Modelling and analysis of p-time event graphs in the (min, max, +) algebra

P-time Petri nets can represent the dynamic behaviour of discrete event systems for which the time evolution of the state is not strictly deterministic but belongs to dynamic intervals. After introducing the modelling of p-time event graphs, we show that the corresponding algebraic model is a subclass of a special model called the interval descriptor system, which uses only maximization, minimization and the addition operations. The following aim is to check the behaviour of the model and to study the existence of a state trajectory. Using the cycle-time vector, we give an approach, which makes it possible to detect the non-synchronization of the transitions and consequently the presence of dead-marks.