Freeway Traffic Modeling and Control in a First Order Hybrid Petri Net Framework

The paper presents a model for freeway traffic performance evaluation and control in a First-Order Hybrid Petri Net (FOHPN) framework. Such a hybrid Petri net formalism includes 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, as described by the stationary flow-density relationship. 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 and control technique to a stretch of a freeway in the North-East of Italy, where a solution of an accident situation is considered. Note to Practitioners-The motivation of the present work is twofold. First, we propose a novel freeway system model in a FOHPN framework, in order to combine both the time-driven dynamics, considering the standard traffic fundamental diagram, and the event-driven dynamics, by modeling accidents, and recovery procedures. Second, we suggest an online optimal control coordination of speed limits with the objective of maximizing the flow density. The obtained model and control strategies can be used on line, when the traffic is congested, to predict the future state and to manage the system by variable speed limits control. Hence, based on the knowledge of the system state and the information about the occurrence of unpredictable events, the model can enable the decision makers to evaluate decisions such as the application of suitable recovery strategies after an accident or the choice of optimal speed limits in congested situations. Future research aims to investigate larger simulation campaigns describing more complex real systems in order to refine the model and the control schemes.