Extension of Batches Petri Nets by Bi-parts Batch Places.

This paper proposes an extension of Batches Petri Nets by a new definition of the batch place called Bi-parts Batch place (BBplace). The flow-density equations that govern the dynamics of controllable batches inside a BB-place is now defined by a triangular relation. To take into account controlled events, the behaviors of batches are discussed according to a variation of speeds and of maximum flows. The switching dynamics of controllable batches is defined on three behaviors: free, congestion and decongestion behaviors. We also propose the computation of the instantaneous firing flow vector associated with continuous and batch transitions thanks to a resolution of a linear programming problem. An example of traffic road illustrates the novel extensions proposed in this paper.