Cycle time of a P-time Event Graph with affine-interdependent residence durations

Abstract

In this paper, we widen the class of P-time Event graphs by introducing affine-interdependent residence durations. This new class is studied through a general algebraic model. Considering a periodic behavior, we provide conditions of existence of a trajectory and propose a technique allowing the determination of extremal solutions. We show that the cycle time is intrinsic to this new model: it depends on the circuits of an associated graph but also on more complex structures.