Generalised batches Petri net: Hybrid model for high speed systems with variable delays

Recently, the possibility of associating both discrete events and continuou s time behaviour in the same formalism has generated a considerable interes t in the Petri net paradigm. A central issue in this field is the concept o f Hybrid Petri net which consists in continuous transitions and places hold ing non negative real number, and discrete transitions and places holding i nteger tokens. By adding a new type of nodes, batch transitions and batch p laces, Batches Petri nets have been defined. A batch node combines both a d iscrete event and a linear continuous dynamic behaviour in a single structu re. Batches Petri nets can then be used in the control design and performan ce analysis of high-speed systems composed of continuous transfer elements which introduce variable delays on continuous flows. In this paper, the com plete formalism of Generalised Batches Petri nets is given through the defi nition of the model, the enabling and firing rules, the time analysis metho ds, and two examples illustrate these notions.