Traffic Network Modeling and Volume Control Using Labeled Petri Nets

Traffic planning and estimation are critical tasks in the management of complex road networks. With appropriate control strategies, traffic congestion can be significantly alleviated. In this paper, we propose approaches for estimating the traffic flow and vehicle distributions based on labeled Petri nets. The traffic network is firstly modeled as a labeled Petri net structure, then the control algorithms are introduced. Different from many existing strategies that focus on avoiding collisions, we assign traffic capacities to places that represent different road segments in the traffic network, then algorithms are developed to maintain the number of tokens within given capacities. The existence of the unobservable transitions makes the problem more challenging. Under some assumptions of the unobservable transitions, we show that the proposed algorithm is efficient and has a complexity that is polynomial in the length of the label observations. An illustrative example is also provided to show the effectiveness of the proposed algorithm.