The paper presents a model for traffic state estimation and management of the freeways. The model is based on First-Order Hybrid Petri Nets (FOHPNs), 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. The paper improves a previous model in order to suitably describe the dynamics of the freeway traffic flow. To this aim we modify the dynamics of the FOHPN and we allow updating the transition firing speed as a function of the markings modeling the freeway traffic. 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 obtained model is a linear discrete-time, time-varying state variable model and is suitable to describe a hybrid system such as a freeway subject to unpredictable events (i.e., accidents or bottlenecks). 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. Some simulation studies illustrate how the proposed model is able to provide a support to analyze the strategies to react to accidents and lane blockings.
