dioid algebra. A strong motivation for investigating the issue is the absence of a general systematic technique which can be used to tackle these problems. (min, +) constraints have been developed to handle resource sharing in Discrete-Event Dynamic Systems. In particular, the part that can be modeled by a Timed Event Graph induce (min, +)-linear equations which are constrained by the resource availability. The proposed algebraic model has been proved to describe the actual behavior of the systems dealt with. This paper will show two examples of systems that are modeled and controlled by means of this approach.