Generalised Batches Petri Net: Hybrid Model For High Speed Systems With Variable Delays

Recently, the possibilityof associating both discrete events and continuous time behaviourin the same formalism has generated a considerable interest inthe Petri net paradigm. A central issue in this field is theconcept of Hybrid Petri net which consists in continuous transitionsand places holding non negative real number, and discrete transitionsand places holding integer tokens. By adding a new type of nodes,batch transitions and batch places, Batches Petri nets have beendefined. A batch node combines both a discrete event and a linearcontinuous dynamic behaviour in a single structure. Batches Petrinets can then be used in the control design and performance analysisof high-speed systems composed of continuous transfer elementswhich introduce variable delays on continuous flows. In thispaper, the complete formalism of Generalised Batches Petri netsis given through the definition of the model, the enabling andfiring rules, the time analysis methods, and two examples illustratethese notions.