Modelling and Control of Computational Processes Using Max-plus Algebra

In this paper we propose a modelling technique for the control of computational processes. The Petri Net model, particularly a Timed Event Graph (TEG) can be used for analyzing. The proposed model enables the determination of state equations. The max-plus algebra represents linear algebraic form of discrete systems and supplies new tools to their modelling. We develop a linear mathematical model under constraints in the Max-plus algebra. When using max-plus algebra with TEG, the arc weights are kept equal to one in order to be able to resolve the state equations. Structure of max-plus algebra is equipped with maximization and addition operations over of the real numbers and minus infinity. It can be used appropriately to determine marking times within a given Petri net and a vector filled with marking state at the beginning. Tools of max-plus algebra are useful to investigate properties of network models. Finally, numerical examples show the use of this model.