Controlled Triangular Batches Petri Nets for hybrid mesoscopic modeling of traffic road networks under VSL control

In the discrete event and hybrid systems theory, Batches Petri Nets (BPN) have been defined as an extension of Hybrid Petri nets for representing in a single node a linear relation between flow and density. This formalism and its extensions allow us to delay flows according to accumulation phenomena. Applied to mesoscopic modeling of traffic road networks, Triangular Batches Petri Nets (TBPN) have been defined as a triangular flow-density relation, allowing the representation of traffic congestion/decongestion phenomena. When variable speed limit (VSL) control is applied on the traffic road networks, i.e., a method that improves the traffic conditions by the reduction of congestion, Controlled Triangular Batches Petri Nets (CTBPN) can be used for analyzing such phenomena. In this paper, we present the hybrid formalism defined in CTBPN, i.e., the hybrid behavior of a batch in free, congestion or decongestion behavior. As an illustrative example, the congestion/decongestion phenomena on a road section and the impact of a VSL control are shown.