From linear programming to graph theory: Standardization of the algebraic model of timed event graphs

The aim of this paper is the standardization of the algebraic model of timed event graphs defined in the conventional algebra. The result of the proposed technique is an auto-regressive model similar to the sampled state equations of the automatic control. Based on standard incidence matrices, this new model is a set of inequalities defined on a reduced horizon which allows an efficient calculation of the state trajectory knowing the initial state and the control. The starting point of the approach is the algebraic model deduced from the initial timed event graph. Using linear programming, we give two dual techniques which allow the building of the standardized model and the corresponding timed event graph. This study improves our understanding of the connections between linear programming and graph theory.