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

Abstract

Recently, the possibility of associating both discrete events and continuous time behaviour in the same formalism has generated a considerable interest in the Petri net paradigm. A central issue in this field is the concept of Hybrid Petri net which consists in continuous transitions and places holding non negative real number, and discrete transitions and places holding integer tokens. By adding a new type of nodes, batch transitions and batch places, Batches Petri nets have been defined. A batch node combines both a discrete event and a linear continuous dynamic behaviour in a single structure. Batches Petri nets can then be used in the control design and performance analysis of high-speed systems composed of continuous transfer elements which introduce variable delays on continuous flows. In this paper, the complete formalism of Generalised Batches Petri nets is given through the definition of the model, the enabling and firing rules, the time analysis methods, and two examples illustrate these notions.