Extended structures of batches Petri nets

Recently, there has been a growing interest in the modelling and analysis of dynamic hybrid systems. 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 numbers, and discrete transitions and places holding integer tokens. By adding a new type of node, new batch transitions and batch places, batches Petri nets have been created. 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 modelling and performance analysis of high throughput production systems composed of continuous transfer elements serially arranged. The paper introduces an extended class of batches Petri nets by adding weights on arcs and by introducing new structures between batch nodes such as parallelism and synchronisation. Thus, generalised batches Petri nets enlarge the fundamental equations, the invariant concepts and the timed evolution graph. Finally, they are a suitable model for the representation and performance evaluation of high throughput production systems with accumulation phenomena and proportional flow transfers on continuous elements put in parallel.