A Freeway Traffic Model in a First Order Hybrid Petri Net Framework

The paper presents a model for traffic state estimation and control of the freeways. The model is based on a First-Order Hybrid Petri Net (FOHPN) framework, a hybrid Petri net formalism including continuous places holding fluid, discrete places containing a non-negative integer number of tokens and transitions, which are either discrete or continuous. In order to suitably describe the dynamics of the freeway traffic flow, we allow updating the transition firing speed as a function of the markings modeling the freeway traffic. Moreover, we propose an online optimal control coordination of speed limits with the objective of maximizing the flow density. The use of FOHPNs offers several significant advantages with respect to the model existing in the related literature: the graphical feature enables an easy modular modeling approach and the mathematical aspects efficiently allow simulating and optimizing the system. The effectiveness of the FOHPN formalism is shown by applying the proposed modeling technique to a stretch of a freeway in the North-East of Italy.